Stage 8 · Fractions & decimals
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 the hundredths, the third the thousandths. 3.472: the 4 is in the tenths, worth 4 × 0.1 = 0.4; the 7 in the hundredths, worth 7 × 0.01 = 0.07; the 2 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 place by place from the tenths — not by which has more digits. 0.7 and 0.65: tenths 7 beats 6, so 0.7 is bigger. Or add zeros at the end so both have the same 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 compares place by place too — the same idea.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
In 5.351, the 3 is worth ?
Show the answer and working
Answer: In 5.351, the 3 is worth 0.3
In 5.351 the 3 is in the tenths, worth 3 × 0.1: 3 × 0.1 = 0.3
Example 2
3 × 0.1 and 7 × 0.01 = ?
Show the answer and working
Answer: 3 × 0.1 and 7 × 0.01 = 0.37
Write each place, 0 where there's none: ones 0, tenths 3, hundredths 7, thousandths 0; 0.3 + 0.07 = 0.37
Example 3
1.094: thousandths digit = ?
Show the answer and working
Answer: 1.094: thousandths digit = 4
1.094: after the point come the tenths, then the hundredths, then the thousandths; the thousandths hold 4 × 0.001: 4 × 0.001 = 0.004, so the digit is 4
Example 4
Max of 3.56, 3.416, 3.504 = ?
Show the answer and working
Answer: Max of 3.56, 3.416, 3.504 = 3.56
Add zeros so all have three places: 3.560, 3.416, 3.504, the same as all × 1000: 3.56 × 1000 = 3560, 3.416 × 1000 = 3416, 3.504 × 1000 = 3504; the biggest is 3.56
Practise decimal place value in the game →Stage 8 · Fractions & decimals · Free to start, unlimited questions, no download