How to Change a Fraction to a Decimal and a Decimal to a Fraction, an Easy Way

There are several situations in which it is not only easier but more convient to work with Fractions instead of Decimals and visa versa. This article will show an easy way of changing a Decimal to a Fraction and a Fraction to a Decimal.

Things You'll Need

• Paper and
• Pencil.

Instructions

1. 

   To change any Decimal to a fraction, write the Decimal Number down, then draw a Horizontal line under the Decimal Number from left to right, begining under the Decimal point and continue until the last digit. Please Click on the Image for a better understanding.

2. 

   Directly under the Decimal point and the horizontal line write the Number One ( 1 ), and to the right of the number 1, write a Zero ( 0 ) for each digit above the line, stopping at the last digit. Please Click on the Image for a better understanding.

3. 

   We now remove the decimal point from the problem and we have the Fraction or Mixed-Fraction depending on the Decimal Number we began with. Remember to reduce the Fraction to lowest terms if possible. In the case of the decimal number being 5.123, then we expect to have a
   Mixed-Fraction, from this decimal number, since there is a whole number in front of the Decimal Point.
   Please Click on the Image for a better understanding.

4. For example to change 0.123 to a Fraction the answer will be 123/1000, this Fraction cannot be reduced to lowest terms. To change 25.124 to a Fraction we will get 25 124/1000, the Fraction part of this Mixed-Number can be reduced to lowest terms, so 25 124/1000 = 25 31/250. Please note, if the last digit of the Decimal number ends in an odd number, 1,3,7,and 9, then the fraction cannot be reduced to lowest terms. If, the last digit of the Decimal Number, ends with a 5, then it can be reduced to lowest terms by dividing the Numerator and Denominator by 5, and if the last digit is an even number, 2,4,6,and 8, then it can be reduced to lowest terms.

5. 

   To change a Fraction to a Decimal we use the Long division algorithm, that is, we divide the Numerator of the Fraction by the Denominator. We now make the Numerator the Dividend and the Denominator the Divisor.
   Please Click on the Image for a better understanding. Also, please read the Article, " How to Divide Decimals ", by this same Author, Z-MATH.