# How to Change a Fraction to a Decimal | Convert Decimals to Fractions

Using conversion techniques, numbers can be represent same information but in different forms, using Fractions, decimals and percentages. See how you can convert amongst these numerical values.

## Fractions and decimals

Converting a fraction to a decimal

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

When you need to convert 3/8 into a decimal, divide 3 by 8.1. Since 8 can't go into 3, you need to add a zero to 3, making it 30. You can do this by adding a decimal point to 3, then including a 0. Include the decimal point the top. 8 goes into 30 3 times, in light of the fact that 8 x 3 = 24. Place the 3 directly after the decimal point. 30 - 24 = 6. Because 8 can't go into 6, you need to add a zero to 6, making it 60. You can do this by including another 0 after 3.0, then conveying the 0 down to directly after the 6.8 goes into 60 7 times, on the grounds that 7 x 8 = 56. Place the 7 directly after the 3.4. 60 - 56 = 4. Since 8 can't go into 4, you need to add a zero to 4, making it 40. You can do this by including another 0 after 3.00, then conveying the 0 down to directly after the 4. 8 goes into 40 5 times, on the grounds that 5 x 8 = 40. Place the 5 directly after the 7.5. 40 - 40 = 0, so there is nothing left over. The answer is 0.375. In this manner, the part 3/8 is equivalent to the decimal 0.375. See converting fraction to decimal example below:

Example To convert 3/8 to a decimal, we calculate 3 ÷ 8

so, 3/8 = 0.375

Some decimals will not simplify (terminate) like the example above, but many will not.

For example 2/7 does not simplify (terminate).

There are some fraction/decimal equivalents that you should be familiar with:

- 1/2 = 0.5

- 1/4 = 0.25

- 3/4 = 0.75

- 1/3 = 0.333333...

## Converting a decimal into a fraction

Converting a terminating decimal to a fraction, the denominator will be 10, or 100, or 1000 or… based on the decimal places.

0.5 means 'five tenths', so 0.5 = 5/10 = 1/2

0.45 means '45 hundredths', so 0.45 = 45/100 = 9/20

0.240 means '240 thousandths', so 0.240 = 240/1000 = 6/25

Later on you will be expected to change recurring decimals to fractions.

Let m = 0.2222222...

Then 10m = 2.222222...

Subtracting these we get

10m – m = 2.2222222...- 0.22222222...

9m = 2, so m = 2/9

0.4444444... = 4/9

0.6666666... = 6/9 = 2/3

If the decimal repeats with two digits,

Let T = 0.24242424...

100T = 24.242424...

Subtracting we have, 99T = 24

T = 24/99

A decimal that cannot be written as a fraction is an irrational number. π is an example of an irrational number. (1) Some divisions can be changed over first to identical parts with a denominator 10, 100, 1000 and so on and afterward from those, into decimals. For instance, 2/5 = 4/10 = 0.4.

(2) But frequently, to change over a part into a decimal, we have to partition the numerator by the denominator, with long division or number cruncher. For instance, to change over 5/7 into a decimal, we basically isolate 5 by 7.

The converting decimals to fractions and converting fractions to decimals is typically studied in 6th grade or 7th grade math.

Here and there, when you partition the numerator by the denominator in long division, the decimal you get closes. All the more regularly however, it is a non-consummation rehashing decimal. We see that when in our long division the same leftovers keep coming up in the same request.

Such decimals rehash a portion of their decimal digits, for example, 0.13131313.... on the other hand 0.83567567567567... 567 repeats

You may inquire as to whether decimals that don't rehash exist. Yes, they do. They are irrational numbers, which means they are NOT fractions; meaning, not rational numbers, and they are truly intriguing subjects in themselves.

Here we discover that you can utilize division to change any fraction into its decimal. The video plainly delineates the 'long division' calculation furthermore instructs the documentation for communicating repeating decimal answers.