Negative Exponents & Scientific Notation (Grade 9) — Worksheet & Memo

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Grade 9 · Exponents

Negative Exponents & Scientific Notation (Grade 9)

MARKING GUIDELINE

Marks

Duration

50 minutes

Questions

Name:

Class:

Date:

Mark

/ 31

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
2⁻³ = …
(1)
A)−8
B)√
C)−6
D)18✓
Answer: D — A negative exponent means the RECIPROCAL: 1/2³ = 1/8.
- A — a negative exponent does not make the answer negative
- B — not a number
- C — multiplied 2 by −3
1.2
x⁻² written with a positive exponent is …
(1)
A)−x²
B)1x²✓
C)x²1
D)−2x
Answer: B — Move the power to the denominator and the sign of the exponent changes.
- A — a negative exponent is not a negative number
- C — that is just x²
- D — multiplied instead of taking a reciprocal
1.3
0,000 045 written in scientific notation is …
(1)
A)4,5 × 10⁵
B)4,5 × 10⁻⁵✓
C)45 × 10⁻⁶
D)4,5 × 10⁻⁴
Answer: B — The comma moves 5 places to the RIGHT, so the exponent is −5.
- A — a number smaller than 1 needs a NEGATIVE exponent
- C — 45 is not between 1 and 10
- D — the comma moves 5 places, not 4
1.4
3,2 × 10⁻³ written in full is …
(1)
A)3 200
B)0,0032✓
C)0,32
D)−3 200
Answer: B — A negative exponent moves the comma LEFT.
- A — that is 3,2 × 10³
- C — moved the comma only one place
- D — the sign of the number does not change
1.5
(2 × 10³) × (4 × 10²) = …
(1)
A)8 × 10⁶
B)8 × 10⁵✓
C)6 × 10⁵
D)8 × 10^2,5
Answer: B — Multiply the numbers and ADD the exponents.
- A — multiplied the exponents
- C — ADDED 2 and 4 instead of multiplying
- D — divided the exponents
1.6
6 × 10⁸3 × 10⁵ = …
(1)
A)2 × 10¹³
B)2 × 10³✓
C)3 × 10³
D)2 × 10^1,6
Answer: B — Divide the numbers and SUBTRACT the exponents.
- A — added the exponents
- C — subtracted the numbers instead of dividing
- D — divided the exponents
1.7
Which one of the following is the SMALLEST?
(1)
A)3 × 10⁻²
B)3 × 10⁻⁴✓
C)3 × 10²
D)3 × 10⁰
Answer: B — The more negative the exponent, the smaller the number: 0,0003.
- A — 0,03
- C — 300
- D — 3
1.8
5⁻¹ + 5⁰ = …
(1)
A)0
B)115✓
C)5
D)15
Answer: B — 1/5 + 1 = 1 1/5.
- A — neither term is 0
- C — added the bases instead of the values
- D — forgot that 5⁰ = 1
1.9
The mass of a dust particle is 7,5 × 10⁻⁷ g. In grams that is …
(1)
A)0,000 007 5
B)0,000 000 75✓
C)75 000 000
D)0,000 075
Answer: B — The comma moves 7 places to the left.
- A — moved the comma 6 places
- C — moved it to the RIGHT
- D — moved it 5 places
1.10
1x⁻³ = …
(1)
A)−x³
B)x³✓
C)1x³
D)−3x
Answer: B — A negative exponent in the DENOMINATOR moves up to the numerator as a positive one.
- A — a negative exponent is not a negative number
- C — that is x⁻³ itself
- D — multiplied instead

Answer grid — marking guideline

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[9 MARKS]

Write the following in scientific notation.

2.1
Light travels 9 500 000 000 000 000 km in one year. Write this speed in scientific notation.
(3)
Move the comma 15 places to the left (1)
= 9,5 × 10¹⁵ km/year (2)
2.2
Write 0,0000125 in scientific notation.
(3)
Move the comma 5 places to the right, so the exponent is negative (1)
= 1,25 × 10⁻⁵ (2)
2.3
Write 3,04 × 10⁻³ as an ordinary decimal number, and state which is larger: 3,04 × 10⁻³ or 3,4 × 10⁻⁴.
(3)
= 0,00304 (1)
3,4 × 10⁻⁴ = 0,00034 (1)
3,04 × 10⁻³ is larger — compare the EXPONENTS first, not the leading digits (1)

Question 3

[12 MARKS]

Calculate the following, leaving your answers in scientific notation.

3.1
(2,4 × 10⁵) × (3 × 10³)
(4)
2,4 × 3 = 7,2 (1)
10⁵ × 10³ = 10⁸ (1)
= 7,2 × 10⁸ (2)
3.2
6 × 10⁷1,5 × 10³
(4)
6 ÷ 1,5 = 4 (1)
10⁷⁻³ = 10⁴ (1)
= 4 × 10⁴ (2)
3.3
The mass of a dust particle is 7,5 × 10⁻⁷ g. Determine the total mass of 2 000 identical dust particles. Give your answer in scientific notation.
(4)
2 000 = 2 × 10³ (1)
(7,5 × 10⁻⁷) × (2 × 10³) = 15 × 10⁻⁴ (2)
= 1,5 × 10⁻³ g (1)

TOTAL: 31 marks

This question paper consists of 3 questions.