Dividing decimals; fractions to decimals · Usually met around P6
Comparing fractions as decimals
Top ÷ bottom, then compare the decimals.
How to do it
Method
Top ÷ bottom, then compare the decimals
38 = 0.375 < 0.4
Another way
Same denominator
38 = 1540, 0.4 = 1640
In full
Turn each fraction into a decimal (top ÷ bottom), then compare place by place from the biggest place: 38 = 3 ÷ 8 = 0.375; against 0.4, the tenths are 3 and 4, so 38 < 0.4. With fractions and decimals mixed together, this is the handiest way. Don't look only at the tops or only at the bottoms: 58 has a bigger top than 35, but 58 = 0.625 and 35 = 0.6, so 58 is bigger. Another way: turn the decimal into a fraction and give both the same denominator: 0.4 = 25 = 1640 and 38 = 1540, and 15 < 16. Or use 0.5 (a half) as a marker: 38 is less than a half, 58 more.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
625 is bigger than 0.22.
True or false?
Show the answer and working
Answer: True
625 = 6 ÷ 25 = 0.24; then compare it with 0.22 place by place.
Example 2
As a decimal, how much bigger is 625 than 0.1?
Show the answer and working
Answer: 0.14
625 = 0.24, and 0.24 − 0.1 = 0.14.
Example 3
0.26 < □/4 < 0.74. Which whole number is □?
Show the answer and working
Answer: 2
Try each □/4 as a decimal: only 24 is between 0.26 and 0.74.
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