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2026-01-01
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2026-02-28
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<p>295 Learners</p>
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<p>Last updated on<strong>December 6, 2025</strong></p>
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<p>The decimal number system uses 10 digits (0 to 9) with a base of 10. This number system has been in use since ancient times and is also known as the Arabic number system. Other number systems used in mathematics are binary, octal, and hexadecimal number systems. In this topic, we will be focusing on the decimal number system.</p>
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<h2>What is a Decimal Number System?</h2>
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<p>What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math</p>
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<p>▶</p>
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<p>We use digits from 0 to 9 in the<a>decimal</a><a>number system</a>. Since the system uses 10 digits, the<a>base</a>is 10. Unless specified, numbers without a base are assumed to be decimal (base 10). In the decimal number system, the place values<a>of</a>a number are read from right to left; the first few place values are ones, tens, hundreds, thousands, and so on. Let’s consider the number 423.</p>
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<p>Here, 3 is in the ones place (\(3 × 1 = 3\))</p>
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<p> 2 is in the tens place (\(2 \times 10 = 20\))</p>
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<p>4 is in the hundreds place (\(4 × 100 = 400 \)) </p>
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<p>Now we can add all of them: </p>
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<p>\(400 + 20 + 3 = 423 \)</p>
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<p>To find the value of a number, we can multiply each digit by its<a>place value</a>and then add the products together.</p>
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<h2>What are the Rules of the Decimal Number System?</h2>
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<p>The base of a decimal<a>number</a>system is 10, and it includes the digits 0 to 9 to represent the number’s place values. The digit in the tens place is 10 times<a>greater than</a>the digit in the ones place. Here are some rules related to the decimal number system: </p>
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<ul><li>0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are the 10 numbers in the decimal number system. </li>
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</ul><ul><li>In the decimal number system, when a digit reaches 9, and we add 1, the digit becomes 10. However, since we only have digits from 0 to 9, we write 0 instead of 10. Then, carry over 1 to the next higher place value. So, when we go from 9 to 10, the number on the right becomes 0, and 1 is added to the left side, making it 10. </li>
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</ul><p>Let us take an example to understand the rules better. If the number is \((142)_{10} \) \({(142)_{10}} ={ 1 × {10^2} }+ {4× {10^1} }+ {2 × {10^0}}\)</p>
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<p>If the numbers have a decimal point, then the place value of the numbers after the decimal point continues in decreasing<a>powers</a>of 10.</p>
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<p>For instance, if the given number is\({(35.27)_{10}}\). \({(35.27)_{10}} = {(3 × {10^1})} + (5 × {10^0})+ (2 × {10^{-1}}) + (7 × 10^{-2}) \)</p>
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<p>Therefore, \({(35.27)_{10}} = 30 + 5 + 0.2 + 0.07 \)</p>
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<h2>How to Convert into Decimal Number System?</h2>
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<p> We use only two digits in the binary number system (0 and 1), and its base is 2. So, to convert a binary number to a decimal number, we must multiply every digit of the binary number by a power of 2. The<a>exponent</a>of 2 depends on the position of the binary number. The rightmost digit is multiplied by \(2^0\), the next digit is multiplied by \(2^1\), and so on. After the<a>multiplication</a>process is done, we add up the results to get the converted value. </p>
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<p> We use only two digits in the binary number system (0 and 1), and its base is 2. So, to convert a binary number to a decimal number, we must multiply every digit of the binary number by a power of 2. The<a>exponent</a>of 2 depends on the position of the binary number. The rightmost digit is multiplied by \(2^0\), the next digit is multiplied by \(2^1\), and so on. After the<a>multiplication</a>process is done, we add up the results to get the converted value. </p>
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<p>Multiply each digit of the binary number by 2 raised to the power of its position from right to left, starting at 0. Then add the results together to get the decimal number. </p>
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<p>Multiply each digit of the binary number by 2 raised to the power of its position from right to left, starting at 0. Then add the results together to get the decimal number. </p>
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<p>The given binary number is \((1011)_2\).</p>
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<p>The given binary number is \((1011)_2\).</p>
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<p>\({ (1011)_2} = (1 × {2^3}) + (0 × {2^2}) + (1 × {2^1}) + (1 × {2^0}) \) \( = (1 × 8) + (0 × 4) + (1 × 2) + (1 × 1) \) \( = 8 + 0 + 2 + 1 \) \(= 11\)</p>
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<p>\({ (1011)_2} = (1 × {2^3}) + (0 × {2^2}) + (1 × {2^1}) + (1 × {2^0}) \) \( = (1 × 8) + (0 × 4) + (1 × 2) + (1 × 1) \) \( = 8 + 0 + 2 + 1 \) \(= 11\)</p>
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<p>Thus, \({(1011)_2} = {(11)_{10}}\)</p>
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<p>Thus, \({(1011)_2} = {(11)_{10}}\)</p>
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<p><strong>Octal to Decimal Conversion:</strong></p>
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<p><strong>Octal to Decimal Conversion:</strong></p>
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<p>The octal number system has a base of 8. It has 8 digits, from 0 to 7, to represent numbers. To convert an octal number to a decimal number, multiply each digit by the decreasing power of 8 and add the products. Let us convert (167)8 to its decimal form. </p>
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<p>The octal number system has a base of 8. It has 8 digits, from 0 to 7, to represent numbers. To convert an octal number to a decimal number, multiply each digit by the decreasing power of 8 and add the products. Let us convert (167)8 to its decimal form. </p>
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<p>\({(167)_8} = {(1 × 8^2)} + ({6 × 8^1)} + {(7 × 8^0)} \) \(= (1 × 64) + (6 × 8) + (7 × 1) \) \(= 64 + 48 + 7 \) \(= 119 \)</p>
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<p>\({(167)_8} = {(1 × 8^2)} + ({6 × 8^1)} + {(7 × 8^0)} \) \(= (1 × 64) + (6 × 8) + (7 × 1) \) \(= 64 + 48 + 7 \) \(= 119 \)</p>
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<p>Thus, \({(167)_8 }= {(119)_{10}} \) After the conversion, the base power changes from 8 to 10.</p>
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<p>Thus, \({(167)_8 }= {(119)_{10}} \) After the conversion, the base power changes from 8 to 10.</p>
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<p><strong>Hexadecimal to Decimal Conversion:</strong></p>
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<p><strong>Hexadecimal to Decimal Conversion:</strong></p>
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<p>The hexadecimal number system uses 16<a>symbols</a>: digits from 0 to 9 and letters from A to F. The conversion of a hexadecimal number to a decimal number happens when we multiply each digit of the hexadecimal number by the powers of 16. Once again, the rightmost digit will be multiplied by 160, the next digit by 161, and so on. After multiplying the digits by the powers of 16, we should add the results to obtain the converted value. </p>
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<p>The hexadecimal number system uses 16<a>symbols</a>: digits from 0 to 9 and letters from A to F. The conversion of a hexadecimal number to a decimal number happens when we multiply each digit of the hexadecimal number by the powers of 16. Once again, the rightmost digit will be multiplied by 160, the next digit by 161, and so on. After multiplying the digits by the powers of 16, we should add the results to obtain the converted value. </p>
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<p>\((18)_{16} = (1 × 16^1) + (8 × 16^0)\)</p>
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<p>\((18)_{16} = (1 × 16^1) + (8 × 16^0)\)</p>
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<p>\(= (1 × 16) + (8 × 1) \) \(= 16 + 8 \) \(= 24 \)</p>
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<p>\(= (1 × 16) + (8 × 1) \) \(= 16 + 8 \) \(= 24 \)</p>
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<p>Thus, \({(18)_{16}} = {(24)_{10}}\)</p>
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<p>Thus, \({(18)_{16}} = {(24)_{10}}\)</p>
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<h2>How to Convert From Decimal Number System to Other Systems</h2>
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<p>The conversion of<a>decimal numbers</a>to other number systems is similar to the conversion from a different number system to decimal. The key element in the conversion is the base number of each number system.</p>
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<p><strong>Decimal to Binary Conversion:</strong></p>
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<p>Decimal numbers can be converted to binary by dividing the number repeatedly by 2 until the<a>quotient</a>becomes 0. In every step, the<a>remainder</a>is noted (either 1 or 0). In the end, the remainders are written from bottom to top to get the binary equivalent of the decimal number.</p>
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<strong>Dividend</strong><strong>Remainder</strong>\({138\div 2} = 69\) 0 \({69 \div 2} = 34\) 1 \(34\div2 = 17\) 0 \(17\div2 = 8\) 1 \(8\div2 = 4\) 0 \(4\div2 = 2\) 0 \(2\div2 = 1\) 0 \(1\div2 = 0\) 1<p>Now write the remainder from bottom to top. Thus, the binary number of \({{(138)}_{₁₀} = {10001010}_₂} \).</p>
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<p><strong>Decimal to Octal Conversion:</strong></p>
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<p> Decimal numbers can be converted to octal by dividing the number by 8 repeatedly until the quotient is<a>less than</a>8. In every step, the remainder is noted. After the<a>division</a>process, the remainders are written from bottom to top to obtain the converted value. In the division process, the first remainder is known as the least significant digit (LSD), and the last remainder is called the most significant digit (MSD). Let’s see how to convert \({(65)_{10}}\) to an octal number.</p>
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<strong>Dividing by 8</strong><strong>Quotient</strong><strong>Remainder</strong>\(65\div8\) 8 1 \(8\div8\) 1 0 \(1\div8\) 0 1<p>Write the numbers obtained as remainders from bottom to top. </p>
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<p>Thus,\( {(65)_{10}} = {(101)_{8}}\).</p>
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<p><strong>Decimal to Hexadecimal Conversion:</strong></p>
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<p> Each decimal number will be divided by the base number of hexadecimal (16) until the quotient becomes 0. For example, convert the decimal number \((150)_{10} \) to hexadecimal. </p>
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<strong>Dividing by 16</strong><strong>Quotient</strong><strong>Remainder</strong>\(150\div16\) 9 6 \(6\div16\) 0 6<p>Now write the remainder from the bottom to the top to get the hexadecimal number. Thus, \({(150)_{10}} = {(96)_{16}}\)</p>
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<h2>Tips and Tricks to Master the Decimal Number System</h2>
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<p>Mastering the decimal system helps students to understand the place value, perform accurate calculations, and apply numbers confidently in real-life situations. In this section, we will learn a few tips and tricks to master the decimal number system. </p>
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<ul><li><strong>Understand Place Value:</strong>Always remember that each digit’s place represents a power of 10. Leftward digits increase in value, and rightward digits (after the decimal) decrease in value. </li>
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<li><strong>Memorize Base Values:</strong>Know the base of each number system: Binary = 2, Octal = 8, Decimal = 10, Hexadecimal = 16. </li>
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<li><strong>Use Expanded Form:</strong>Break numbers into their<a>expanded form</a>(e.g., 345.27 = 300 + 40 + 5 + 0.2 + 0.07) to understand the contribution of each digit. </li>
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<li><strong>Practice Conversions:</strong>Convert numbers between decimal, binary, octal, and hexadecimal to strengthen your grasp of bases and place values. </li>
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<li><strong>Visualize with Charts:</strong>Use place value charts to clearly see the value of each digit in large or decimal numbers. </li>
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<li>Introduce the idea that computers use binary numbers (0s and 1s). Explain that decimal has 10 digits (0-9) while numbers in binary use only two digits (0 and 1). This helps children understand why the binary number system is called binary. </li>
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<li>Encourage children to notice decimals in<a>money</a>, measurements, temperature, shopping<a>discounts</a>, or time. This helps them see decimals as practical rather than abstract. </li>
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<li>Use number lines to visually<a>compare decimal</a>values, helping children understand<a>ordering</a>, spacing, and relationships among closely spaced decimal numbers. </li>
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<li>Create engaging games involving decimal comparison, quick conversions, and number challenges to make practice enjoyable and improve confidence with decimals. </li>
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</ul><h2>Common Mistakes and How to Avoid Them in Decimal Number System</h2>
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<p>It is easy to make mistakes while dealing with the decimal number system. Even the slightest of errors can change the final result completely. Therefore, it is important to avoid commonly made mistakes, and some of them are mentioned below: </p>
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<h2>Real-life Applications of Decimal Number System</h2>
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<p>The decimal number system plays a crucial role in determining the place value of each digit. The place value of each digit in a number is based on powers of 10. Here are some real-world applications of the decimal number system: </p>
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<ul><li>The decimal system helps students determine the<a>place value of digits</a>and perform<a>arithmetic operations</a>and build a string foundation in mathematics</li>
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</ul><ul><li>The decimal number system helps us determine the value of the money we have. For example, if we have $288, we can easily understand its value, such as we have two hundred eighty-eight dollars. </li>
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</ul><ul><li>Mobile numbers, PIN codes, and numerical passwords are based on the decimal number system. It helps us to recognize and memorize, and use these numbers efficiently. </li>
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<li>From weighing items to measuring lengths, volumes, and temperatures, the decimal system ensures<a>accuracy</a>and standardization in everyday measurements. </li>
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<li>The decimal system is used to record hours, minutes, and seconds, enabling consistent and precise time calculations.</li>
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</ul><h3>Problem 1</h3>
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<p>Convert the binary number (1010)₂ to a decimal number.</p>
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<p>Okay, lets begin</p>
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<p>\((10)_{10}\)</p>
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<h3>Explanation</h3>
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<p>Here, we must multiply each digit of the binary number by the decreasing power of 2, starting from the rightmost digit. The given binary number is \({(1010)_2} \)</p>
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<p>\({(1010)_2} = (1 × 2^3) + (0 × 2^2) + (1 × 2^1) + (0 × 2^0) \)</p>
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<p>Now we can calculate the individual terms: </p>
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<p>\( = (1 × 8) + (0 × 4) + (1 × 2) + (0 × 1) \)</p>
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<p>Then, add the results together to get the decimal number. </p>
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<p>\( = 8 + 0 + 2 + 0\)</p>
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<p>\(= 10\)</p>
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<p>Thus, \( (1010)_{2} = (10)_{10}\)</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<p>Convert (67)₈ to a decimal number.</p>
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<p>Okay, lets begin</p>
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<p>\((55)_{10}\)</p>
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<h3>Explanation</h3>
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<p>We multiply each digit of the octal number (67)8 by the decreasing power of 8, beginning at the rightmost digit. After that, we add the products to convert an octal number to a decimal number.</p>
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<p>The given number is \((67)_8\).</p>
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<p>\((67)_8 = (6 × 8^1) + (7 × 8^0) \)</p>
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<p>\(= (6 × 8) + (7 × 1) \)</p>
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<p>Now multiply the values:</p>
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<p> \(= 48 + 7 \)</p>
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<p> \(= 55 \)</p>
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<p>Thus, \((67)_8 = (55)_{10}\)</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<p>Convert (2B)₁₆ to a decimal number.</p>
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<p>Okay, lets begin</p>
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<p>\((43)_{10}\)</p>
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<h3>Explanation</h3>
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<p>The given hexadecimal number is \((2B)_{16}\).</p>
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<p>\( (2B)_{16} = (2 × 16^1) + (B × 16^0)\)</p>
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<p>In the hexadecimal number system, B is equal to 11. </p>
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<p>\(= (2 × 16^1) + (11 × 16^0)\)</p>
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<p> \( = (2 × 16) + (11 × 1)\)</p>
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<p>Now we can multiply the values:</p>
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<p> \(= 32 + 11\)</p>
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<p> \(= 43 \)</p>
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<p>Therefore, \((2B)_{16} = (43)_{10}\)</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<p>Convert (12)_10 to a binary number.</p>
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<p>Okay, lets begin</p>
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<p>\((1100)_2\)</p>
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<h3>Explanation</h3>
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<p>The given number is \((12)_{10}\). To convert a decimal number to binary, we will divide the decimal number by 2 repeatedly, noting the remainder each time.</p>
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<p>Divide 12 by 2:</p>
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<p> \(12 ÷ 2 = 6\) Remainder = 0</p>
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<p>Divide 6 by 2:</p>
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<p> \(6 ÷ 2 = 3\) Remainder = 0</p>
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<p>Divide 3 by 2:</p>
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<p> \(3 ÷ 2 = 1\) Remainder = 1 </p>
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<p>Divide 1 by 2:</p>
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<p> 1 ÷ 2 = 0 Remainder = 1 </p>
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<p>Now, we can write the remainder from bottom to top:</p>
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<p> \( (12)_{10} = (1100)_{2}\)</p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<p>Convert (18)_10 to an octal number.</p>
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<p>Okay, lets begin</p>
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<p>\((22)_8 \)</p>
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<h3>Explanation</h3>
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<p>Here, the given number is \(18_{10}\). To convert a decimal number to an octal number, we divide the decimal number by 8, which is the base of the octal number system. We then note the quotients and remainders, continuing the division until the quotient becomes 0. </p>
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<p>Divide 18 by 8:</p>
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<p> \(18 ÷ 8 = 2\) (Quotient) Remainder = 2</p>
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<p>Divide the quotient 2 by 8:</p>
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<p> \(2 ÷ 8 = 0\) (Quotient) Remainder = 2</p>
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<p>Write the remainder from bottom to top: </p>
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<p> \((18)_{10} = (22)_8 \)</p>
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<p>Well explained 👍</p>
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<h2>FAQs for Decimal Number System</h2>
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<h3>1.What is the decimal number system?</h3>
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<p>The decimal number system is a base-10 system that uses the digits 0-9 to write and represent the numbers we use every day.</p>
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<h3>2.How can parents explain decimals to their children?</h3>
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<p>Parents can use examples like money (₹10.50), measuring cups, or rulers to show how decimals represent parts of a whole. </p>
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<h3>3.How can parents explain the difference between the decimal system and the binary number system?</h3>
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<p>Parents can explain that decimals use the digits 0-9, while the binary number system uses only 0 and 1, mainly in computers. </p>
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<h3>4.Why should parents teach children that 0.5 and 0.50 are the same?</h3>
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<p>Parents can teach that both represent the same value, and the extra zero only adds more precision, not a different amount.</p>
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<h2>Hiralee Lalitkumar Makwana</h2>
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<h3>About the Author</h3>
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<p>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.</p>
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<h3>Fun Fact</h3>
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<p>: She loves to read number jokes and games.</p>