Number, Year 8: significant figures and order of operations

0.0041

提示The counting starts at the first non-zero digit.

为什么The first two significant figures are 4 and 0. The next digit is 6, so the 0 rounds up to 1. The zeros at the front stay as placeholders.

50,000

提示Keep zeros as placeholders so the size is not lost.

为什么The first significant figure is 4 and the next digit is 5, so it rounds up to 5. Four zeros keep the number in the tens of thousands.

3

提示The zeros at the front only fix the place value.

为什么The significant figures are 3, 0 and 5. A zero between non-zero digits counts; the zeros before the 3 do not.

4.00

提示Rounding up a 9 carries into the next column.

为什么The third figure, 9, rounds up because the next digit is 6. That makes 10, which carries twice. The two zeros are kept to show three significant figures.

13

提示The calculator follows the order of operations.

为什么It multiplies first: 5 × 2 = 10, then adds 3. A scientific calculator does not simply work from left to right.

Brackets round the top and round the bottom

提示Without them the calculator obeys its own priority order.

为什么Typed without brackets, the calculator works out 3 + (5 ÷ 2) × 4 = 13. With them the answer is 8 ÷ 8 = 1.

No — the estimate is about 600

提示Round each number to one significant figure and multiply.

为什么20 × 30 = 600, so an answer near 50 must be a keying error, such as pressing + in place of ×. The true answer is 611.52.

No — the display has rounded a recurring decimal

提示Look closely at the very last digit shown.

为什么2 ÷ 3 is 0.666… for ever. The calculator can show only so many digits, so it rounds the last one up to 7. Entering 2/3 as a fraction keeps the exact value.

38

提示Powers come before multiplying, and multiplying before adding.

为什么3² = 9, then 9 × 4 = 36, then 2 + 36 = 38.

25

提示The bracket is done before the power.

为什么2 + 3 = 5 and 5² = 25. The bracket makes the square apply to the whole sum.

24

提示Start with the innermost bracket.

为什么4 − 1 = 3, then 3² = 9, then 3 + 9 = 12, and finally 2 × 12 = 24.

2

提示Square first, then multiply, and subtract last.

为什么3² = 9, then 2 × 9 = 18, then 20 − 18 = 2.