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# Converting Fractions to Decimals

To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number) using long division or a calculator.

• Converting Fractions to Decimals
• Formula
• Solved Examples
• FAQs

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## Converting Fractions to Decimals

To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number) using long division or a calculator.

Here’s an example: Convert 3/4 to a decimal.

Solution:

Divide 3 by 4: 0 .75

____

4 | 3.00

– 0

3

The quotient is 0.75, so 3/4 is equal to 0.75 as a decimal.

Another example:

Convert 5/8 to a decimal.

Solution:

Divide 5 by 8:

0 .625

_____

8 | 5.000

– 4.0

—-

1.00

– .8

20

The quotient is 0.625, so 5/8 is equal to 0.625 as a decimal.

Note that sometimes the division will result in a repeating decimal, such as when converting 1/3 to a decimal (which is 0.3333…). In these cases, it may be necessary to round the decimal to a certain number of decimal places, depending on the desired level of precision.

## Formula The formula to convert a fraction to a decimal is:

Decimal = Numerator / Denominator

For example, if you want to convert the fraction 3/4 to a decimal, you would divide 3 by 4:

Decimal = 3 / 4 = 0.75

If the fraction has a repeating decimal, you can use the following formula to represent it:

Fraction = Whole number + (Repeating decimal / (10^n – 1))

For example, the fraction 1/3 can be represented as:

1/3 = 0.3333… = 0 + (0.3 / (10^1 – 1))

Where the repeating decimal 0.3 is divided by 10^1 – 1 = 9 to get 0.3/9 = 0.03. So, 1/3 can be represented as:

1/3 = 0.3(Repeating) = 0 + 0.03/9

Note that this formula works only for repeating decimals that have one digit repeating. For more complicated repeating decimals, other methods may be necessary.

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## Solved Examples

Sure! Here are some examples of converting fractions to decimals:

Example 1: Convert 2/5 to a decimal

To convert 2/5 to a decimal, divide the numerator (2) by the denominator (5):

2 ÷ 5 = 0.4

Therefore, 2/5 is equal to 0.4 as a decimal.

Example 2: Convert 3/8 to a decimal

To convert 3/8 to a decimal, divide the numerator (3) by the denominator (8):

3 ÷ 8 = 0.375

Therefore, 3/8 is equal to 0.375 as a decimal.

Example 3: Convert 7/12 to a decimal

To convert 7/12 to a decimal, divide the numerator (7) by the denominator (12):

7 ÷ 12 = 0.5833…

Since the decimal repeats, we can either round to a certain number of decimal places or use the formula for a repeating decimal. Let’s round to two decimal places:

7/12 = 0.58 (rounded to two decimal places)

Example 4: Convert 5/6 to a decimal

To convert 5/6 to a decimal, divide the numerator (5) by the denominator (6):

5 ÷ 6 = 0.8333…

Since the decimal repeats, we can use the formula for a repeating decimal:

5/6 = 0.83(Repeating) = 0 + 0.03/9

Therefore, 5/6 is equal to 0.83(Repeating) or 0.8333…

## Converting Fractions to Decimals FAQS

##### What does it mean to convert a fraction to a decimal?

Converting a fraction to a decimal means expressing a fraction as a decimal number, typically with a decimal point and decimal places.

##### How do I convert a fraction to a decimal?

To convert a fraction to a decimal, divide the numerator (the top number) of the fraction by the denominator (the bottom number).

##### Can all fractions be converted to decimals?

Yes, all fractions can be converted to decimals. However, the resulting decimal may be a terminating decimal (a decimal with a finite number of digits) or a repeating decimal (a decimal with a recurring pattern of digits).

##### What is a terminating decimal?

A terminating decimal is a decimal that ends after a finite number of digits. For example, 0.5, 0.75, and 0.125 are examples of terminating decimals.

##### What is a repeating decimal?

A repeating decimal is a decimal that has a repeating pattern of digits. The repeating pattern is indicated by placing a line or bar over the repeating digits. For example, 0.333… and 0.714285714285… are examples of repeating decimals. Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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