Free Math Guide
Learn how to convert fractions to decimals using division and how to convert decimals to fractions using place value and simplification.
Fractions and decimals are two ways of representing the same quantity. A fraction describes a value using a numerator and denominator, while a decimal describes the value using place value. Converting between the two forms helps with measurement, money, probability, algebra, and many other areas of mathematics.
Changing a fraction into a decimal does not change the amount. It only changes the way the amount is written.
Equivalent Forms
1 2 = 0.5 = 50%The numerator shows the number of selected parts, and the denominator shows the total number of equal parts in one whole.
The decimal uses place value to show seventy-five hundredths.
The fraction 3/4 and the decimal 0.75 are equal because they represent the same portion of one whole.
To convert a fraction to a decimal, divide the numerator by the denominator.
The expression 3/4 means exactly the same thing as 3 ÷ 4.
The numerator becomes the dividend, which is the number being divided.
The denominator becomes the divisor, which is the number dividing the numerator.
Divide the numerator by the denominator using long division or a calculator when permitted.
Record the quotient and determine whether the decimal terminates or repeats.
Some fractions produce decimals that end, while others produce decimal patterns that continue forever.
A terminating decimal ends after a finite number of decimal places.
A repeating decimal contains a digit or pattern of digits that continues forever.
The digit 6 repeats forever.
The two-digit pattern 18 repeats forever.
The decimal 0.333 is close to one-third, but the exact decimal representation is 0.333... because the threes continue forever.
Use the decimal's place value to create a fraction, and then simplify the fraction if possible.
Determine whether the final digit is in the tenths, hundredths, or thousandths place.
Use the decimal digits as the numerator.
Use 10, 100, or 1,000 according to the decimal's final place value.
Divide the numerator and denominator by their greatest common factor.
The number of digits to the right of the decimal point determines the unsimplified denominator.
Tenths
One decimal place means a denominator of 10.
Hundredths
Two decimal places mean a denominator of 100.
Thousandths
Three decimal places mean a denominator of 1,000.
Ten-Thousandths
Four decimal places mean a denominator of 10,000.
| Decimal | Final Place Value | Unsimplified Fraction |
|---|---|---|
| 0.4 | Tenths | 4/10 |
| 0.36 | Hundredths | 36/100 |
| 0.125 | Thousandths | 125/1000 |
| 0.0625 | Ten-thousandths | 625/10000 |
Zeros between the decimal point and the first nonzero digit still count when identifying the place-value denominator.
After writing the decimal as a fraction, divide the numerator and denominator by their greatest common factor.
For example, 0.37 becomes 37/100. Since 37 and 100 have no common factor greater than one, 37/100 is already in simplest form.
The same conversion rules work when the value is greater than one. The resulting fraction may be improper and can also be rewritten as a mixed number.
The fraction 7/4 and the mixed number 1 3/4 are both equal to 1.75. Use the form requested by the problem.
Reverse the conversion to confirm that both forms represent the same value.
The quotient matches the original decimal, so the conversion is correct.
Divide the numerator by the denominator. For 3/4, calculate 3 ÷ 4.
Since 0.36 has two decimal places, the denominator must be 100.
Four tenths means 4/10, which simplifies to 2/5.
Divide both values by 25 to obtain the simplest fraction, 1/4.
The exact decimal continues forever. Write 0.333... or use repeating-decimal notation.
The 8 is in the thousandths place, so the correct fraction is 8/1000.
Use these questions before submitting your answer.
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