Numbers and operations · Ages 13–14
Zero and negative indices worksheet
Part of: Laws of integral indices
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Zero and negative indices worksheet
Numbers and operations · Ages 13–14
Numsprite
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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.
Part A: Working out and filling in (2 marks each)
1.As a fraction: 4−1 =
Answer in simplest form
Answer:
2.880 × 12 =
Answer:
3.(13)−4 =
Answer:
4.As a decimal: 10−1 =
Answer:
5.As a fraction: (38)−3 =
Answer in simplest form
Answer:
6.3−2 = 1 ÷ 3□ = 1
Fill in each blank
Answer:
7.As a decimal: 10−4 =
Answer:
8.As a fraction: 70 + 7−1 + 7−2 =
Answer in simplest form
Answer:
9.As a fraction: 90 + 9−1 + 9−2 =
Answer in simplest form
Answer:
Part B: Choose, or true or false (2 marks each)
10.3−3 = 19
True or false?
Answer:
11.3−3 = ?
- A. −9
- B. −27
- C. 127
- D. 19
Choose the right answer
Answer:
12.(−8)−2 = ?
- A. 64
- B. −164
- C. 164
- D. −64
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.1 micrometre is 10−6 m and 1 millimetre is 10−3 m. How many millimetres is 579 micrometres?
Working:
Answer:
14.A kind of bacterium splits once an hour, doubling the number. There are 16 now. How many were there 2 hours ago?
Working:
Answer:
15.The amount of a medicine in the blood halves every hour. It starts at 224 mg, and after t hours 224 × 2−t mg is left. If 28 mg is left, what is t?
Working:
Answer:
16.What is 18 as a power of 2?
- A. 2−4
- B. −23
- C. 23
- D. 2−3
Choose the right answer
Working:
Answer:
17.Ka-yee says (49)−3 is less than 1. Ka-yee is right.
True or false?
Working:
Answer:
18.Work out (29)−3. Put the steps in order.
- A. 1 ÷ (29)3 = 1 ÷ 8729
- B. 1 ÷ 8729 = 7298
- C. (29)−3 = 1 ÷ (29)3
Write the letters in the right order
Working:
Answer:
Show the answers and working
Zero and negative indices worksheet: Answers and working
Part A: Working out and filling in
1. 14
4−1 = 141 = 14. A negative index isn't a negative number.
2. 12
Any number but 0 to the power 0 is 1: 880 = 1, and 1 × 12 = 12.
3. 81
A fraction to a negative index: turn it over first. (13)−4 = 34 = 81.
4. 0.1
10−1 = 1101 = 110 = 0.1.
5. 51227
Turn the fraction over first: (38)−3 = (83)3 = 51227.
6. 2, 9
a−n = 1 ÷ an: 3−2 = 1 ÷ 32 = 19.
7. 0.0001
10−4 = 1104 = 110000 = 0.0001.
8. 5749
70 = 1, 7−1 = 17, 7−2 = 149; over 49: 4949 + 749 + 149 = 5749.
9. 9181
90 = 1, 9−1 = 19, 9−2 = 181; over 81: 8181 + 981 + 181 = 9181.
Part B: Choose, or true or false
10. False
3−3 = 133, and 33 is 3 lots of 3 multiplied, 27, not 3 × 3.
11. C. 127
3−3 = 133 = 127.
12. C. 164
(−8)−2 = 1(−8)2 = 164.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 0.579 mm
1 micrometre = 10−6 ÷ 10−3 = 10−3 mm, so 579 micrometres = 579 × 10−3 = 0.579 mm.
14. 4 bacteria
Each hour back divides by 2: 16 × 2−2 = 16 ÷ 22 = 4.
15. 3 hours
224 × 2−t = 28, so 2t = 224 ÷ 28 = 23 and t = 3.
16. D. 2−3
8 = 23, so 18 = 123 = 2−3.
17. False
(49)−3 = (94)3: when 94 is under 1 its powers are too; over 1, they are over 1.
18. C → A → B
a−n = 1 ÷ an; a fraction's power raises top and bottom; dividing by a fraction multiplies by its reciprocal: 7298.
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