How do you convert a decimal to a fraction?

Decimals can be written in fraction form. To convert a decimal to a fraction, place the decimal number over its place value . For example, in 0.6, the six is in the tenths place, so we place 6 over 10 to create the equivalent fraction, 6/10. If needed, simplify the fraction.

How to change a fraction into a decimal?

How do you convert a fraction to a decimal? To convert a fraction to a decimal, divide the numerator by the denominator . If the fraction is a mixed number, be sure to convert it to an improper fraction first.

How do you convert fractions to decimals without a calculator?

How can you convert a fraction to a decimal without a calculator? The solution is using long division . For example, if you wanted to convert the fraction 7/8 to a decimal without using a calculator, you would have to use long division where the dividend is 7 and the divisor is 8.

How to turn decimals into fractions on iPhone calculator?

Launch the calculator application on your iPhone. Rotate your iPhone into landscape mode and notice there are additional functions available on the left side of the screen. Enter a number you wish to make into a fraction, which will be the denominator and press the 1/x button. More items...

What is an example of a decimal fraction?

The fractions in which the denominator is equal to 10 or multiples of 10 (such as 100, 1000, 1000, 10000, etc.), are known as decimal fractions. Examples: 1/10 = 0.1 . 2/100 = 0.02 .

How to convert decimal into fraction?

Steps for Conversion: Step 1- Identify the place value of the digits after the decimal, in the number. Step 2- Use that to determine what the denominator of the fraction would be. Step 3- Remove the decimal point. Re-write in the fraction form and simplify it. Step 4- Express in terms of the lowest Equivalent fraction.

How do you convert a decimal to a fraction of an inch?

If you want to convert a decimal to a fraction of an inch, first decide what fraction you want to use - the nearest sixteenth of an inch, nearest eighth of an inch, etc. Then, multiply the decimal by the fraction you desire and round off the answer to the nearest whole number . Use the answer as the top of the fraction.

How do you turn 0.33333 into a fraction?

Answer: 0.33333 as a fraction is 1/3 .

What is 0.5 as a fraction?

Answer: 0.5 as a fraction is written as 1/2 .

Decimal to Fraction Calculator (2024)

Calculator Use

This calculator converts a decimal number to a fraction or a decimal number to a mixed number. For repeating decimals enter how many decimal places in your decimal number repeat.

Entering Repeating Decimals

For a repeating decimal such as 0.66666... where the 6 repeats forever, enter 0.6 and since the 6 is the only one trailing decimal place that repeats, enter 1 for decimal places to repeat. The answer is 2/3
For a repeating decimal such as 0.363636... where the 36 repeats forever, enter 0.36 and since the 36 are the only two trailing decimal places that repeat, enter 2 for decimal places to repeat. The answer is 4/11
For a repeating decimal such as 1.8333... where the 3 repeats forever, enter 1.83 and since the 3 is the only one trailing decimal place that repeats, enter 1 for decimal places to repeat. The answer is 1 5/6
For the repeating decimal 0.857142857142857142..... where the 857142 repeats forever, enter 0.857142 and since the 857142 are the 6 trailing decimal places that repeat, enter 6 for decimal places to repeat. The answer is 6/7

How to Convert a Negative Decimal to a Fraction

Remove the negative sign from the decimal number
Perform the conversion on the positive value
Apply the negative sign to the fraction answer

If a = b then it is true that -a = -b.

How to Convert a Decimal to a Fraction

Step 1: Make a fraction with the decimal number as the numerator (top number) and a 1 as the denominator (bottom number).
Step 2: Remove the decimal places by multiplication. First, count how many places are to the right of the decimal. Next, given that you have x decimal places, multiply numerator and denominator by 10^x.
Step 3: Reduce the fraction. Find the Greatest Common Factor (GCF) of the numerator and denominator and divide both numerator and denominator by the GCF.
Step 4: Simplify the remaining fraction to a mixed number fraction if possible.

Example: Convert 2.625 to a fraction

1. Rewrite the decimal number number as a fraction (over 1)

\( 2.625 = \dfrac{2.625}{1} \)

2. Multiply numerator and denominator by by 10³ = 1000 to eliminate 3 decimal places

\( \dfrac{2.625}{1}\times \dfrac{1000}{1000}= \dfrac{2625}{1000} \)

3. Find the Greatest Common Factor (GCF) of 2625 and 1000 and reduce the fraction, dividing both numerator and denominator by GCF = 125

\( \dfrac{2625 \div 125}{1000 \div 125}= \dfrac{21}{8} \)

4. Simplify the improper fraction

\( = 2 \dfrac{5}{8} \)

Therefore,

\( 2.625 = 2 \dfrac{5}{8} \)

Decimal to Fraction

For another example, convert 0.625 to a fraction.
Multiply 0.625/1 by 1000/1000 to get 625/1000.
Reducing we get 5/8.

Convert a Repeating Decimal to a Fraction

Create an equation such that x equals the decimal number.
Count the number of decimal places, y. Create a second equation multiplying both sides of the first equation by 10^y.
Subtract the second equation from the first equation.
Solve for x
Reduce the fraction.

Example: Convert repeating decimal 2.666 to a fraction

1. Create an equation such that x equals the decimal number
Equation 1:

\( x = 2.\overline{666} \)

2. Count the number of decimal places, y. There are 3 digits in the repeating decimal group, so y = 3. Ceate a second equation by multiplying both sides of the first equation by 10³ = 1000
Equation 2:

\( 1000 x = 2666.\overline{666} \)

3. Subtract equation (1) from equation (2)

\( \eqalign{1000 x &= &\hfill2666.666...\cr x &= &\hfill2.666...\cr \hline 999x &= &2664\cr} \)

We get

\( 999 x = 2664 \)

4. Solve for x

\( x = \dfrac{2664}{999} \)

5. Reduce the fraction. Find the Greatest Common Factor (GCF) of 2664 and 999 and reduce the fraction, dividing both numerator and denominator by GCF = 333

\( \dfrac{2664 \div 333}{999 \div 333}= \dfrac{8}{3} \)

Simplify the improper fraction

\( = 2 \dfrac{2}{3} \)

Therefore,

\( 2.\overline{666} = 2 \dfrac{2}{3} \)

Repeating Decimal to Fraction

For another example, convert repeating decimal 0.333 to a fraction.
Create the first equation with x equal to the repeating decimal number:
x = 0.333
There are 3 repeating decimals. Create the second equation by multiplying both sides of (1) by 10³ = 1000:
1000X = 333.333 (2)
Subtract equation (1) from (2) to get 999x = 333 and solve for x
x = 333/999
Reducing the fraction we get x = 1/3
Answer: x = 0.333 = 1/3

Related Calculators

To convert a fraction to a decimal see the Fraction to Decimal Calculator.

References

Wikipedia contributors. "Repeating Decimal," Wikipedia, The Free Encyclopedia. Last visited 18 July, 2016.