Can you explain how you convert decimals to fractions?

Answer 1

The digits after the decimal place represent multiples of negative powers of 10. The first digit is in the tenths column (10-1), the second digit is in the hundredths column (10-2) and so on. We can use this to write the number as an integer divided by the appropriate power of 10.

Example 1.

0.5

There is only one digit here and it is representing 5 * 10-1. This is 5 tenths. We can therefore write this as 5 divided by 10. So as a fraction 0.5 = 5/10. We can simplify (if desired) this to 1/2 by dividing top and bottom by 5.

Example 2.

0.37

There are two digits after the decimal place and so this number is telling us how many hundredths (10-2) there are. Here there are thirty seven hundredths (37 * 10-2) which we can write as 37/100. We can not simplify this fraction any further.

Example 3.

0.1234567

There are 7 digits here and so this is telling us the number is equal to 1234567 ten millionths (1234567 * 10-7). We write this as 1,234,567/10,000,000.

We can therefore use this principle to convert any decimal value to a fraction.