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Convert Fraction to Decimal: Definition and Example | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Convert Fraction to DecimalConvert Fraction to Decimal: Definition and ExampleTable of ContentsDefinition of Converting Fractions to Decimals

Fraction-to-decimal conversion is the process of expressing a fraction in its equivalent decimal form, which allows for more accurate and precise mathematical calculations. The conversion follows the simple principle of division: to convert a fraction to a decimal, divide the numerator by the denominator. For example, when converting 34\frac{3}{4}43​ to a decimal, we get 0.750.750.75, where 000 is the whole number part and 0.750.750.75 is the decimal part.

Fractions can result in two types of decimal forms: terminating and repeating decimals. A fraction produces a terminating decimal when its denominator (in lowest form) has prime factorization consisting only of 222s and/or 555s. For instance, 716\frac{7}{16}167​ results in the terminating decimal 0.43750.43750.4375 because 161616 = 242^424. Conversely, if the denominator's prime factorization includes factors other than 222s and 555s, the result is a repeating decimal. For example, 512\frac{5}{12}125​ gives 0.41666...0.41666...0.41666...(with 666 repeating) because 121212 = 22×32^2 \times 322×3.

Examples of Converting Fractions to Decimals Example 1: Converting an Improper Fraction Using Long Division Problem:

Find the decimal form of 75\frac{7}{5}57​ using the long division method.

Step-by-step solution: Step 1, Identify what we're dividing: the numerator 777 is the dividend and the denominator 555 is the divisor. Step 2, Set up a long division problem where we divide 777 by 555: 7÷5=1.47 \div 5 = 1.47÷5=1.4 Step 3, Breaking it down: 555 goes into 777 once: 1×5=51 \times 5 = 51×5=5 Subtract: 7−5=27 - 5 = 27−5=2 Bring down a 000 after placing a decimal point: 2.02.02.0 Divide 202020 by 555: 20÷5=420 \div 5 = 420÷5=4 So we have 1.41.41.4 as our answer Step 4, Therefore, 75=1.4\frac{7}{5} = 1.457​=1.4 Example 2: Converting a Fraction by Changing to Powers of 10 Problem:

Convert 45\frac{4}{5}54​ into a decimal by changing the denominator into a power of 101010.

Step-by-step solution: Step 1, Identify what we need: we want to convert the denominator 555 into a power of 101010. Step 2, Think: What number, when multiplied by 555, gives a power of 101010? 5×2=105 \times 2 = 105×2=10 (which is 10110^1101) Step 3, Multiply both numerator and denominator by this number to maintain the fraction's value: 45=4×25×2=810\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}54​=5×24×2​=108​ Step 4, Now, the denominator is a power of 101010, so we can easily convert to decimal: 810=0.8\frac{8}{10} = 0.8108​=0.8 Step 5, Remember: When the denominator is a power of 101010, the decimal point moves to the left by the same number of zeros in the denominator. Step 6, Therefore, 45=0.8\frac{4}{5} = 0.854​=0.8 Example 3: Comparing a Fraction with a Decimal Value Problem:

Compare 1120\frac{11}{20}2011​ and 0.50.50.5.

Step-by-step solution: Step 1, To compare these values effectively, we need to convert 1120\frac{11}{20}2011​ to a decimal. Step 2, Think: How can we change 202020 to a power of 101010? 20×5=10020 \times 5 = 10020×5=100 (which is 10210^2102) Step 3, Multiply both numerator and denominator by 555: 1120=11×520×5=55100=0.55\frac{11}{20} = \frac{11 \times 5}{20 \times 5} = \frac{55}{100} = 0.552011​=20×511×5​=10055​=0.55 Step 4, Now, we can directly compare the decimals: 0.50.50.5 and 0.550.550.55 Step 5, Compare: Since 0.550.550.55 is greater than 0.50.50.5, we conclude that: 0.511200.5 0.52011​ or 1120>0.5\frac{11}{20} > 0.52011​>0.5 Step 6, Therefore, 1120\frac{11}{20}2011​ is greater than 0.50.50.5. Comments(7)CCarEnthusiastJakeNovember 6, 2025This glossary page is a lifesaver! I've used it to teach my students how to convert fractions to decimals. The examples are super helpful.

PPRSpecialistVinceNovember 4, 2025I've used this to teach my students. The step - by - step examples are great! Helped them grasp converting fractions to decimals easily.

NNatureLover25September 10, 2025This guide on converting fractions to decimals was a lifesaver! My kid finally understood the difference between terminating and repeating decimals. The examples made it so easy to explain—thank you!

NNatureLover85August 27, 2025I used the 'Convert Fraction to Decimal' page to help my kids with their math homework—it's super clear and the examples made things click for them! Great resource for parents!

SSunnyTravelerAugust 20, 2025I’ve been using this page to help my kids grasp fractions and decimals. The step-by-step examples made it so easy for them to follow! Loved the tips on identifying repeating decimals too.

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