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Decimal to Hexadecimal: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Decimal to HexadecimalDecimal to Hexadecimal: Definition and ExamplesTable of ContentsDecimal to Hexadecimal Conversion Definition of Decimal to Hexadecimal Conversion

The decimal to hexadecimal conversion changes a decimal number (base-101010) into its hexadecimal (base-161616) equivalent. The decimal number system uses ten digits from 000 to 999, with place values defined by powers of 101010. In contrast, the hexadecimal system uses sixteen symbols: 0−90-90−9 and A−FA-FA−F (where A=10A=10A=10, B=11B=11B=11, C=12C=12C=12, D=13D=13D=13, E=14E=14E=14, F=15F=15F=15), with place values based on powers of 161616.

Converting from decimal to hexadecimal uses a method of successive division by 161616. This process generates remainders which, when written in reverse order, form the hexadecimal number. For decimal numbers with fractional parts, the whole number and fractional parts are converted separately, then combined to create the complete hexadecimal representation.

Examples of Decimal to Hexadecimal Conversion Example 1: Converting a Basic Decimal Number to Hexadecimal Problem:

Convert (152)10(152)_{10}(152)10​ into hexadecimal.

Step-by-step solution: Step 1, Divide the number by 161616. 152÷16=9152 \div 16 = 9152÷16=9 with remainder 888 Step 2, Divide the quotient by 161616. 9÷16=09 \div 16 = 09÷16=0 with remainder 999 Step 3, Since the quotient is now 000, we stop the division process. Step 4, Write the remainders in reverse order. The remainders are 888 and 999, so in reverse order, we get 989898. Step 5, Therefore, (152)10=(98)16(152)_{10} = (98)_{16}(152)10​=(98)16​ Example 2: Converting a Larger Decimal to Hexadecimal Problem:

Convert from decimal to hexadecimal: 45010450_{10}45010​

Step-by-step solution: Step 1, Divide the number by 161616. 450÷16=28450 \div 16 = 28450÷16=28 with remainder 222 Step 2, Divide the quotient by 161616. 28÷16=128 \div 16 = 128÷16=1 with remainder 121212 Step 3, Divide the quotient by 161616. 1÷16=01 \div 16 = 01÷16=0 with remainder 111 Step 4, Since the quotient is now 000, we stop the division process. Step 5, Write the remainders in reverse order. The remainders are 222, 121212, and 111. Step 6, Replace 121212 with its hexadecimal symbol CCC. Step 7, Therefore, 45010=(1C2)16450_{10} = (1C2)_{16}45010​=(1C2)16​ Example 3: Converting a Decimal Number with Fractional Part Problem:

Convert 15.51015.5_{10}15.510​ into the hexadecimal system.

Step-by-step solution: Step 1, Split the number into whole number part (151515) and fractional part (0.50.50.5). Step 2, Convert the whole number part 151015_{10}1510​ to hexadecimal: From the decimal to hexadecimal table, 1510=F1615_{10} = F_{16}1510​=F16​ Step 3, Convert the fractional part 0.5100.5_{10}0.510​ to hexadecimal: Multiply 0.50.50.5 by 161616: 0.5×16=8+0.00.5 \times 16 = 8 + 0.00.5×16=8+0.0 Since the fractional part is now 000, we stop here. Therefore, 0.510=0.8160.5_{10} = 0.8_{16}0.510​=0.816​ Step 4, Combine the whole number and fractional parts: 15.510=F.81615.5_{10} = F.8_{16}15.510​=F.816​ Comments(1)DDadOf3BoysNovember 6, 2025This page on decimal to hexadecimal is a lifesaver! It's helped my students grasp the concept easily with its clear examples.

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