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2026-01-01
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2026-02-28
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<p>240 Learners</p>
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<p>Last updated on<strong>December 4, 2025</strong></p>
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<p>In mathematics and computer science, numbers can be represented in various numeral systems, such as decimal, binary, octal, or hexadecimal. The decimal system is the most commonly used and is based on the number 10, employing digits from 0 to 9. The binary system, however, is based on the number 2, using only the digits 0 and 1. Decimal to binary conversion is essential in computing and digital electronics, as computers use binary language to process data. In this topic, we will learn how to convert decimal numbers to binary.</p>
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<p>In mathematics and computer science, numbers can be represented in various numeral systems, such as decimal, binary, octal, or hexadecimal. The decimal system is the most commonly used and is based on the number 10, employing digits from 0 to 9. The binary system, however, is based on the number 2, using only the digits 0 and 1. Decimal to binary conversion is essential in computing and digital electronics, as computers use binary language to process data. In this topic, we will learn how to convert decimal numbers to binary.</p>
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<h2>What is Decimal?</h2>
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<p>A<a>decimal</a>system is a<a>base</a>-10 numeral system, which is the standard system for denoting<a>integers</a>and non-integers. It is the most widely used system in daily life for expressing<a>numbers</a>.</p>
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<p>The decimal system utilizes ten<a>symbols</a>: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.</p>
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<p>Each digit's position in a number represents a<a>power</a>of 10, making it straightforward to perform<a>arithmetic operations</a>.</p>
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<h2>What is Binary?</h2>
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<p>The binary numeral system, or base-2 system, represents numeric values using two symbols: 0 and 1.</p>
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<p>It is the foundation of all binary code, which is used in computing and digital systems.</p>
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<p>Each digit in a<a>binary number</a>represents a power of 2, and the binary system is essential for computer operations and digital circuit design.</p>
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<h2>What Is Decimal to Binary Conversion?</h2>
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<p>Decimal to binary conversion is the process of changing a number from the decimal system (base 10) into the binary system (base 2).</p>
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<p>The decimal system is the<a>number system</a>we use every day, made up of digits from 0 to 9. In contrast, the binary system is used in computers and digital devices and includes only two digits: 0 and 1.</p>
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<p>Computers store and process all information in binary. Converting<a>decimal numbers</a>to binary helps students understand how digital systems represent<a>data</a>, perform calculations, and execute commands.</p>
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<p>This conversion builds a strong foundation for computer science, coding, logic circuits, and understanding how digital technology works.</p>
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<h3>Explore Our Programs</h3>
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<p>No Courses Available</p>
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<h2>Decimal to Binary Formula</h2>
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<p>To convert a decimal number to binary, follow these steps:</p>
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<ul><li>Repeatedly divide the decimal number by 2.</li>
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<li>Write down the<a>remainder</a>after each<a>division</a>(this will be either 0 or 1).</li>
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<li>Continue dividing the<a>quotient</a>by 2 until the quotient becomes 0.</li>
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<li>Read the remainders from bottom to top to get the binary number.</li>
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</ul><p><strong>Formula: Binary = Read the remainders of (Decimal ÷ 2) from bottom to top</strong></p>
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<p><strong>\( N_{i+1} = \left[ \frac{N_i}{2} \right] \)</strong></p>
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<p>This method converts the integer part of a decimal number to binary by repeatedly dividing by 2 until the quotient reaches 0.</p>
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<h2>How to Convert Decimal to Binary?</h2>
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<p>Converting a decimal number to binary involves dividing the number by 2 and keeping track of the remainders.</p>
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<h3><strong>Step-by-Step Process to Convert Decimal to Binary</strong></h3>
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<h4><strong>Step 1:</strong>Write down the decimal number.</h4>
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<h4><strong>Step 2:</strong>Divide the number by 2.</h4>
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<h4><strong>Step 3:</strong>Record the remainder (0 or 1).</h4>
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<h4><strong>Step 4:</strong>Repeat the process with the quotient until it is 0.</h4>
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<h4><strong>Step 5:</strong>The binary number is obtained by reading the remainders in reverse order.</h4>
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<h2>Decimal to Binary Conversion Table</h2>
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<p>When dealing with numbers, we often use decimal and binary systems.</p>
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<p>Here is a conversion table to help understand how decimal numbers are represented in binary.</p>
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<h2>Common Mistakes and How to Avoid Them in Decimal to Binary Conversion</h2>
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<p>When converting decimal numbers to binary, beginners often make mistakes. Here are some common errors to help understand the conversion process better.</p>
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<h3>Problem 1</h3>
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<p>Convert 45 to binary</p>
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<p>Okay, lets begin</p>
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<p>45 in decimal is 101101 in binary.</p>
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<h3>Explanation</h3>
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<p>To convert 45:</p>
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<p>45 ÷ 2 = 22 remainder 1</p>
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<p>22 ÷ 2 = 11 remainder 0</p>
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<p>11 ÷ 2 = 5 remainder 1</p>
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<p>5 ÷ 2 = 2 remainder 1</p>
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<p>2 ÷ 2 = 1 remainder 0</p>
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<p>1 ÷ 2 = 0 remainder 1</p>
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<p>Binary: 101101</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<p>Convert 78 to binary.</p>
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<p>Okay, lets begin</p>
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<p>Solution: 78 in decimal is 1001110 in binary.</p>
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<h3>Explanation</h3>
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<p>Convert 78:</p>
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<p>78 ÷ 2 = 39 remainder 0</p>
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<p>39 ÷ 2 = 19 remainder 1</p>
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<p>19 ÷ 2 = 9 remainder 1</p>
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<p>9 ÷ 2 = 4 remainder 1</p>
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<p>4 ÷ 2 = 2 remainder 0</p>
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<p>2 ÷ 2 = 1 remainder 0</p>
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<p>1 ÷ 2 = 0 remainder 1</p>
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<p>Binary: 1001110</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<p>What is 15 in binary?,A sports merchandise shop in New York City is preparing digital codes for customers who buy official NFL jerseys. One customer purchases a limited-edition jersey costing $24, and the shop’s system requires converting the decimal number 24 into binary to generate a discount voucher. What is 24 in binary? Solution:</p>
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<p>Okay, lets begin</p>
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<p>15 in decimal is 1111 in binary.</p>
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<p>11000</p>
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<h3>Explanation</h3>
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<p>Convert 15:</p>
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<p>15 ÷ 2 = 7 remainder 1</p>
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<p>7 ÷ 2 = 3 remainder 1</p>
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<p>3 ÷ 2 = 1 remainder 1</p>
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<p>1 ÷ 2 = 0 remainder 1</p>
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<p>Binary: 1111</p>
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<p>Since the system uses binary for generating voucher IDs, we convert 24 from decimal to binary.</p>
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<p>We repeatedly divide by 2 and record remainders:</p>
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<p>24 ÷ 2 = 12 → remainder 0</p>
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<p>12 ÷ 2 = 6 → remainder 0</p>
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<p>6 ÷ 2 = 3 → remainder 0</p>
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<p>3 ÷ 2 = 1 → remainder 1</p>
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<p>1 ÷ 2 = 0 → remainder 1</p>
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<p>Reading remainders bottom-up gives 11000.</p>
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<p>This code is later printed on the customer's NFL receipt.</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<p>A Walgreens pharmacy in Chicago prints dosage instruction barcodes using binary numbers. A cold medicine formula includes an ingredient ID number of 37, which must be converted to binary before printing. What is 37 in binary?</p>
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<p>Okay, lets begin</p>
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<p>100101</p>
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<h3>Explanation</h3>
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<p>Walgreens converts decimal numbers like 37 into binary for internal tracking.</p>
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<p>Divide repeatedly by 2:</p>
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<p>37 ÷ 2 = 18 → remainder 1</p>
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<p>18 ÷ 2 = 9 → remainder 0</p>
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<p>9 ÷ 2 = 4 → remainder 1</p>
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<p>4 ÷ 2 = 2 → remainder 0</p>
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<p>2 ÷ 2 = 1 → remainder 0</p>
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<p>1 ÷ 2 = 0 → remainder 1</p>
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<p>Read from bottom to top → 100101.</p>
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<p>This binary ID goes into their nationwide medicine-tracking database.</p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<p>A sports merchandise shop in New York City is preparing digital codes for customers who buy official NFL jerseys. One customer purchases a limited-edition jersey costing $24, and the shop’s system requires converting the decimal number 24 into binary to generate a discount voucher. What is 24 in binary?</p>
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<p>Okay, lets begin</p>
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<p>11000</p>
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<h3>Explanation</h3>
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<p>Since the system uses binary for generating voucher IDs, we convert 24 from decimal to binary.</p>
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<p>We repeatedly divide by 2 and record remainders:</p>
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<p>24 ÷ 2 = 12 → remainder 0</p>
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<p>12 ÷ 2 = 6 → remainder 0</p>
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<p>6 ÷ 2 = 3 → remainder 0</p>
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<p>3 ÷ 2 = 1 → remainder 1</p>
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<p>1 ÷ 2 = 0 → remainder 1</p>
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<p>Reading remainders bottom-up gives 11000.</p>
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<p>This code is later printed on the customer's NFL receipt.</p>
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<p>Well explained 👍</p>
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<h2>FAQs on Decimal to Binary</h2>
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<h3>1.What is the binary of 7?</h3>
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<p>7 in decimal is 111 in binary.</p>
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<h3>2.What is 50 in binary?</h3>
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<p>50 in decimal is 110010 in binary.</p>
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<h3>3.Is 128 a power of 2?</h3>
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<p>Yes, 128 is a power of 2. It is 2^7.</p>
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<h3>4.How do I convert 64 to binary?</h3>
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<p>64 in decimal is 1000000 in binary.</p>
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<h3>5.Who invented binary code?</h3>
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<p>Binary code was primarily invented by Gottfried Wilhelm Leibniz, a German mathematician and philosopher, in the 17th century.</p>
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<h3>6.Does NASA use binary code?</h3>
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<p>Yes, NASA uses binary code extensively in its operations, especially in the development and functioning of its space missions, satellites, and spacecraft.</p>
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<h2>Important Glossaries for Decimal to Binary Conversion</h2>
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<p>Conversion: The process of changing one number from one numeral system to another, such as from decimal to binary. Binary Number: A number expressed in the base-2 numeral system, using only the digits 0 and 1. Decimal Number: A number expressed in the base-10 numeral system, using digits from 0 to 9. Remainder: The amount left over after division, crucial for determining binary digits. Power of 2: Numbers like 1, 2, 4, 8, etc., which are the result of raising 2 to an integer power.</p>
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<p>What Is Measurement? 📏 | Easy Tricks, Units & 🎯 Fun Learning for Kids | ✨BrightCHAMPS Math</p>
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<p>▶</p>
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<h2>Seyed Ali Fathima S</h2>
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<h3>About the Author</h3>
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<p>Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.</p>
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<h3>Fun Fact</h3>
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<p>: She has songs for each table which helps her to remember the tables</p>