KS3 Maths · Year 7 · Chapter 8: Number · Lesson 4

Multiplying with numbers in standard form

Year 7About 60 minutesCalculator allowed47 marks

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Date

Do Now

Quick questions to start.

A1
Needed today
Write $72000$ in standard form.
[1 mark]
Answer
A2
Needed today
Write $1 0^{3} \times 1 0^{5}$ as a single power of $10$ .
[1 mark]
Answer
A3
Last lesson
Write $3.08 \times 1 0^{5}$ as an ordinary number.
[1 mark]
Answer
A4
From chapter 6
How many cm³ are there in $1$ litre?
[1 mark]
Answer

Example, then your turn

Year 7

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

Example 1

Work out each calculation. Give your answers in standard form. Do not use a calculator.

(a) $(2 \times 1 0^{3}) \times (4 \times 1 0^{5})$

(b) $(1.3 \times 1 0^{2}) \times (3 \times 1 0^{6})$

Hint Multiply the front numbers. Multiply the powers of

10

by adding the powers:

1 0^{3} \times 1 0^{5} = 1 0^{8}

B1
Give your answers in standard form. Do not use a calculator.
(a) $(3 \times 1 0^{4}) \times (3 \times 1 0^{2})$
(b) $(1.6 \times 1 0^{5}) \times (4 \times 1 0^{3})$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Example 2

Give your answers in standard form. Do not use a calculator.

(a) $(6 \times 1 0^{4}) \times (5 \times 1 0^{3})$

(b) $(8 \times 1 0^{2})^{2}$

Hint If the front numbers multiply to

10

or more, the answer is not yet in standard form. Write the front number as a number between

1

and

10

times

10

, and add

1

to the power.

B2
Give your answers in standard form. Do not use a calculator.
(a) $(7 \times 1 0^{5}) \times (4 \times 1 0^{6})$
(b) $(9 \times 1 0^{3})^{2}$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Example 3

Work out $(25 \times 1 0^{3}) \times (3 \times 1 0^{5})$ . Give your answer in standard form. Do not use a calculator.

Hint You can multiply first and change to standard form at the end.

B3
Give your answers in standard form. Do not use a calculator.
(a) $(0.7 \times 1 0^{5}) \times (4 \times 1 0^{2})$
(b) $(15 \times 1 0^{3}) \times (6 \times 1 0^{4})$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Example 4

Use a calculator to work out $(4.27 \times 1 0^{5}) \times (6.83 \times 1 0^{3})$ . Give your answer in standard form, correct to $3$ significant figures.

Hint Enter

4.27 \times 1 0^{5}

with the

\times 1 0^{x}

key (or EXP), not with the

\times

key. Then round the front number.

B4
Use a calculator to work out $(5.96 \times 1 0^{4}) \times (3.18 \times 1 0^{6})$ . Give your answer in standard form, correct to $3$ significant figures.
[2 marks]
Answer

Example 5

Sound travels $3.4 \times 1 0^{2}$ metres each second. How far does sound travel in $1$ hour? Give your answer in standard form.

Hint Change

1

hour into seconds first:

60 \times 60 = 3600 = 3.6 \times 1 0^{3}

B5
A machine prints $2.5 \times 1 0^{3}$ labels each minute. It runs for $8$ hours. How many labels does it print? Give your answer in standard form.
[3 marks]
Answer

Practice

Year 7

C1
Work out $(1.25 \times 1 0^{6}) \times (8 \times 1 0^{3})$ . Give your answer in standard form. Do not use a calculator.
[2 marks]
Answer
C2
Write down the missing numbers.
(a) $(4 \times 1 0^{□}) \times (2 \times 1 0^{5}) = 8 \times 1 0^{11}$
(b) $(□ \times 1 0^{3}) \times (5 \times 1 0^{4}) = 1.5 \times 1 0^{8}$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

C3
Use a calculator to work out $(7.04 \times 1 0^{3})^{2}$ . Give your answer in standard form, correct to $3$ significant figures.
[2 marks]
Answer
C4
Work out $4$ million $\times$ $3$ thousand. Give your answer in standard form.
[2 marks]
Answer
C5
Which is larger, $(3 \times 1 0^{4}) \times (2 \times 1 0^{5})$ or $(5 \times 1 0^{3}) \times (1.4 \times 1 0^{6})$ ? Show how you decide.
[2 marks]
Answer

Exam-style questions

GCSE Foundation

D1
Work out each calculation. Give your answers in standard form.
(a)
$(4 \times 1 0^{6}) \times (2 \times 1 0^{3})$
[1 mark]
Answer
(b)
$(9 \times 1 0^{5}) \times (6 \times 1 0^{2})$
[2 marks]
Answer
Total for D1: 3 marks

D2
Leah works out $(5 \times 1 0^{4}) \times (6 \times 1 0^{3})$ . She writes $30 \times 1 0^{7}$ and says her answer is in standard form.
Explain why Leah is wrong. Write her answer in standard form.
[2 marks]
Answer
D3
A camera takes $2.5 \times 1 0^{3}$ photos. Each photo uses $4.8 \times 1 0^{6}$ bytes of memory.
(a)
Work out the total number of bytes the photos use. Give your answer in standard form.
[2 marks]
Answer
(b)
One gigabyte is $1 0^{9}$ bytes. How many gigabytes do the photos use?
[1 mark]
Answer
(c)
Ravi's memory card holds $16$ gigabytes. Will all the photos fit on it? Give a reason for your answer.
[2 marks]
Answer
Total for D3: 5 marks
D4
A spacecraft travels $1.1 \times 1 0^{4}$ metres every second.
(a)
Show that there are $8.64 \times 1 0^{4}$ seconds in one day.
[2 marks]
Answer
(b)
Work out how far the spacecraft travels in one day. Give your answer in metres, in standard form, correct to $3$ significant figures.
[2 marks]
Answer
Total for D4: 4 marks
D5
Use a calculator to work out $(6.25 \times 1 0^{7}) \times (3.9 \times 1 0^{4})$ .
(a)
Give your answer in standard form. Do not round your answer.
[2 marks]
Answer
(b)
Write your answer to part (a) correct to $2$ significant figures.
[1 mark]
Answer
Total for D5: 3 marks

Extension

Stretch

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

E1
$a$ , $b$ and $c$ are three whole numbers in a row, with $a < b < c$ .
$(6 \times 1 0^{a}) \times (8 \times 1 0^{b}) \times (5 \times 1 0^{c}) = 2.4 \times 1 0^{20}$
Find $a$ , $b$ and $c$ .
[5 marks]
Hint 1 · What to try
Multiply the front numbers first and write the result in standard form.
Hint 2 · The first line
$6 \times 8 \times 5 = 240 = 2.4 \times 1 0^{2}$ , so $1 0^{2} \times 1 0^{a + b + c} = 1 0^{20}$ .
Hint 3 · The full method
So $a + b + c = 18$ . Three whole numbers in a row that add to $18$ are $5$ , $6$ and $7$ .
Answer $a = \dots$ $b = \dots$ $c = \dots$

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can multiply numbers in standard form without a calculator.
I can write an answer like $30 \times 1 0^{7}$ in standard form.
I can multiply numbers in standard form on a calculator and round.
I can use standard form in a problem with units.

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