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.

Table of Contents:

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

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.

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

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• Fractions to Decimals (New)
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