Changing fractions to decimals can at times be a little bit trickier than converting decimal numbers to fractions.
Some simple fractions though can be fairly straight-forward, such as \frac{1}{2}.
Changing Fractions to Decimals Steps:
An effective approach for a fraction such as this, is to firstly look at the lower number, the denominator.Trying to establish another number that the denominator can be multiplied by.
In order to give a number starting with a 1, followed by just zero’s, such as 10 or 100.
For \frac{1}{2}, 2 × 5 = 10.
So: \frac{1 \space \times \space 5}{2 \space \times \space 5} = \frac{5}{10}
( Multiplication of top and bottom keeps overall fraction value the same )
We now have a reasonable division sum set out as a fraction that can be solved.
\frac{5}{10} = 0.5
Thus the decimal form of the fraction \frac{1}{2} is 0.5.
Examples
1.1
Convert \frac{54}{100} to a decimal.
Solution
Three zeroes in 100, we just move the decimal point three places left.
\frac{54}{100} = 0.54
1.2
Convert \frac{3}{5} to a decimal.
Solution
\frac{3 \space \times \space 20}{5 \space \times \space 20} = \frac{60}{100} = 0.6
1.3
Convert \frac{22}{40} to a decimal number.
Solution
\frac{22 \space \times \space 25}{40 \space \times \space 25} = \frac{725}{1000} = 0.725
1.4
Convert 5\frac{3}{4} to a decimal number.
Solution
Firstly we look to leave the whole number part 5 to one side, and focus just on the fraction part.
\frac{3 \space \times \space 25}{4 \space \times \space 25} = \frac{75}{100} = 0.75
We can then bring the whole number back, placing in front of the decimal point, to form the complete decimal number.
5\frac{3}{4} = 5.75
Changing Fractions to Decimals,
Further Examples
Another effective approach that can be used when changing fractions to a more specific decimal place is to treat the fraction as a standard division sum.
We can see how to do this in some examples below.
Examples
2.1
Convert the fraction \frac{5}{8} to decimal form.
Solution
Treat it as the sum 5 ÷ 8.
1)
Set up the division sum as usual.
8 5
2)
Next we place a decimal point after the 5, and also above in the same position where the answer will be.
.
8 5.
3)
The next step is to place some zeroes after the decimal point beside the 5.
How many decimals depends on how many decimal places we wish to find.
We’ll look to try 4 zeroes and see what we get.
.
8 5. 0 0 0 0
At this point we treat this sum like we would 50000 ÷ 8.
4)
0. 6 2 5 0
8 5. 0 20 40 0
We see that there is a 0 at the 4th decimal place, and that there would also be just 0‘s from division from then on.
As we’d just be doing 0 divided by 8 again and again.
So the fraction \frac{5}{8} gives a terminating decimal, which ends at 3 decimal places.
\frac{5}{8} is 0.625 in decimal form.
2.2
Convert the fraction \frac{9}{7} to decimal form.
Solution
Not all fractions convert to a decimal number that terminates, or terminates early.
An example of such a fraction is \frac{9}{7}.
1)
.
7 9.
2)
We’ll try initially to obtain a decimal number with 4 decimal places.
But we need an extra 0 below, so that we’ll know whether to round the 4th decimal place up or down.
.
7 9. 0 0 0 0 0
3)
1. 2 8 5 7 1
7 9. 20 60 40 50 10
Ignoring any remainders, the 5th division results in a 1, as 7 goes into 10 once.
So we round down, and the 7 in the 4th decimal place stays as is.
\frac{9}{7} is 0.2857 to 4 decimal places.
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