Decimals · Usually met around P4
Decimal place value
0.1s, 0.01s, 0.001s: compare place by place.
How to do it
Method
0.1s, 0.01s, 0.001s: compare place by place
3.472 = 3 + 0.4 + 0.07 + 0.002
Another way
A place-value table
0.7 = 0.70, tenths 7 > 6, so 0.7 > 0.65
In full
The decimal point splits a decimal into its whole part and its decimal part. The first place after the point is the tenths, the second is the hundredths and the third is the thousandths. In 3.472, the 4 is in the tenths, worth 4 × 0.1 = 0.4. The 7 is in the hundredths, worth 7 × 0.01 = 0.07. The 2 is in the thousandths, worth 0.002. So 3.472 = 3 + 0.4 + 0.07 + 0.002. To compare decimals, compare the whole parts first, then go place by place from the tenths. Don't go by which one has more digits. 0.7 and 0.65: in the tenths, 7 beats 6, so 0.7 is bigger. Or add zeros at the end so both have the same number of places: 0.70 and 0.65, 70 > 65. Adding or removing zeros at the end of a decimal doesn't change its value. A place-value table also compares place by place.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
In 0.156, the 5 is worth ?
Show the answer and working
Answer: In 0.156, the 5 is worth 0.05
In 0.156 the 5 is in the hundredths, worth 5 × 0.01: 5 × 0.01 = 0.05
Example 2
6 × 0.1 and 7 × 0.01 = ?
Show the answer and working
Answer: 6 × 0.1 and 7 × 0.01 = 0.67
Write each place, 0 where there's none: ones 0, tenths 6, hundredths 7, thousandths 0; 0.6 + 0.07 = 0.67
Example 3
7.727: thousandths digit = ?
Show the answer and working
Answer: 7.727: thousandths digit = 7
7.727: after the point come the tenths, then the hundredths, then the thousandths; the thousandths hold 7 × 0.001: 7 × 0.001 = 0.007, so the digit is 7
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