6.2.3. Converting Decimals to Fractions
Both decimals and fractions are used to denote parts of a whole. Thus, every decimal has a fractional equivalent. Hence, one can be converted to the other.
To convert terminating decimal to fraction, we do the following steps:
1) Move the decimal point to the right of the last digit.
2) Write the resulting number as a numerator of an equivalent fraction.
3) The denominator is a power of 10 and takes the form 10^n where n is number of places the decimal point was moved.
4) Reduce the resulting fraction.
Example
Convert each terminating decimal to fraction.
1) 0.35
2) 1.3
3.) 0.0002
Solutions
1) 0.35
Since there are two digits after the decimal point, we move the decimal point two places to the right.
Write this as a numerator of the equivalent fraction.
35
?
Since we moved the decimal point two places to the right, the denominator must be 10^2 or 100.
Thus, the fraction equivalent to 0.35 is 35/100. By simplification, that is, dividing both the numerator and denominator by 5, the
final answer is 7/20.
Therefore, 0.35 = 7/20.
2) 1.3
Move one decimal point to the right. So 1.3 becomes 13.
13
?
Since we only moved one decimal place to the right, so we divide 13 by 10^1 or simply 10.
Therefore, 1.3 = 13/10.
3.) 0.0002
Move the decimal point 4 places to the right. The numerator of the equivalent fraction is 2.
2
?
Since we moved 4 decimal places to the right, we then divide 2 by 10^4 or 10000.
Therefore, 0.0002 = 2 / 10000 or 1 / 5000.
To convert terminating decimal to fraction, we do the following steps:
1) Move the decimal point to the right of the last digit.
2) Write the resulting number as a numerator of an equivalent fraction.
3) The denominator is a power of 10 and takes the form 10^n where n is number of places the decimal point was moved.
4) Reduce the resulting fraction.
Example
Convert each terminating decimal to fraction.
1) 0.35
2) 1.3
3.) 0.0002
Solutions
1) 0.35
Since there are two digits after the decimal point, we move the decimal point two places to the right.
Write this as a numerator of the equivalent fraction.
35
?
Since we moved the decimal point two places to the right, the denominator must be 10^2 or 100.
Thus, the fraction equivalent to 0.35 is 35/100. By simplification, that is, dividing both the numerator and denominator by 5, the
final answer is 7/20.
Therefore, 0.35 = 7/20.
2) 1.3
Move one decimal point to the right. So 1.3 becomes 13.
13
?
Since we only moved one decimal place to the right, so we divide 13 by 10^1 or simply 10.
Therefore, 1.3 = 13/10.
3.) 0.0002
Move the decimal point 4 places to the right. The numerator of the equivalent fraction is 2.
2
?
Since we moved 4 decimal places to the right, we then divide 2 by 10^4 or 10000.
Therefore, 0.0002 = 2 / 10000 or 1 / 5000.
