Fraction to Decimal Conversion: Methods, Formula and Examples
Fraction to Decimal Conversion changes a fraction into its equivalent decimal form. The basic method is to divide the numerator by the denominator. Fractions with denominators containing only 2 and 5 after simplification give terminating decimals, while other denominators generally produce recurring decimals.
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What Is Fraction to Decimal Conversion?
For a fraction a/b, the decimal value is a ÷ b, where b ≠ 0. For example, 3/4 = 3 ÷ 4 = 0.75. A decimal may terminate, such as 0.25, or repeat indefinitely, such as 0.333... for 1/3.
Fraction to Decimal Conversion Formula & Tricks
Important Formulas
Divide the numerator by the denominator to obtain the decimal equivalent.
Make the denominator 10, 100, 1000 or another power of 10, then place the decimal point according to the number of zeros.
A reduced fraction has a terminating decimal only when its denominator has no prime factors other than 2 and 5.
Quick Tricks
Remember common fractions with denominators 2, 4, 5, 8, 10 and 20. Their decimal equivalents can be used directly.
Multiply the numerator and denominator by the same number so that the denominator becomes 10, 100 or 1000.
When the denominator cannot be changed to a power of 10, continue division. A repeated remainder produces a repeating decimal.
Fraction to Decimal Conversion Concepts
Division Method for Fraction to Decimal Conversion
Add a decimal point and zeros to the dividend when the numerator is smaller than the denominator. For 3/8, divide 3.000 by 8: 30 ÷ 8 gives 3 with remainder 6, 60 ÷ 8 gives 7 with remainder 4, and 40 ÷ 8 gives 5. Therefore, 3/8 = 0.375.
Converting a Fraction by Making the Denominator 10, 100 or 1000
Multiply both numerator and denominator by the same factor. The value of the fraction remains unchanged. For 9/25, multiply by 4 to get 36/100, so the decimal is 0.36.
Terminating and Recurring Decimals
The denominator 40 = 2³ × 5 gives a terminating decimal because it contains only 2 and 5. In contrast, 1/6 has reduced denominator 6 = 2 × 3, so its decimal is recurring: 1/6 = 0.1666....
Number of Decimal Places in a Terminating Decimal
The smaller power is balanced by multiplying the numerator and denominator by the missing factor. For 3/40, 40 = 2³ × 5, so at most max(3, 1) = 3 decimal places are needed. Indeed, 3/40 = 0.075.
Mixed Fractions and Improper Fractions
For a mixed fraction, retain the whole-number part and convert the proper fraction. Thus, 2 3/5 = 2 + 0.6 = 2.6. For an improper fraction, divide the numerator by the denominator directly: 17/5 = 3.4.
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Fraction to Decimal Conversion: Quick Revision
Use these rules to convert fractions accurately into terminating or recurring decimals.
- a/b = a ÷ b, with b ≠ 0.
- To use place value directly, make the denominator 10, 100, 1000 or another power of 10.
- Reduce the fraction before checking whether its decimal terminates.
- A reduced denominator containing only factors 2 and 5 gives a terminating decimal.
- A reduced denominator containing any prime factor other than 2 or 5 gives a recurring decimal.
- For denominator 2ᵐ × 5ⁿ, the maximum number of decimal places is max(m, n).
- For mixed fractions, add the decimal value of the fractional part to the whole-number part.
Fraction to Decimal Conversion FAQs
What is the formula for converting a fraction into a decimal?
Use a/b = a ÷ b, where b is not zero. For example, 5/8 = 5 ÷ 8 = 0.625.
How do you convert 7/20 into a decimal without long division?
Multiply the numerator and denominator by 5: 7/20 = 35/100 = 0.35.
Why does 1/3 produce a recurring decimal?
After reduction, the denominator 3 has a prime factor other than 2 or 5. Therefore, 1/3 = 0.333..., written as 0.\overline{3}.
How do you convert 3/40 into a decimal?
Since 3/40 = 75/1000, its decimal form is 0.075.
How many decimal places can 9/80 have?
Since 80 = 2⁴ × 5, it can have at most max(4, 1) = 4 decimal places. In fact, 9/80 = 0.1125.
How do you convert a mixed fraction such as 2 1/4 into decimal form?
Convert the fractional part and add it to the whole number: 2 1/4 = 2 + 0.25 = 2.25.