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Secondary 3 Mathematics · Scientific notation and significant figures

Name: ______________________

Date: ____________

1. Write 52 000 in scientific notation.
- ☐ (a) 52 × 10³
- ☐ (b) 5.2 × 10⁴
- ☐ (c) 5.2 × 10³
- ☐ (d) 0.52 × 10⁵
2. Write 0.0009 in scientific notation.
- ☐ (a) 9 × 10⁻⁴
- ☐ (b) 9 × 10⁴
- ☐ (c) 9 × 10⁻³
- ☐ (d) 0.9 × 10⁻³
3. Write 6.1 × 10⁻² as an ordinary number.
- ☐ (a) 0.61
- ☐ (b) 0.061
- ☐ (c) 0.0061
- ☐ (d) 610
4. Round 3.14159 to 3 significant figures.
- ☐ (a) 3.14
- ☐ (b) 3.142
- ☐ (c) 3.1
- ☐ (d) 3.15
5. Write 7.25 × 10³ as an ordinary number.
6. Write 640 000 in scientific notation.
7. Round 0.006 382 to 2 significant figures.
8. How many significant figures does 0.04050 have?

Answer sheet

1. 5.2 × 10⁴ — The first part must be from 1 to less than 10, so use 5.2. The point moves 4 places: 5.2 × 10⁴. (52 × 10³ and 0.52 × 10⁵ have the right value but are not in scientific notation.)
2. 9 × 10⁻⁴ — The point moves 4 places to the right to give 9, so the index is −4.
3. 0.061 — A negative index of −2 means move the point 2 places left: 0.061.
4. 3.14 — The first three significant figures are 3, 1 and 4. The next digit is 1, so round down: 3.14.
5. 7250 — Move the point 3 places right: 7.25 → 7250.
6. 6.4 × 10⁵ — Put the point after the 6 to get 6.4. The point moves 5 places, so 6.4 × 10⁵.
7. 0.0064 — The first two significant figures are 6 and 3. The next digit is 8, so round up to 64: 0.0064.
8. 4 — Start at the first non-zero digit (4). The digits 4, 0, 5 and the final 0 are all significant: 4 significant figures.