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Grade 9 · Exponents
Negative Exponents & Scientific Notation (Grade 9)
MARKING GUIDELINE
Marks
31
Duration
50 minutes
Questions
3
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.
- 1.12−3 = …(1)A)−8B)8C)1/8✓D)−6Answer: C — A negative exponent means the RECIPROCAL: 1/23 = 1/8.
- A — a negative exponent does not make the answer negative
- B — ignored the minus sign in the exponent — that is 23
- D — multiplied 2 by −3
- 1.2x−2 written with a positive exponent is …(1)A)−2xB)x2/1C)−x2D)1/x2✓Answer: D — Move the power to the denominator and the sign of the exponent changes.
- A — multiplied instead of taking a reciprocal
- B — that is just x2
- C — a negative exponent is not a negative number
- 1.30,000 045 written in scientific notation is …(1)A)4,5 × 10−5✓B)4,5 × 105C)45 × 10−6D)4,5 × 10−4Answer: A — The comma moves 5 places to the RIGHT, so the exponent is −5.
- B — a number smaller than 1 needs a NEGATIVE exponent
- C — 45 is not less than 10
- D — the comma moves 5 places, not 4
- 1.43,2 × 10−3 written in full is …(1)A)−3 200B)0,0032✓C)0,32D)3 200Answer: B — A negative exponent moves the comma LEFT.
- A — the sign of the number does not change
- C — moved the comma only one place
- D — that is 3,2 × 103
- 1.5(2 × 103) × (4 × 102) = …(1)A)8 × 102,5B)8 × 106C)8 × 105✓D)6 × 105Answer: C — Multiply the numbers and ADD the exponents.
- A — averaged the exponents: (3 + 2) ÷ 2 = 2,5
- B — multiplied the exponents
- D — ADDED 2 and 4 instead of multiplying
- 1.6(6 × 108)/(3 × 105) = …(1)A)2 × 101,6B)3 × 103C)2 × 103✓D)2 × 1013Answer: C — Divide the numbers and SUBTRACT the exponents.
- A — divided the exponents
- B — subtracted the numbers instead of dividing
- D — added the exponents
- 1.7Which one of the following is the SMALLEST?(1)A)3 × 10−2B)3 × 10−4✓C)3 × 102D)3 × 100Answer: B — The more negative the exponent, the smaller the number: 0,0003.
- A — 0,03
- C — 300
- D — 3
- 1.85−1 + 50 = …(1)A)5B)1/5C)0D)11/5✓Answer: D — 1/5 + 1 = 1 1/5.
- A — added the bases instead of the values
- B — forgot that 50 = 1
- C — neither term is 0
- 1.9The mass of a dust particle is 7,5 × 10−7 g. In grams that is …(1)A)0,000 075B)0,000 000 75✓C)75 000 000D)0,000 007 5Answer: B — The comma moves 7 places to the left.
- A — moved it 5 places
- C — moved it to the RIGHT
- D — moved the comma 6 places
- 1.101/x−3 = …(1)A)x3✓B)−3xC)−x3D)1/x3Answer: A — A negative exponent in the DENOMINATOR moves up to the numerator as a positive one.
- B — multiplied instead
- C — a negative exponent is not a negative number
- D — that is x−3 itself
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.
- 2.1Light travels about 9 460 000 000 000 km in one year. Write this distance in scientific notation.(3)Move the comma 12 places to the left (1)
= 9,46 × 1012 km (2) - 2.2Write 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) - 2.3Write 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 × 107)/(1,5 × 103)(4)6 ÷ 1,5 = 4 (1)
107 − 3 = 104 (1)
= 4 × 104 (2) - 3.3The 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.