Number, Year 8: significant figures and order of operations

0.0041

HintThe counting starts at the first non-zero digit.

The whyThe 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

HintKeep zeros as placeholders so the size is not lost.

The whyThe 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

HintThe zeros at the front only fix the place value.

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

4.00

HintRounding up a 9 carries into the next column.

The whyThe 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

HintThe calculator follows the order of operations.

The whyIt 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

HintWithout them the calculator obeys its own priority order.

The whyTyped 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

HintRound each number to one significant figure and multiply.

The why20 × 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

HintLook closely at the very last digit shown.

The why2 ÷ 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

HintPowers come before multiplying, and multiplying before adding.

The why3² = 9, then 9 × 4 = 36, then 2 + 36 = 38.

25

HintThe bracket is done before the power.

The why2 + 3 = 5 and 5² = 25. The bracket makes the square apply to the whole sum.

24

HintStart with the innermost bracket.

The why4 − 1 = 3, then 3² = 9, then 3 + 9 = 12, and finally 2 × 12 = 24.

2

HintSquare first, then multiply, and subtract last.

The why3² = 9, then 2 × 9 = 18, then 20 − 18 = 2.