Every card in Number, Year 8: significant figures and order of operations
The whole deck, in order — so you can read it through before your child ever sees it.
← Back to Number, Year 8: significant figures and order of operations
- Round 0.004062 to 2 significant figures.
0.0041
HintThe counting starts at the first non-zero digit.
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.
- Round 45,278 to 1 significant figure.
50,000
HintKeep zeros as placeholders so the size is not lost.
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.
- How many significant figures does 0.0305 have? (number only)
3
HintThe zeros at the front only fix the place value.
WhyThe significant figures are 3, 0 and 5. A zero between non-zero digits counts; the zeros before the 3 do not.
- Round 3.996 to 3 significant figures.
4.00
HintRounding up a 9 carries into the next column.
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.
- You type 3 + 5 × 2 into a scientific calculator. What answer does it show?
13
HintThe calculator follows the order of operations.
WhyIt multiplies first: 5 × 2 = 10, then adds 3. A scientific calculator does not simply work from left to right.
- You want to work out (3 + 5) ÷ (2 × 4) by typing it on one line with the ÷ key. What must you include?
Brackets round the top and round the bottom
HintWithout them the calculator obeys its own priority order.
WhyTyped without brackets, the calculator works out 3 + (5 ÷ 2) × 4 = 13. With them the answer is 8 ÷ 8 = 1.
- A calculator shows 49.8 for 19.6 × 31.2. Use an estimate to decide whether the display is believable.
No — the estimate is about 600
HintRound each number to one significant figure and multiply.
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.
- A calculator display shows 0.6666666667 for 2 ÷ 3. Is the answer exactly this decimal?
No — the display has rounded a recurring decimal
HintLook closely at the very last digit shown.
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.
- Work out 2 + 3² × 4.
38
HintPowers come before multiplying, and multiplying before adding.
Why3² = 9, then 9 × 4 = 36, then 2 + 36 = 38.
- Work out (2 + 3)².
25
HintThe bracket is done before the power.
Why2 + 3 = 5 and 5² = 25. The bracket makes the square apply to the whole sum.
- Work out 2 × (3 + (4 − 1)²).
24
HintStart with the innermost bracket.
Why4 − 1 = 3, then 3² = 9, then 3 + 9 = 12, and finally 2 × 12 = 24.
- Work out 20 − 2 × 3².
2
HintSquare first, then multiply, and subtract last.
Why3² = 9, then 2 × 9 = 18, then 20 − 18 = 2.
1★ KS3-MATH-NUM-0044
2★ KS3-MATH-NUM-0045
3★ KS3-MATH-NUM-0046
4★ KS3-MATH-NUM-0047
5★ KS3-MATH-NUM-0048
6★ KS3-MATH-NUM-0049
7★ KS3-MATH-NUM-0050
8★ KS3-MATH-NUM-0051
9★ KS3-MATH-NUM-0052
10★ KS3-MATH-NUM-0053
11★ KS3-MATH-NUM-0054
12★ KS3-MATH-NUM-0055
Keep what you learn
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