GCSE Maths · Higher · Chapter 14: Powers and standard form · Lesson 2

Standard form

Grades 4–7About 45 minutesNo calculator33 marks

Hints online, answers free with an account:
mathswariz.uk/worksheets/gcse-standard-form/

NameClassDate

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

A1
Needed today
Write $3^{4} \times 3^{3} \div 3^{5}$ as a single power of 3.
[1 mark]
Answer
A2
From chapter 4
Each term is the sum of the two before. Find the next term: $4, 2, 6, 8, 14, \dots$
[1 mark]
Answer
A3
From chapter 9
Find the surface area of a 3 cm by 5 cm by 9 cm cuboid.
[1 mark]
Answer
A4
From chapter 12
Similar shapes have matching sides 8 cm and 32 cm. Find the scale factor.
[1 mark]
Answer

Grades 4–6

Your teacher works through each example with you. Then try the one beside it.

Example 1

Write $0.000 93$ in standard form.

Hint Move the point until the number is between 1 and 10. Count the places: a small number has a negative power.

Example 2

Work out $(3.5 \times 1 0^{4}) \times (2 \times 1 0^{6})$ . Give your answer in standard form.

Hint Multiply the front numbers. Add the powers of 10.

B2
Work out $(4 \times 1 0^{- 3}) \times (6 \times 1 0^{8})$ . Give your answer in standard form.
[2 marks]
Answer

Grades 5–6

C1
Write $5.08 \times 1 0^{6}$ as an ordinary number.
[1 mark]
Answer
C2
Work out $(6.3 \times 1 0^{9}) \div (1.4 \times 1 0^{2})$ . Give your answer in standard form.
[2 marks]
Answer

C3
Work out $6.3 \times 1 0^{5} + 4.9 \times 1 0^{4}$ . Give your answer in standard form.
[2 marks]
Answer
C4
Write these numbers in order of size. Start with the smallest: $4.6 \times 1 0^{- 3}$ , $0.0047$ , $4.07 \times 1 0^{- 4}$ , $4.6 \times 1 0^{- 2}$
[2 marks]
Answer
C5
Write $4260000000$ in standard form.
[1 mark]
Answer
C6
$0.25 \times 1 0^{- 3}$ is not in standard form. Write it in standard form.
[1 mark]
Answer
C7
Work out $8.2 \times 1 0^{6} - 5 \times 1 0^{5}$ . Give your answer in standard form.
[2 marks]
Answer
C8
Work out $3.6 \times 1 0^{9}$ . Give your answer in standard form.
[2 marks]
Answer

Grades 6–7

D1
Ben says, " $0.000 74 = 7.4 \times 1 0^{4}$ , because the point moves 4 places."
Explain why Ben is wrong, and write $0.000 74$ correctly in standard form.
[2 marks]
Answer

Grade 8 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can write large and small numbers in standard form, and back again.
I can multiply, divide, add, subtract and compare numbers in standard form.
I can use standard form in a real problem and find a square root.

The worked answers and the full mark scheme are free with a Mathswariz account. Teachers and students can both sign up.