1. Decimal places and significant figures
Learning Objective:
Can I round a decimal to a given number of decimal places or significant figures?
Grade E

2. What does this mean?
We can round numbers to a certain number of decimal places and significant figures. Decimal places refer to how many digits we want after the decimal point. Significant figures refer to how many digits aren’t zero and not sandwiched between non-zeroes.

3. Decimal places
Remember that the decimal point does not move! The number needs to be “cut off” at the given number of decimal places. We then round up or down, depending on what the following number is.

4. Decimal places example:
Round to 1 decimal place. Up until the first decimal place, everything stays the same, so we can write everything up to that point. We may need to round the number in the first decimal place though. The following number is “over halfway” so we round up. 8 8 3 3 . . 7 7 6 6 4 9
Answer: 8 3 . 8

5. Another decimal places example:
Round to 2 decimal places. Up until the second decimal place, everything stays the same, so we can write everything up to that point. We may need to round the number in the second decimal place though. The following number is “under halfway” so we round down. 8 8 3 3 . . 7 7 6 6 4 4 9
Answer: 8 3 . 7 6

6. Round these numbers to the given number of decimal places
2.365 [1 dp]
6.739 [1 dp]
[2 dp]
[1 dp]
2.4
6.7
13.73
10.0

7. All numbers have significant figures. 7 6 0 2 3 . 9 8
1st significant figure
6th significant figure

8. Significant figures – careful with decimals
Decimals are slightly different
1st significant figure
5th significant figure
These zeroes aren’t significant
This zero is significant

9. Rounding to significant figures
Round 4534 to 2 sf The 5 is the 2nd significant figure, so anything before that stays the same. The 3rd significant figure is less than 5 so we round down. Fill up to the decimal point with zeroes.
2nd significant figure
Answer: 4500

10. Rounding to significant figures 2
Round to 1 sf The 5 is the 1st significant figure, so anything before that stays the same. The 2nd significant figure is more than 5 so we round up.
1st significant figure
Answer: 0.006

11. Have a go at rounding these:
7238 [1 sf]
[2 sf]
[1 sf]
[3 sf]
7000
930000
0.04