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

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.

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.

Decimal places example: Round 83.7649 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

Another decimal places example: Round 83.7649 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

Round these numbers to the given number of decimal places 2.365 [1 dp] 6.739 [1 dp] 13.7328 [2 dp] 9.9999 [1 dp] 2.4 6.7 13.73 10.0

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

Significant figures – careful with decimals Decimals are slightly different. 0 . 0 0 2 3 7 0 8 1st significant figure 5th significant figure These zeroes aren’t significant This zero is significant

Rounding to significant figures Round 4534 to 2 sf. 4 5 3 7 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

Rounding to significant figures 2 Round 0.00576 to 1 sf. 0 . 0 0 5 7 6 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

Have a go at rounding these: 7238 [1 sf] 926706 [2 sf] 0.0435 [1 sf] 0.00076498 [3 sf] 7000 930000 0.04 0.000765