In the introduction to decimals, it was shown that
0.1 = 1/10
i.e. 0.1 equals the proper fraction (numerator less than denominator) 1/10.
1.2 = 1 + 2/10
1.2 = 1 2/10
i.e. 1.2 is equal to the mixed fraction (whole number + fraction) 1 2/10.
156.6 = 156 + 6/10
156.6 = 156 6/10
i.e. 156.6 equals the mixed fraction 156 6/10.
These are straightforward conversions of decimals to fractions.
... it was also shown that
2.13 = 2 + 1/10 + 3/100
While this provides a neat breakdown, the decimal 2.13 can be expressed as a whole number plus a single fraction.
Start by adding fractions 1/10 and 3/100.
Find the least common denominator, the lowest number into which the denominators 10 and 100 will both divide exactly - the answer's 100.
Leave 3/100 alone - its denominator's already 100. Convert 1/10 into an equivalent fraction containing denominator 100 by multiplying numerator and denominator by factor 10
Now you can write
2.13 = 2 + 10/100 + 3/100
Leaving the denominators alone and adding the numerators
2.13 = 2 + 13/100
2.13 = 2 13/100
i.e. 2.13 is equal to the mixed fraction 2 13/100.
Yes! You probably wouldn't have time in an exam to break down a decimal into a whole number plus tenths (1/10s), hundredths (1/100s) and/or thousandths (1/1000s), then convert to a whole number plus single fraction!
However, you may have already noticed ...
Just write down the
whole number (2 in the case of 2.13)
followed by a
- the numerator comprises the digits to the right of the decimal point (13 in 2.13's case)
- the denominator depends on the
least place value - the position occupied by the last digit in the decimal (in the case of 2.13, the last digit 3 occupies the hundredths [1/100s] position, so the denominator's 100)
2.13 = 2 13/100
To the right of the decimal point the
i.e. the decimal 13.089 equals the mixed fraction 13 89/1000.
0.991 = 991/1000
The whole number's zero, meaning you only need write down a single fraction - the numerator comprises the digits to the right of the decimal point 991, the last digit 1 occupies the thousandths (1/1000s) position, so the denominator's 1000. The decimal 0.991 is equal to the proper fraction 991/1000.
2236.47 = 2236 47/100
Write down the whole number 2236, the numerator of the fraction consists of the digits to the right of the decimal point 47, the last digit 7 occupies the hundredths (1/100s) position, making the denominator 100. The decimal 2236.47 equals the mixed fraction 2236 47/1000.
Remember you can also go on to convert any mixed fraction to an improper fraction - for example, 1.2 = 1 2/10 = 1 + 2/10 = 10/10 + 2/10 = 12/10 = 6/5. To learn how to do this click here.
For more on decimals click:
Convert decimal to fraction