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 = 720

 

4.66 \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 6

Using 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