Numbers and operations · Ages 13–14

Scientific notation worksheet

Part of: Laws of integral indices

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Numbers and operations · Ages 13–14

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Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

1.As an ordinary number: 1.1 × 10² =
Answer:
2.In scientific notation: 0.00066 = × 10^−
Fill in each blank
Answer:
3.In scientific notation: 31,000 = × 10^□
Fill in each blank
Answer:
4.In scientific notation: 2500 = × 10^□
Fill in each blank
Answer:
5.In scientific notation: (2 × 10⁸) × (4 × 10³) = × 10^□
Fill in each blank
Answer:
6.As a decimal: 5.6 × 10⁻² =
Answer:
7.In scientific notation: (2 × 10⁻¹) ÷ (4 × 10⁻⁴) = × 10^□
Fill in each blank
Answer:
8.7 × 10⁸ + 1 × 10⁷ = × 10⁸
Answer:

13.Here are the sizes of four kinds of cell, in metres. Which is the smallest?
- A. 1.5 × 10⁻⁶
- B. 8.4 × 10⁻⁴
- C. 6.7 × 10⁻⁶
- D. 6.1 × 10⁻⁵
Choose the right answer
Working:
Answer:
14.Put these numbers in order, smallest first.
- A. 4.6 × 10⁵
- B. 9.2 × 10⁴
- C. 6.7 × 10⁶
- D. 1.2 × 10⁴
Write the letters in the right order
Working:
Answer:
15.A city has about 8,200,000 people. In scientific notation that is × 10^□ people.
Fill in each blank
Working:
Answer:
16.Ka-lok writes 460,000 in scientific notation as 4.6 × 10⁵. Ka-lok is right.
True or false?
Working:
Answer:
17.A computer does 2 × 10⁹ operations a second. How many seconds does it take for 8 × 10¹² operations?
Working:
Answer:
18.Light travels about 3 × 10⁵ km a second. In 9 × 10³ seconds it travels about × 10^□ km.
Fill in each blank
Working:
Answer:

Show the answers and working

Scientific notation worksheet: Answers and working

1. 110
Times 10² moves the point 2 places right: 1.1 → 110.
2. 6.6, 4
Move the point 4 places right to get 6.6; moved right, the index is negative: 6.6 × 10⁻⁴.
3. 3.1, 4
Move the point 4 places left to get 3.1, with 1 ≤ 3.1 < 10: 3.1 × 10⁴.
4. 2.5, 3
Move the point to get 2.5 (1 ≤ 2.5 < 10): moved left, the index is positive; right, negative. So 2.5 × 10³.
5. 8, 11
2 × 4 = 8 and 10⁸ × 10³ = 10^(8 + 3); the front number must be from 1 to under 10, so adjust: 8 × 10¹¹.
6. 0.056
Times 10⁻² is dividing by 10²: the point moves 2 places left, 0.056.
7. 5, 2
2 ÷ 4 = 0.5 and 10⁻¹ ÷ 10⁻⁴ = 10^(−1 − (−4)); the front number must be from 1 to under 10, so adjust: 5 × 10².
8. 7.1
Make the powers of 10 the same first: 1 × 10⁷ = 0.1 × 10⁸; then add, 7 + 0.1 = 7.1.

9. False
Scientific notation a × 10ⁿ needs 1 ≤ a < 10: check whether 0.8 is from 1 up to, but not including, 10.
10. True
Scientific notation a × 10ⁿ needs 1 ≤ a < 10: check whether 7.3 is from 1 up to, but not including, 10.
11. A. 3.4 × 10⁸
The point moves 8 places left to give 3.4: 340,000,000 = 3.4 × 10⁸.
12. A. 2.3 × 10⁹
The bigger index of 10 wins; with equal indices, the bigger front number.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. A. 1.5 × 10⁻⁶
Compare the indices of 10 first: the lowest (most negative) is smallest; with equal indices, the smaller front number.
14. D → B → A → C
Compare the indices of 10 first; with equal indices, the front numbers: 1.2 < 9.2.
15. 8.2, 6
Move the point 6 places left to get 8.2: 8,200,000 = 8.2 × 10⁶.
16. True
4.6 × 10⁵ does equal 460,000, but in scientific notation the front number is from 1 to under 10: 4.6 × 10⁵.
17. 4000 s
Time = (8 × 10¹²) ÷ (2 × 10⁹) = 4 × 10³ = 4,000 s.
18. 2.7, 9
Distance = (3 × 10⁵) × (9 × 10³) = 27 × 10^(5 + 3); the front number must be from 1 to under 10: 2.7 × 10⁹ km.

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