KS3 Maths · Year 8 · Chapter 9: Decimal numbers · Lesson 4

Dividing with numbers in standard form

Year 8About 60 minutesNo calculator48 marks

Hints online, answers free with an account:
mathswariz.uk/worksheets/ks3-year-8-dividing-with-numbers-in-standard-form/

Date

Do Now

Quick questions to start.

A1
Needed today
Write $1 0^{9} \div 1 0^{3}$ as a single power of $10$ .
[1 mark]
Answer
A2
Last lesson
Work out $(2 \times 1 0^{4}) \times (4 \times 1 0^{- 7})$ . Give your answer in standard form.
[1 mark]
Answer
A3
From chapter 8
Expand $3 x (2 x - 5)$ .
[1 mark]
Answer
A4
Year 7
Work out $2.4 \div 0.6$ .
[1 mark]
Answer

Example, then your turn

Year 8

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

Example 1

Work out each answer. Give your answers in standard form.

(a) $(8 \times 1 0^{7}) \div (2 \times 1 0^{3})$

(b) $(9 \times 1 0^{- 3}) \div (3 \times 1 0^{5})$

Hint Divide the front numbers. Then divide the powers of

10

by subtracting the indices.

B1
Work out each answer. Give your answers in standard form.
(a) $(6.4 \times 1 0^{9}) \div (2 \times 1 0^{4})$
(b) $(7.5 \times 1 0^{- 2}) \div (2.5 \times 1 0^{- 6})$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Example 2

Work out each answer. Give your answers in standard form.

(a) $(3 \times 1 0^{8}) \div (5 \times 1 0^{2})$

(b) $(1.4 \times 1 0^{- 4}) \div (7 \times 1 0^{3})$

Hint

3 \div 5 = 0.6

, which is less than

1

. Write

0.6

6 \times 1 0^{- 1}

B2
Work out each answer. Give your answers in standard form.
(a) $(2 \times 1 0^{9}) \div (8 \times 1 0^{4})$
(b) $(3.6 \times 1 0^{- 2}) \div (9 \times 1 0^{- 6})$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Example 3

Work out each answer. Give your answers in standard form.

(a) $1.6 \times 1 0^{7}$

(b) $4.9 \times 1 0^{- 5}$

Hint Make the power of

10

even first:

1.6 \times 1 0^{7} = 16 \times 1 0^{6}

. Then take the square root of each part.

B3
Work out each answer. Give your answers in standard form.
(a) $3.6 \times 1 0^{9}$
(b) $8.1 \times 1 0^{- 7}$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Example 4

A virus is $4 \times 1 0^{- 5}$ m wide. How many of these viruses would fit side by side across a gap $2$ cm wide? Give your answer in standard form.

Hint Change

2

cm into metres first:

2

= 0.02

= 2 \times 1 0^{- 2}

B4
A cell is $5 \times 1 0^{- 6}$ m wide. How many of these cells would fit side by side across a line $3$ mm long? Give your answer in standard form.
[3 marks]
Answer

Example 5

A country uses $4.8 \times 1 0^{10}$ litres of water a day. It has $6 \times 1 0^{7}$ people. Work out the litres for each person, in standard form.

Hint Divide the total by the number of people.

B5
A city's $1.2 \times 1 0^{7}$ homes use $3.6 \times 1 0^{9}$ kWh of electricity in a year. Work out the mean kWh for one home, in standard form.
[3 marks]
Answer

Practice

Year 8

C1
Write down the missing number. Give it in standard form.
$□ \div (4 \times 1 0^{3}) = 2 \times 1 0^{5}$
[2 marks]
Answer
C2
Work out each answer. Give your answers in standard form, correct to $2$ significant figures.
(a) $(7 \times 1 0^{5}) \div (3 \times 1 0^{2})$
(b) $(2 \times 1 0^{- 3}) \div (6 \times 1 0^{4})$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

C3
Radio signals travel $3 \times 1 0^{8}$ m each second. A satellite is $3.6 \times 1 0^{7}$ m above the Earth. How many seconds does a signal take to reach it? Give your answer in standard form.
[2 marks]
Answer
C4
Work out $\frac{( 6 \times 1 0 ^{5} ) \times ( 4 \times 1 0 ^{3} )}{8 \times 1 0 ^{2}}$ . Give your answer in standard form.
[2 marks]
Answer
C5
Which is larger, P or Q? Show your working.
P $= (8 \times 1 0^{6}) \div (4 \times 1 0^{- 2})$ Q $= (9 \times 1 0^{5}) \div (3 \times 1 0^{- 3})$
[2 marks]
Answer

Exam-style questions

GCSE Foundation

D1
Work out each answer. Give your answers in standard form.
(a)
$(8 \times 1 0^{6}) \div (4 \times 1 0^{2})$
[1 mark]
Answer
(b)
$(6 \times 1 0^{- 3}) \div (2 \times 1 0^{- 7})$
[1 mark]
Answer
(c)
$(4 \times 1 0^{3}) \div (5 \times 1 0^{7})$
[1 mark]
Answer
Total for D1: 3 marks

D2
Ana says, " $(6 \times 1 0^{8}) \div (3 \times 1 0^{- 2}) = 2 \times 1 0^{6}$ , because $8 - 2 = 6$ ."
Explain what Ana has done wrong. Write the correct answer in standard form.
[2 marks]
D3
A spacecraft travels $3.6 \times 1 0^{8}$ km in $4.8 \times 1 0^{2}$ hours.
(a)
Work out its mean speed in kilometres per hour. Give your answer in standard form.
[2 marks]
Answer
(b)
Work out its mean speed in kilometres per minute. Give your answer in standard form.
[2 marks]
Answer
Total for D3: 4 marks
D4
The table shows the number of people and the area of two countries.
(a)
Work out the number of people for each km² in country P. Give your answer in standard form.
[2 marks]
Answer
(b)
Work out the number of people for each km² in country Q. Give your answer in standard form.
[2 marks]
Answer
(c)
How many times as many people for each km² does country P have as country Q?
[1 mark]
Answer
Total for D4: 5 marks
D5
A plastic card is $7.5 \times 1 0^{- 4}$ m thick. A stack of these cards is $9$ cm high. Work out the number of cards in the stack. Give your answer in standard form.
[4 marks]
Answer

Extension

Stretch

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

E1
A cube has a volume of $2.7 \times 1 0^{- 5}$ m³. Work out its surface area, in m². Give your answer in standard form.
[4 marks]
Hint 1 · What to try
The volume is the side length cubed. First find the side length.
Hint 2 · The first line
$2.7 \times 1 0^{- 5} = 27 \times 1 0^{- 6}$ , and the cube root of $27$ is $3$ .
Hint 3 · The full method
The side is $3 \times 1 0^{- 2}$ m. A cube has $6$ square faces.
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can divide numbers in standard form by dividing the front numbers and subtracting the powers.
I can put an answer such as $0.6 \times 1 0^{6}$ back into standard form.
I can use dividing to find how many fit, or an amount for each one.

Answers and mark scheme

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

Get the answers