Changing Decimals to Fractions

Changing Decimals to Fractions

I have written a post on changing fractions to decimals, here comes the vice versa (from decimal back to fraction).

When changing from decimals to fractions, 

•  put all the digits in the number you want to change to the numerator(top). When I say all digits, if zero is written in front, you don`t need to write it with the other number in the numerator, it`s just a terminating zero).

•  And put 1 to start the number in the denominator(bottom) follow by zero(s) as the count of digit(s) after the decimal point.

Example 1.  

Because of the only digit, before the decimal point is 2 (one-digit) after writing the two at the top, then 1 followed by only one zero at the bottom of the fraction bar.




Example 2. 

342 is written in the numerator without writing the zero in front of it, and 1 follows by three zeros in the denominator.




Example 3. 

342 is also put in the numerator, even there is a decimal point between the 3 and 4 (3.42), followed by 1 and two zeros because 42 which is after the decimal point is a two-digit number.



Example 5.

720 is written and place in the numerator and 1 follow by the three zeros which are written in the denominator.





NOTE: When zeros are in front of a decimal or in front of an integer number, it is leading zero, it must be removed to give a proper answer, but if it is present in the middle of numbers (2.805) or at the end (3.220) you can`t remove it. Keep this in your mind.

Example 6.

0.3636363636..., this type of decimal number is called a repeating decimal (because it has a repeating pattern) eg. 2.781781781781, 0.21212121.




NOTE: To change a repeating decimal to fraction,

• write the repeating digits in the numerator.
• In the denominator write as many nines as the digit(s) of the repeating digits.
• reduce the fraction if necessary.