Question 1(a): [1 mark]
Write 1.24 \times 10^6 as an ordinary number.
Answer type: Simple text answer
ANSWER: 1240000
Question 1(b): [1 mark]
Which of the following numbers represents 742000 in standard form?
Answer type: Multiple choice type 2
A: 0.742 \times 10^6
B: 7.42 \times 10^5
C: 7.42 \times 10^6
D: 74.2 \times 10^4
ANSWER: B: 7.42 \times 10^5
Question 1(c): [1 mark]
Write 6.3 \times 10^{-7} as an ordinary number.
Answer type: Simple text answer
ANSWER: 0.00000063
Question 2(a): [1 mark]
Write 9.9 \times 10^{-4} as an ordinary number.
Answer type: Simple text answer
ANSWER: 0.00099
Question 2(b): [1 mark]
Which of the following numbers represents 0.068 in standard form.
Answer type: Multiple choice type 2
A: 6.8 \times 10^{-1}
B: 6.8 \times 10^{-3}
C: 0.68 \times 10^{-1}
D: 6.8 \times 10^{-2}
ANSWER: D: 6.8 \times 10^{-2}
Question 2(c): [2 mark]
Which of the following numbers represents (6 \times 10^3) \times (9 \times 10^4) in standard form.
Answer type: Multiple choice type 2
A: 54 \times 10^{7}
B: 5.4 \times 10^{8}
C: 5.4 \times 10^{7}
D: 0.54 \times 10^{9}
ANSWER: B: 5.4 \times 10^{8}
WORKING: 6 \times 9 \times 10^3 \times 10^4 = 54 \times 10^7 = 5.4 \times 10^8.
Question 3(a): [1 mark]
Write 5 \times 10^{1} as an ordinary number.
Answer type: Simple text answer
ANSWER: 50
Question 3(b): [1 mark]
Write 2.7027 \times 10^{-2} as an ordinary number.
Answer type: Simple text answer
ANSWER: 0.027027
Question 3(c): [2 marks]
Work out the value of (4 \times 10^6) \div (2 \times 10^4).
Give your answer as an ordinary number.
Answer type: Simple text answer
ANSWER: 200
WORKING: 2 \times 10^2 = 200
Question 4(a): [1 mark]
Write 4.7 \times 10^5 as an ordinary number in words.
Answer type: Simple text answer
ANSWER: four hundred and seventy thousand
Question 4(b): [2 marks]
The following numbers are not in ascending order.
\text{forty six}, 7.2 \times 10^2, 6311, 4.66 \times 10^5, 0.87, 3.3 \times 10^{-4}
Write them in ascending order, by their matching letters.
Answer type: Multiple answers type 1
ANSWER:
Smallest: 3.3 \times 10^{-4}
0.87
\text{forty six}
7.2 \times 10^2
6311
Largest: 4.66 \times 10^5
WORKING:
7.2 \times 10^2 = 7204.66 \times 10^5 = 466000
3.3 \times 10^{-4}
Question 5: [2 marks]
Jake noted that speed of light is approximately 1.1 \times 10^9 km/h;
the speed of sound is approximately 1.2 \times 10^3 km/h; and
11 \div 12 = 0.91 \dot 6Using Jake’s figures how many times faster is light than speed in standard form? Choose the correct answer.
Answer type: Multiple choice type 2
A: 9.1\dot 6 \times 10^6
B: 9.1 \dot 6 \times 10^5
C: 0.91\dot 6 \times 10^6
D: 9.1 \dot 6 \times 10^4
ANSWER: B: 9.1 \dot 6 \times 10^5
WORKING: 1.1 \div 1.2 = 11 \div 12 = 0.91 \dot 6
10^9 \div 10^3 = 10^6
0.91 \dot 6 = 9.1 \dot 6 \times 10^{-1}
9.1 \dot 6 \times 10^{-1} \times 10^6 = 9.1 \dot 6 \times 10^5
Question 6: [2 marks]
k = \dfrac{ab}{b - c}a = 2 \times 10^4
b = 6 \times 10^6
c = 1 \times 10^5
Find the value of k in standard form correct to 2 significant figures. Choose the correct answer.
Hint: 12 \div 59 \approx 0.20
Answer type: Multiple choice type 2
A: 0.20 \times 10^5
B: 0.24 \times 10^5
C: 2.0 \times 10^4
D: 2.4 \times 10^4
ANSWER: C: 2.0 \times 10^4
WORKING: k = \dfrac{2 \times 6 \times 10^4 \times 10^6}{6 \times 10^6 - 2 \times 10^4} = \dfrac{12 \times 10^{10}}{6000000 - 100000} = \dfrac{1.2 \times 10^{11}}{5900000} = \dfrac{1.2 \times 10^{11}}{5.9 \times 10^6}
1.2 \div 5.9 \approx 0.20
10^{11} \div 10^6 = 10^5
k = 0.20 \times 10^5 = 2.0 \times 10^4