KS3 Maths · Year 7 · Chapter 8: Number · Lesson 3

Standard form with large numbers

Year 7About 60 minutesNo calculator46 marks

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Date

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Quick questions to start.

A1
Needed today
Write $10 \times 10 \times 10 \times 10 \times 10$ as a power of $10$ .
[1 mark]
Answer
A2
Needed today
Work out $4.06 \times 1 0^{3}$ .
[1 mark]
Answer
A3
Last lesson
Round $7352$ to $2$ significant figures.
[1 mark]
Answer
A4
From chapter 1
Work out $(- 6) \times (- 9)$ .
[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

Write each number in standard form.

(a) $640000$ (b) $93080$

Hint Standard form is

a \times 1 0^{n}

, where

a

is at least

1

and less than

10

. Count how many places the digits move to give a number between

1

and

10

B1
Write each number in standard form.
(a) $5720000$ (b) $408$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Example 2

Write each number as an ordinary number.

(a) $3.9 \times 1 0^{6}$ (b) $7.025 \times 1 0^{4}$

Hint Multiply by the power of

10

: the digits move that many places to the left. Fill the empty places with zeros.

B2
Write each number as an ordinary number.
(a) $6.14 \times 1 0^{5}$ (b) $2.3 \times 1 0^{8}$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Example 3

These numbers are not in standard form. Write each one in standard form.

(a) $46 \times 1 0^{5}$ (b) $0.52 \times 1 0^{7}$

Hint Make the front number between

1

and

10

. If you divide it by

10

, multiply the power of

10

10

(add

1

to the power). If you multiply it by

10

, take

1

off the power.

B3
Write each number in standard form.
(a) $730 \times 1 0^{4}$ (b) $0.081 \times 1 0^{9}$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Example 4

Write each number in standard form.

(a) $4.6$ million (b) $52$ billion

Hint One million is

1000000 = 1 0^{6}

. One billion is one thousand million,

1000000000 = 1 0^{9}

B4
Write each number in standard form.
(a) $830$ thousand (b) $6.15$ billion
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Example 5

Work out the square of each number. Give each answer in standard form.

(a) $6000$ (b) $90000$

Hint Square the non-zero part, then count the zeros: a number with

3

zeros squared has

6

zeros.

B5
Work out the square of each number. Give each answer in standard form.
(a) $500$ (b) $120000$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Practice

Year 7

C1
Which of these numbers are written in standard form?
$3.2 \times 1 0^{5}$ $12 \times 1 0^{3}$ $9.99 \times 1 0^{7}$ $1 \times 1 0^{4}$ $0.8 \times 1 0^{6}$
[2 marks]
Answer
C2
Write these numbers in order of size. Start with the smallest.
$4.1 \times 1 0^{6}$ $9.8 \times 1 0^{5}$ $2.6 \times 1 0^{7}$ $3.95 \times 1 0^{6}$
[2 marks]
Answer

C3
A calculator shows $5.07E08$ . This means $5.07 \times 1 0^{8}$ .
Write the number as an ordinary number.
[1 mark]
Answer
C4
Write down the missing numbers.
(a) $57000000 = 5.7 \times 1 0^{□}$
(b) $□ \times 1 0^{4} = 26000$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$
C5
(a) How many zeros does $8 \times 1 0^{11}$ have when it is written as an ordinary number?
(b) How many digits does $8.42 \times 1 0^{11}$ have when it is written as an ordinary number?
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Exam-style questions

GCSE Foundation

D1
Answer each part.
(a)
Write $36400$ in standard form.
[1 mark]
Answer
(b)
Write $5.09 \times 1 0^{6}$ as an ordinary number.
[1 mark]
Answer
(c)
Write $0.27 \times 1 0^{8}$ in standard form.
[1 mark]
Answer
Total for D1: 3 marks

D2
Sami says, " $9 \times 1 0^{6}$ is bigger than $4.5 \times 1 0^{7}$ , because $9$ is bigger than $4.5$ ."
Is Sami right? Give a reason for your answer.
[2 marks]
Answer
D3
The table shows the number of visits to four websites in one year.
(a)
Which website had the most visits?
[1 mark]
Answer
(b)
Write the number of visits to Site B as an ordinary number.
[1 mark]
Answer
(c)
Work out how many more visits Site A had than Site B. Give your answer in standard form.
[3 marks]
Answer
Total for D3: 5 marks
D4
A solar farm is a square of side $4000$ m.
(a)
Work out the area of the solar farm in m². Give your answer in standard form.
[2 marks]
Answer
(b)
One hectare is $10000$ m². Work out the area of the solar farm in hectares.
[2 marks]
Answer
Total for D4: 4 marks
D5
Add $4 \times 1 0^{3}$ and $6 \times 1 0^{5}$ . Give your answer in standard form.
[2 marks]
Answer
D6
Write down the value of $n$ in each.
(a)
$840000 = 8.4 \times 1 0^{n}$
[1 mark]
Answer
(b)
$56$ million $= 5.6 \times 1 0^{n}$
[1 mark]
Answer
Total for D6: 2 marks

Extension

Stretch

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

E1
$N = 2^{10} \times 5^{13}$
Write $N$ in standard form. How many digits does $N$ have when it is written as an ordinary number?
[5 marks]
Hint 1 · What to try
$2 \times 5 = 10$ . Pair each $2$ with a $5$ .
Hint 2 · The first line
$2^{10} \times 5^{13} = 2^{10} \times 5^{10} \times 5^{3} = 1 0^{10} \times 125$ .
Hint 3 · The full method
$125 \times 1 0^{10} = 1.25 \times 1 0^{2} \times 1 0^{10} = 1.25 \times 1 0^{12}$ . As an ordinary number it is $125$ followed by $10$ zeros, so it has $13$ digits.
Answer $N = \dots\dots$ digits $\dots\dots$

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can write a large number in standard form.
I can write a number in standard form as an ordinary number.
I can change a number like $46 \times 1 0^{5}$ into standard form.
I can compare and order numbers in standard form.

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