Checking and securing understanding of writing small numbers in standard form | Maths

Starter quiz

A number written in exponential form represents a repeated __________.

addition

division

multiplication ✓

subtraction
Match each fraction to its equivalent exponential form.

${1}\over{10}$

⇔

$10^{-1}$ ✓

${1}\over{100}$

⇔

$10^{-2}$ ✓

${1}\over{1000}$

⇔

$10^{-3}$ ✓

${1}\over{10 000}$

⇔

$10^{-4}$ ✓
$3\times10^{-2}+2\times10^{-5}+8\times10^{-6}$ represents the number ______.

'0.030028' ✓
Why is standard form important?

It helps concisely write very big or very small numbers. ✓

It saves time. ✓

It minimises errors. ✓

It guarantees no errors when calculating with big or small numbers.
${2.45}\times10^{6}$ as an ordinary number is ______.

'2 450 000 ' ✓
Work out $\frac{1}{10} + 10^{-1} + \frac{1}{100} + 10^{-2} + \frac{1}{1000}+ 10^{-3}$ . The answer as a decimal is ______.

'0.222' ✓

Exit quiz

Match each ordinary number to its standard form equivalent.

$0.000034$

⇔

$3.4\times10^{-5}$ ✓

$0.0034$

⇔

$3.4\times10^{-3}$ ✓

$0.000043$

⇔

$4.3\times10^{-5}$ ✓

$0.0000043$

⇔

$4.3\times10^{-6}$ ✓
Which of the following have not been written in standard form?

$4\times10^{-5}$

$0.4\times10^{-5}$

$0.34\times10^{-5}$ ✓

$340\times10^{-5}$ ✓

$34\times10^{-5}$ ✓
Match each number to its correct standard form equivalent.

$44.4\times10^{-5}$

⇔

$4.44\times10^{-4}$ ✓

$0.34\times10^{-5}$

⇔

$3.4\times10^{-6}$ ✓

$340\times10^{-5}$

⇔

$3.4\times10^{-3}$ ✓

$34\times10^{-5}$

⇔

$3.4\times10^{-4}$ ✓
Starting with the smallest, put these numbers into ascending order of size.

1

⇔

$0.00000049$

2

⇔

$0.00002$

3

⇔

$0.9\times10^{-4}$

4

⇔

$78.2\times10^{-4}$

5

⇔

$9.9\times10^{-3}$
Some Oak pupils estimate the size of a cell. Their teacher says, "Well done! The person who has written down the smallest answer is correct!" Who has the right answer?

Aisha: $5\times10^{-8}$ m ✓

Alex: $500\times10^{-4}$ mm

Jacob: $349\times10^{-5}$ cm

Jun: $0.0000043\times10^{8}$ mm

Sam: $0.4\times10^{-4}$ mm
Match each living creature to its length.

Tick

⇔

$5\times10^{-3}$ m ✓

Ant

⇔

$0.2\times10^{1}$ mm ✓

Ladybird

⇔

$1.1\times10^{-2}$ m ✓

Tarantula

⇔

$13\times10^{-2}$ m ✓

Snake

⇔

$1\times10^{2}$ cm ✓

Worksheet

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Lesson Details

Key learning points

It is difficult to read very small numbers, due to the number of digits involved.
It can be more efficient to write these very small numbers in standard form.
There is a convention for standard form.

Common misconception

When a number is not quite written in standard form, pupils can incorrectly convert the number.

When the A number is greater than 10, add the necessary multiplications of 10 to the index of 10. When the A number is less than 10, subtract the necessary multiplications of 10 from the index of 10.

Keywords

Standard form - Standard form is when a number is written in the form A × 10^n, (where 1 ≤ A < 10 and n is an integer).
Associative law - The associative law states that a repeated application of the operation produces the same result regardless of how pairs of values are grouped. We can group using brackets.