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3 Both whole numbers and fractions can be represented using the decimal number system. A fraction is written as a/b, and a decimal point (.) separates the whole number from the fraction. In this article, we will learn about the concepts and properties of decimals and fractions in detail.

4 <h2>What is a Decimal Fraction?</h2>

5 What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math

6 ▶

7 A<a>decimal fraction</a>is a fraction where the<a>denominator</a>is a<a>power</a><a>of</a>10, such as 10, 100, or 1000. The bottom<a>number</a>of a fraction, known as the denominator, is a power of 10, such as 10, 100, 1000, and so on.

8 In a decimal fraction, we write the fraction without the denominator by using a decimal point. Using decimals instead of fractions makes<a>arithmetic operations</a>like<a>addition</a>and multiplication easier.

9 Example:

10 <ul><li>0.7($\frac{7}{10}$)

11 </li>

12 <li>0.23($\frac{23}{100}$)

13 </li>

14 <li>0.009($\frac{9}{1000}$)

15 </li>

16 <li>5.4($\frac{54}{10}$)

17 </li>

18 </ul><h2>What are Decimals?</h2>

19 A<a>decimal</a>point (.) separates<a>whole numbers</a>from the fractional part of a number. The numbers to the right of the decimal point are called decimal places, and the numbers to the left are whole numbers or<a>integers</a>.

20 The place values of whole numbers start from ones, then move to tens, hundreds, thousands, and so on. Each<a>place value</a>is ten times more than the previous number. However, the place values of decimal numbers start from tenths, hundredths, and thousandths.

21 A decimal number can be read using the<a>term</a>“point.” For example, 68.54 is read as sixty-eight point five four. The given table represents the place values of decimal numbers.

22 <h2>What are Fractions?</h2>

23 A<a>fraction</a>is a mathematical way to represent equal parts of a whole or a collection. It consists of two distinct numbers separated by a line (called a vinculum):

24 <ul><li>The Numerator (Top Number):This number shows how many parts you are counting or have selected.</li>

25 <li>The Denominator (Bottom Number):This number shows the total number of equal parts the whole is divided into.</li>

26 </ul>Examples:

27 <ul><li>1/5 (One part out of five)</li>

28 <li>3/8 (Three parts out of eight)</li>

29 <li>7/9 (Seven parts out of nine)</li>

30 </ul><h3>Explore Our Programs</h3>

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32 <h2>Decimals and fractions</h2>

31 <h2>Decimals and fractions</h2>

33 We can represent every decimal number in the form of a fraction. To express a decimal number as a fraction, follow these steps:

32 We can represent every decimal number in the form of a fraction. To express a decimal number as a fraction, follow these steps:

34 Step 1:Remove the decimal point and make the number a whole number.

33 Step 1:Remove the decimal point and make the number a whole number.

35 Step 2:Based on the<a>decimal place value</a>, write the number using the power of 10. For example, 0.46 is a decimal number, and the place value of the decimal places is in hundredths. So we can write this number as a fraction:

34 Step 2:Based on the<a>decimal place value</a>, write the number using the power of 10. For example, 0.46 is a decimal number, and the place value of the decimal places is in hundredths. So we can write this number as a fraction:

36 $0.46 = \frac{46}{100} $

35 $0.46 = \frac{46}{100} $

37 If possible, we can simplify the fraction to its lowest form by finding the<a>greatest common divisor</a>of both<a>numerator and denominator</a>. Thus, $\frac{46}{100} $ can be simplified to $\frac{23}{50} $.

36 If possible, we can simplify the fraction to its lowest form by finding the<a>greatest common divisor</a>of both<a>numerator and denominator</a>. Thus, $\frac{46}{100} $ can be simplified to $\frac{23}{50} $.

38 $\frac{46}{100} = \frac{23}{50} $

37 $\frac{46}{100} = \frac{23}{50} $

39 We can also convert a<a>recurring decimal</a>to a fraction. For instance, $0.444\ldots = \frac{4}{9} $.

38 We can also convert a<a>recurring decimal</a>to a fraction. For instance, $0.444\ldots = \frac{4}{9} $.

40 Similarly, we can convert a fraction to a decimal by using the<a>long division</a>method or<a>multiplication</a>method. In the long division method, we divide the numerator by the denominator. However, in the multiplication method, we multiply both the numerator and denominator by a number that makes the denominator a power of 10. Then, the result will be written as a decimal.

39 Similarly, we can convert a fraction to a decimal by using the<a>long division</a>method or<a>multiplication</a>method. In the long division method, we divide the numerator by the denominator. However, in the multiplication method, we multiply both the numerator and denominator by a number that makes the denominator a power of 10. Then, the result will be written as a decimal.

41 Example

40 Example

42 We can convert $\frac{3}{5} $ into a decimal:

41 We can convert $\frac{3}{5} $ into a decimal:

43 Step 1:To make the denominator a power of 10, multiply the numerator and denominator by 2.

42 Step 1:To make the denominator a power of 10, multiply the numerator and denominator by 2.

44 $\frac{3 \times 2}{5 \times 2} = \frac{6}{10} $

43 $\frac{3 \times 2}{5 \times 2} = \frac{6}{10} $

45 Step 2:6 divided by 10 gives 0.6. Hence, write the answer in the decimal form.

44 Step 2:6 divided by 10 gives 0.6. Hence, write the answer in the decimal form.

46 Thus, $\frac{3}{5} = 0.6 $

45 Thus, $\frac{3}{5} = 0.6 $

47 Additionally, we can convert a fraction to a decimal by direct division. For example, convert 3/5 into a decimal: 3 ÷ 5 = 0.6

46 Additionally, we can convert a fraction to a decimal by direct division. For example, convert 3/5 into a decimal: 3 ÷ 5 = 0.6

48 <h2>Decimals and percentages</h2>

47 <h2>Decimals and percentages</h2>

49 Just<a>like fractions</a>, we can represent every decimal as a<a>percentage</a>. To compare two numbers easily, we can convert the decimals to percentages. To convert a decimal to a percentage, follow these steps:

48 Just<a>like fractions</a>, we can represent every decimal as a<a>percentage</a>. To compare two numbers easily, we can convert the decimals to percentages. To convert a decimal to a percentage, follow these steps:

50 Step 1:Multiply the decimal number by 100.

49 Step 1:Multiply the decimal number by 100.

51 Step 2:Place the %<a>symbol</a>on the answer.

50 Step 2:Place the %<a>symbol</a>on the answer.

52 Example:

51 Example:

53 We can convert 0.67 to a percentage.

52 We can convert 0.67 to a percentage.

54 0.67 × 100 = 67%

53 0.67 × 100 = 67%

55 We can also convert a percentage into a decimal by following these steps:

54 We can also convert a percentage into a decimal by following these steps:

56 Step 1:Divide the given percentage by 100.

55 Step 1:Divide the given percentage by 100.

57 Step 2:Remove the % symbol.

56 Step 2:Remove the % symbol.

58 Example:

57 Example:

59 We can convert 56% to a decimal.

58 We can convert 56% to a decimal.

60 56 ÷ 100 = 0.56

59 56 ÷ 100 = 0.56

61 <h2>How to Read Decimal Fraction?</h2>

60 <h2>How to Read Decimal Fraction?</h2>

62 To read a decimal number, start by reading the whole number to the left of the decimal point, normally. If the whole number is zero, you can simply say 'zero.' Next, read the decimal point as the word 'point.' Finally, read the digits to the right of the decimal point individually, one by one. For instance, 235.87 is read as 'two hundred thirty-five point eight seven'-never as 'eighty-seven.' Similarly, 0.45 is read as 'zero point four, five'.

61 To read a decimal number, start by reading the whole number to the left of the decimal point, normally. If the whole number is zero, you can simply say 'zero.' Next, read the decimal point as the word 'point.' Finally, read the digits to the right of the decimal point individually, one by one. For instance, 235.87 is read as 'two hundred thirty-five point eight seven'-never as 'eighty-seven.' Similarly, 0.45 is read as 'zero point four, five'.

63 Examples:Here are a few more examples showing how this rule applies to different types of decimals:

62 Examples:Here are a few more examples showing how this rule applies to different types of decimals:

64 <ul><li>Whole number with a decimal:<ul><li>15.2 $\rightarrow$ Fifteen point two</li>

63 <ul><li>Whole number with a decimal:<ul><li>15.2 $\rightarrow$ Fifteen point two</li>

65 <li>7.14 $\rightarrow$ Seven point one four </li>

64 <li>7.14 $\rightarrow$ Seven point one four </li>

66 </ul></li>

65 </ul></li>

67 <li>Decimals starting with zero:<ul><li>0.3 $\rightarrow$ Zero point three</li>

66 <li>Decimals starting with zero:<ul><li>0.3 $\rightarrow$ Zero point three</li>

68 <li>0.99 $\rightarrow$ Zero point nine nine </li>

67 <li>0.99 $\rightarrow$ Zero point nine nine </li>

69 </ul></li>

68 </ul></li>

70 <li>Decimals with placeholders (zeros in the middle):<ul><li>6.05 $\rightarrow$ Six point zero five</li>

69 <li>Decimals with placeholders (zeros in the middle):<ul><li>6.05 $\rightarrow$ Six point zero five</li>

71 <li>12.001 $\rightarrow$ Twelve point zero zero one</li>

70 <li>12.001 $\rightarrow$ Twelve point zero zero one</li>

72 </ul></li>

71 </ul></li>

73 </ul><h2>How to Represent Decimal Fraction?</h2>

72 </ul><h2>How to Represent Decimal Fraction?</h2>

74 In a decimal fraction, we write the fraction without its denominator by using a decimal point. The denominator of a decimal fraction is a power of 10. We can represent a decimal fraction as a fraction and the denominator will be a power of 10, such as 10, 100, 1000, etc.

73 In a decimal fraction, we write the fraction without its denominator by using a decimal point. The denominator of a decimal fraction is a power of 10. We can represent a decimal fraction as a fraction and the denominator will be a power of 10, such as 10, 100, 1000, etc.

75 Example:

74 Example:

76 $0.7 = \frac{7}{10} $

75 $0.7 = \frac{7}{10} $

77 Furthermore, a decimal point can be used to represent a decimal fraction. For instance,

76 Furthermore, a decimal point can be used to represent a decimal fraction. For instance,

78 $\frac{30}{100} = 0.30 $.

77 $\frac{30}{100} = 0.30 $.

79 A decimal fraction can also be expressed in words. For instance, 0.56 is read as “fifty-six hundredths” because it represents $\frac{56}{100} $.

78 A decimal fraction can also be expressed in words. For instance, 0.56 is read as “fifty-six hundredths” because it represents $\frac{56}{100} $.

80 <h2>What are the Operations on Decimal Fractions?</h2>

79 <h2>What are the Operations on Decimal Fractions?</h2>

81 We can perform the four basic mathematical operations: addition,<a>subtraction</a>, multiplication, and<a>division</a>, on decimals.

80 We can perform the four basic mathematical operations: addition,<a>subtraction</a>, multiplication, and<a>division</a>, on decimals.

82 Addition of decimal fraction:When we add two fractions together, we must first convert them into a decimal form.

81 Addition of decimal fraction:When we add two fractions together, we must first convert them into a decimal form.

83 For example, add $\frac{35}{100} $ and $\frac{35}{1000} $.

82 For example, add $\frac{35}{100} $ and $\frac{35}{1000} $.

84 $\frac{35}{100} = 0.35 $

83 $\frac{35}{100} = 0.35 $

85 $\frac{35}{1000} = 0.035 $

84 $\frac{35}{1000} = 0.035 $

86 Now we can easily add the decimals.

85 Now we can easily add the decimals.

87 0.35 + 0.035 = 0.385

86 0.35 + 0.035 = 0.385

88 Subtraction of decimal fractions:If we need to subtract fractions, we must convert them into decimal forms.

87 Subtraction of decimal fractions:If we need to subtract fractions, we must convert them into decimal forms.

89 For instance, subtract $\frac{35}{1000} $ from $\frac{35}{100} $.

88 For instance, subtract $\frac{35}{1000} $ from $\frac{35}{100} $.

90 $\frac{35}{1000} = 0.035 $

89 $\frac{35}{1000} = 0.035 $

91 $\frac{35}{100} = 0.35 $

90 $\frac{35}{100} = 0.35 $

92 Now, we can easily subtract the two decimals.

91 Now, we can easily subtract the two decimals.

93 0.35 - 0.035 = 0.315

92 0.35 - 0.035 = 0.315

94 Multiplication of decimal fraction:When multiplying a decimal by a power of 10, move the decimal point to the right by as many places as there are zeros.

93 Multiplication of decimal fraction:When multiplying a decimal by a power of 10, move the decimal point to the right by as many places as there are zeros.

95 For example, multiply 4.4321 × 100 = 443.21

94 For example, multiply 4.4321 × 100 = 443.21

96 Here, the power of 10 (100) has two zeros, so we move the decimal two places to the right.

95 Here, the power of 10 (100) has two zeros, so we move the decimal two places to the right.

97 Division of decimal fractions:When dividing a decimal by a power of 10, move the decimal point to the left by as many places as there are zeros.

96 Division of decimal fractions:When dividing a decimal by a power of 10, move the decimal point to the left by as many places as there are zeros.

98 For instance, 4333.4 ÷ 100 = 43.334

97 For instance, 4333.4 ÷ 100 = 43.334

99 Here, we shift the decimal two places to the left.

98 Here, we shift the decimal two places to the left.

100 <h2>What are the types of decimal fractions?</h2>

99 <h2>What are the types of decimal fractions?</h2>

101 The types of decimals are:

100 The types of decimals are:

102 Terminating decimal:The digits after the decimal point of a<a>terminating decimal</a>are limited and do not continue indefinitely. For example, 1.4, 2.54, 4.984, etc.

101 Terminating decimal:The digits after the decimal point of a<a>terminating decimal</a>are limited and do not continue indefinitely. For example, 1.4, 2.54, 4.984, etc.

103 Non-terminating decimal:The<a>non-terminating decimals</a>have an infinite number of digits after the decimal point. It goes infinitely and may or may not repeat again and again. For instance, 1.8666…, 4.782118…etc

102 Non-terminating decimal:The<a>non-terminating decimals</a>have an infinite number of digits after the decimal point. It goes infinitely and may or may not repeat again and again. For instance, 1.8666…, 4.782118…etc

104 Repeating decimals:The numbers after the decimal point of a repeating decimal follow a pattern in which the digits repeat endlessly. For example, 1. 323232…, 1.151515….etc.

103 Repeating decimals:The numbers after the decimal point of a repeating decimal follow a pattern in which the digits repeat endlessly. For example, 1. 323232…, 1.151515….etc.

105 Non-repeating decimals:Non-repeating decimals continue endlessly but should not follow a specific pattern. For example, 1.252552555…., 1.141441444 ... .etc.

104 Non-repeating decimals:Non-repeating decimals continue endlessly but should not follow a specific pattern. For example, 1.252552555…., 1.141441444 ... .etc.

106 <h2>Tips and Tricks to Master Decimals and Fractions</h2>

105 <h2>Tips and Tricks to Master Decimals and Fractions</h2>

107 Fractions and decimals are essentially two different languages used to describe the exact same thing: parts of a whole. Helping students realize that these are connected concepts rather than isolated topics is the key to building mathematical fluency. Instead of memorizing rules blindly, building a strong conceptual foundation allows learners to switch between the two forms effortlessly. Here are a few tips and tricks to help navigate these concepts.

106 Fractions and decimals are essentially two different languages used to describe the exact same thing: parts of a whole. Helping students realize that these are connected concepts rather than isolated topics is the key to building mathematical fluency. Instead of memorizing rules blindly, building a strong conceptual foundation allows learners to switch between the two forms effortlessly. Here are a few tips and tricks to help navigate these concepts.

108 <ul><li>Use Money as a Concrete Model:Money is the most intuitive real-world application where decimal and fractions coexist naturally. Explain that a quarter is named "quarter" because it is literally 1/4 of a dollar, which is written as 0.25. Using physical coins to build a dollar helps learners visualize that decimals represent specific fractional parts of a whole unit. </li>

107 <ul><li>Use Money as a Concrete Model:Money is the most intuitive real-world application where decimal and fractions coexist naturally. Explain that a quarter is named "quarter" because it is literally 1/4 of a dollar, which is written as 0.25. Using physical coins to build a dollar helps learners visualize that decimals represent specific fractional parts of a whole unit. </li>

109 <li>Read Decimals by Place Value:Discourage reading 0.5 as "zero point five" and instead encourage reading it as "five-tenths." When the number is spoken using its proper place value name, the conversion from decimal to fractions becomes auditory and automatic. If a student hears "five-tenths," they can easily write down 5/10 without needing a conversion<a>formula</a>. </li>

108 <li>Read Decimals by Place Value:Discourage reading 0.5 as "zero point five" and instead encourage reading it as "five-tenths." When the number is spoken using its proper place value name, the conversion from decimal to fractions becomes auditory and automatic. If a student hears "five-tenths," they can easily write down 5/10 without needing a conversion<a>formula</a>. </li>

110 <li>The Division Bar Visualization:To simplify the process of changing fractions to decimal, remind students that the line separating the<a>numerator</a>and denominator is actually a division symbol. A helpful visual trick is to imagine the top number (numerator) "falling" into the division box (inside the house), while the bottom number (denominator) stays outside. This reinforces that 3/4 is simply the calculation $3 \div 4$. </li>

109 <li>The Division Bar Visualization:To simplify the process of changing fractions to decimal, remind students that the line separating the<a>numerator</a>and denominator is actually a division symbol. A helpful visual trick is to imagine the top number (numerator) "falling" into the division box (inside the house), while the bottom number (denominator) stays outside. This reinforces that 3/4 is simply the calculation $3 \div 4$. </li>

111 <li>Focus on Base-10 Denominators:Before tackling<a>complex numbers</a>, ensure there is a mastery of decimal fractions-fractions specifically with denominators of 10, 100, or 1000. Using a 10 \times 10 grid helps visualize that coloring 7 columns is 70/100, which is 0.70. Mastering these "friendly" fractions bridges the gap between the two concepts. </li>

110 <li>Focus on Base-10 Denominators:Before tackling<a>complex numbers</a>, ensure there is a mastery of decimal fractions-fractions specifically with denominators of 10, 100, or 1000. Using a 10 \times 10 grid helps visualize that coloring 7 columns is 70/100, which is 0.70. Mastering these "friendly" fractions bridges the gap between the two concepts. </li>

112 <li>The Double Number Line:Draw two parallel number lines, marking one with fractions (0, 1/4, 1/2, 3/4, 1) and the other directly beneath it with decimals (0, 0.25, 0.5, 0.75, 1.0). Seeing that these numbers occupy the exact same physical space on the line reinforces that decimal and fractions are equal values, just written differently. </li>

111 <li>The Double Number Line:Draw two parallel number lines, marking one with fractions (0, 1/4, 1/2, 3/4, 1) and the other directly beneath it with decimals (0, 0.25, 0.5, 0.75, 1.0). Seeing that these numbers occupy the exact same physical space on the line reinforces that decimal and fractions are equal values, just written differently. </li>

113 <li>Memorize the "Famous Families":Just like<a>multiplication tables</a>, certain conversions should be memorized for speed. Create "families" of benchmarks to memorize: the "Halves" (0.5 = 1/2), the "Quarters" (0.25 = 1/4), and the "Fifths" (0.2 = 1/5). Knowing these anchors makes estimating<a>complex fractions</a>to decimal conversions much less intimidating. </li>

112 <li>Memorize the "Famous Families":Just like<a>multiplication tables</a>, certain conversions should be memorized for speed. Create "families" of benchmarks to memorize: the "Halves" (0.5 = 1/2), the "Quarters" (0.25 = 1/4), and the "Fifths" (0.2 = 1/5). Knowing these anchors makes estimating<a>complex fractions</a>to decimal conversions much less intimidating. </li>

114 <li>The "Zeros" Trick for Expansion:When converting decimal to fractions, the number of digits behind the decimal point tells you how many zeros belong in the denominator. For example, in 0.45, there are two digits after the point, so the fraction is over 100 (45/100). In 0.125, there are three digits, so it is over 1000 (125/1000). This eliminates the guesswork of whether to use 10, 100, or 1000.</li>

113 <li>The "Zeros" Trick for Expansion:When converting decimal to fractions, the number of digits behind the decimal point tells you how many zeros belong in the denominator. For example, in 0.45, there are two digits after the point, so the fraction is over 100 (45/100). In 0.125, there are three digits, so it is over 1000 (125/1000). This eliminates the guesswork of whether to use 10, 100, or 1000.</li>

115 </ul><h2>Common Mistakes and How to Avoid Them on Decimals and Fractions</h2>

114 </ul><h2>Common Mistakes and How to Avoid Them on Decimals and Fractions</h2>

116 Understanding the concept and properties of decimals and fractions helps make mathematical problems and calculations simpler and easier. Here are some common mistakes and helpful solutions to avoid errors:

115 Understanding the concept and properties of decimals and fractions helps make mathematical problems and calculations simpler and easier. Here are some common mistakes and helpful solutions to avoid errors:

117 <h2>Real-Life Applications of Decimals and Fractions</h2>

116 <h2>Real-Life Applications of Decimals and Fractions</h2>

118 In our daily lives, we use decimals and fractions in various situations, from counting to distributing resources fairly. Here are some real-world applications of decimals and fractions:

117 In our daily lives, we use decimals and fractions in various situations, from counting to distributing resources fairly. Here are some real-world applications of decimals and fractions:

119 <ul><li>Finance and banking: Decimals and fractions are used to represent<a>money</a>accurately, such as $45.50. Additionally, bankers use<a>fractions and decimals</a>to calculate interest rates, loan amounts, and savings balances for account holders. For example, if a bank offers 2.5% annual interest on a savings account, it means customers can earn $2.50 for every $100 saved each year. </li>

118 <ul><li>Finance and banking: Decimals and fractions are used to represent<a>money</a>accurately, such as $45.50. Additionally, bankers use<a>fractions and decimals</a>to calculate interest rates, loan amounts, and savings balances for account holders. For example, if a bank offers 2.5% annual interest on a savings account, it means customers can earn $2.50 for every $100 saved each year. </li>

120 <li>Cooking: We can measure ingredients precisely using fractions and decimals. For example, baking a cake requires 1/5 cup of flour and 1.5 liters of milk, and measuring them in decimals and fractions ensures an exact<a>measurement</a>. </li>

119 <li>Cooking: We can measure ingredients precisely using fractions and decimals. For example, baking a cake requires 1/5 cup of flour and 1.5 liters of milk, and measuring them in decimals and fractions ensures an exact<a>measurement</a>. </li>

121 <li>Companies and stores: Calculate the price of items with<a>discounts</a>, offers, and<a>taxes</a>, such as 25% off or a $45 discount. Fractions are used to divide items fairly, such as dividing a 10-pack of items into 1/2 and 1/4 portions. </li>

120 <li>Companies and stores: Calculate the price of items with<a>discounts</a>, offers, and<a>taxes</a>, such as 25% off or a $45 discount. Fractions are used to divide items fairly, such as dividing a 10-pack of items into 1/2 and 1/4 portions. </li>

122 <li>Sports: Coaches and players can track performance using decimal values that show accurate timing and scores. For example, an athlete completes a 100 m sprint in 8.39 seconds helps coaches and players to figure out areas for improvement. </li>

121 <li>Sports: Coaches and players can track performance using decimal values that show accurate timing and scores. For example, an athlete completes a 100 m sprint in 8.39 seconds helps coaches and players to figure out areas for improvement. </li>

123 <li>Engineering and construction:Decimal fractions are used in construction for precise cut of materials. For example, 2.75 mm rod, 2.5m beam, etc.</li>

122 <li>Engineering and construction:Decimal fractions are used in construction for precise cut of materials. For example, 2.75 mm rod, 2.5m beam, etc.</li>

124 - </ul><h3>Problem 1</h3>

123 + </ul><h2>Download Worksheets</h2>

124 + <h3>Problem 1</h3>

125 Mary bought 100 oranges from the store, but she later found out that 9 of them were rotten. What fraction and decimal represent the rotten oranges compared to the total oranges?

126 Okay, lets begin

127 Fraction: $\frac{9}{100} $

128 Decimal: 0.09

129 <h3>Explanation</h3>

130 Total number of oranges = 100

131 Number of rotten oranges = 9

132 To find the fraction of rotten oranges compared to the total number of oranges, we can write it as:

133 $\frac{\text{Rotten oranges}}{\text{Total oranges}} = \frac{9}{100} $

134 The fraction $\frac{9}{100} $ is in its simplest form because 9 and 100 have no common factors other than 1.

135 Now we can convert the fraction to a decimal. So, divide 9 by 100:

136 9 ÷ 100 = 0.09

137 Thus, the fraction of rotten oranges compared to the total oranges is $\frac{9}{100} $, and in decimal form, it is 0.09.

138 Well explained 👍

139 <h3>Problem 2</h3>

140 Victoria ran 4.2 km on Sunday and 6.5 km on Monday. What fraction of her total distance did she run on Sunday, and what is the decimal equivalent?

141 Okay, lets begin

142 Fraction: $\frac{42}{107} $

143 Decimal form: 0.3925 (approximate value)

144 <h3>Explanation</h3>

145 Victoria ran 4.2 km on Sunday and 6.5 km on Monday.

146 So, the total distance is:

147 4.2 + 6.5 = 10.7 km

148 Next, we can find the fraction of the distance run on Sunday.

149 Distance on Sunday / Total distance = 4.2/10.7

150 4.2/10.7 is the fraction.

151 Now we can convert 4.2 and 10.7 into fractions:

152 4.2 = 42/10

153 10.7 = 107/10

154 We can divide the fractions.

155 4.2/10.7 = (42/10) ÷ (107/10) = 42/107

156 Next, multiply the numerators and denominators:

157 42 × 1010 × 107 = 4201070

158 Now we can simplify the fraction by dividing both the numerator and denominator by its greatest common divisor (GCD) of 420 and 1070.

159 So, the prime factorization of 420 is:

160 420 = 2 × 2 × 3 × 5 × 7

161 1070 = 2 × 5 × 107

162 2 and 5 are the common factors, and the GCD is 10.

163 Next, we can simplify the fraction:

164 4201070 ÷ 1010 = 42 107

165 Now, we can convert the fraction into decimal form. So, we can divide 42 by 107:

166 42 ÷ 107 ≈ 0.3925 (rounded to 4 decimal places)

167 Thus, Victoria ran about 39.25% of the total distance on Sunday.

168 Well explained 👍

169 <h3>Problem 3</h3>

170 A school library has 1000 books, out of which 340 are History books. What fraction of the total books are history books, and what is the decimal equivalent?

171 Okay, lets begin

172 Fraction: $\frac{17}{50} $

173 Decimal form: 0.34

174 <h3>Explanation</h3>

175 Total number of books in the library = 1000

176 Number of History books = 340

177 Now we can find the fraction of books that are History books:

178 $\frac{\text{Number of History books}}{\text{Total number of books}} = \frac{340}{1000} $

179 To simplify the fraction, we must find the greatest common divisor of 340 and 1000.

180 Prime factorization of 340 = 2 × 2 × 5 × 17

181 Prime factorization of 1000 = 2 × 2 × 2 × 5 × 5 × 5

182 Hence, the GCD is 20.

183 Next, we can divide both the numerator and denominator by 20:

184 3401000 ÷ 2020 = 1750

185 Thus, the simplified fraction is 1750

186 Next, we can convert the fraction to decimal. So, divide 17 by 50:

187 17 ÷ 50 = 0.34

188 34% of the total books in the library are History books.

189 Well explained 👍

190 <h3>Problem 4</h3>

191 Allen made 20 cakes and sold 14 of them. What fraction and decimal of the total cakes were sold?

192 Okay, lets begin

193 Fraction of cakes sold: $\frac{7}{10} $

194 Decimal form: 0.7

195 <h3>Explanation</h3>

196 Total cakes made by Allen = 20

197 Cakes sold by Allen = 14

198 The fraction of cakes that were sold is:

199 $\frac{\text{Cakes sold}}{\text{Total cakes}} = \frac{14}{20} $

200 To simplify the obtained fraction, we must divide both the numerator and denominator by its greatest common divisor.

201 Prime factorization of 14 = 2 × 7

202 Prime factorization of 20 = 2 × 2 × 5

203 Thus, the GCD is 2.

204 Next, we can divide 14 and 20 by 2:

205 1420 ÷ 22 = 710

206 The simplified fraction of $\frac{14}{20} $ is $\frac{7}{10} $.

207 Now we can convert a fraction to a decimal form.

208 Divide 7 by 10:

209 7 ÷ 10 = 0.7

210 Therefore, Allen sold 70% of the total cakes.

211 Well explained 👍

212 <h3>Problem 5</h3>

213 Philip bought 30 chocolate bars and gave 15 to his friends. What fraction of the chocolates did he give away, and what is the decimal equivalent?

214 Okay, lets begin

215 Fraction: $\frac{1}{2} $ Decimal form: 0.5

216 <h3>Explanation</h3>

217 Total chocolate bars Philip bought = 30

218 Chocolate bars given to his friends = 15

219 Now we can find the fraction of chocolates given to his friends is:

220 $\frac{\text{Chocolate given away}}{\text{Total chocolates}} = \frac{15}{30} $

221 Next, simplify the fraction by finding the greatest common divisor (GCD) of 15 and 30.

222 The factors of 15 are 1, 3, 5, and 15

223 The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30

224 Hence, the GCD is 15.

225 Here, we can divide the numerator and denominator by 15.

226 15 ÷ 15 = 1, 30 ÷ 15 = 2. So, fraction = $\frac{1}{2} $.

227 So, the fraction of chocolates given away is, $\frac{1}{2} $

228 Next, we can convert the fraction into a decimal form.

229 Divide 1 by 2:

230 1 ÷ 2 = 0.5

231 Hence, Philip gave away 50% of the chocolates.

232 Well explained 👍

233 <h2>FAQs on Decimals and Fractions</h2>

234 <h3>1.What do you mean by decimals and fractions?</h3>

235 A decimal number separates a whole number from a fractional part using a decimal point. A fraction represents a portion of a whole and is written as a/b. A fraction contains a numerator (top number) and a denominator (bottom number). For example, Decimals: 2.67, 1.76, and 4.987…etc. Fraction: $\frac{3}{9}, \frac{1}{4}, \frac{10}{12} $…etc.

236 <h3>2.How to read 234.76 and 1786.656 in decimal form?</h3>

237 We can read a decimal number using the term “point” for the decimal point. Hence, 234.76 is read as two hundred thirty-four point seven six. Also, 1786.656 is read as one thousand seven hundred eighty-six point six five six.

238 <h3>3.How to convert fractions into decimals?</h3>

239 To convert a fraction to a decimal, we must divide the numerator by the denominator. We can easily convert a fraction into a decimal by the direct division method. For example, to convert $\frac{2}{5} $ into a fraction: 2 ÷ 5 = 0.4

240 <h3>4.How may decimals be converted to percentages?</h3>

241 We can convert a decimal to a percentage, by following these steps: Step 1: Multiply the decimal number by 100. Step 2: Place the % symbol to the answer. For example, convert 0.57 to a percentage. 0.57 × 100 = 57%

242 <h3>5.Differentiate repeating and non-repeating decimals.</h3>

243 The numbers after the decimal point of a repeating decimal follow a pattern in which the digits repeat endlessly. For example, 1. 323232…, 1.151515….etc. Non-repeating decimals continue endlessly but should not follow a specific pattern. For example, 1.252552555…., 1.141441444 ... .etc.

244 <h3>6.At what age should my child learn decimal fraction?</h3>

245 Typically, decimal and fractions are introduced in grades 4 to 6. Children should first become comfortable with fractions and basic division.

246 <h3>7.How can I explain decimals and fractions easily?</h3>

247 Try to relate them to money, measurements, or quantities. Show to them that tenths, hundredths, thousandths are a part of a whole.

248 <h3>8.How can I make learning decimals and fractions fun?</h3>

249 Use some of the real-life situations to teach them. That will help them access more knowledge. For example, use problems related to money, measurements, recipes, etc.

250 <h2>Hiralee Lalitkumar Makwana</h2>

251 <h3>About the Author</h3>

252 Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

253 <h3>Fun Fact</h3>

254 : She loves to read number jokes and games.