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Year 9

Writing small numbers in standard form

I can write very small numbers in the form A × 10^(−n), (where 1 ≤ A < 10) and appreciate the real-life contexts where this format is usefully used.

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Year 9

Writing small numbers in standard form

I can write very small numbers in the form A × 10^(−n), (where 1 ≤ A < 10) and appreciate the real-life contexts where this format is usefully used.

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Lesson details

Key learning points

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

Keywords

  • Exponential form - When a number is multiplied by itself multiple times, it can be written more simply in exponential form.

  • 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.

  • 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).

Common misconception

Pupils can incorrectly write a number in standard form or use a number in incorrect standard form whereby the number A does not satisfy 1 ≤ A < 10 or pupils use division of positive powers of 10.

Standard form represents a multiplicative relationship, so there should always be a multiplication. Embedding the understanding that negative exponents refer to 1/10^n is important. Using the place value chart with fractional and exponent form helps.

Using standard form with very small numbers allows pupils to explore real life examples of very small numbers. Discuss with pupils which careers, industries, etc. will use very small numbers. This discussion point allows pupils to see the importance of standard form.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
form follows this convention: $$A \times 10^B$$ and $$1 ≤ A < 10$$ and $$B$$ is an integer.
Correct Answer: Standard, standard
Q2.
Which of the following are written in standard form?
Correct answer: $${3.76}\times10^{4}$$
$${26}\times10^{3}$$
$${0.98}\times10^{8}$$
Correct answer: $${9.04}\times10^{2}$$
$${597}\times10^{6}$$
Q3.
Write 480 000 in standard form.
$${480}\times10^{3}$$
$${48}\times10^{4}$$
$${4.8}\times10^{4}$$
Correct answer: $${4.8}\times10^{5}$$
$${0.48}\times10^{6}$$
Q4.
Match each ordinary number to the equivalent number written in standard form.
Correct Answer:$$60 300$$,$${6.03}\times10^{4}$$

$${6.03}\times10^{4}$$

Correct Answer:$$6 300 000$$,$${6.3}\times10^{6}$$

$${6.3}\times10^{6}$$

Correct Answer:$$603$$,$${6.03}\times10^{2}$$

$${6.03}\times10^{2}$$

Correct Answer:$$603 000$$,$${6.03}\times10^{5}$$

$${6.03}\times10^{5}$$

Correct Answer:$$6300$$,$${6.3}\times10^{3}$$

$${6.3}\times10^{3}$$

Correct Answer:$$63 000$$,$${6.3}\times10^{4}$$

$${6.3}\times10^{4}$$

Q5.
$${2.45}\times10^{6}$$ as an ordinary number is .
Correct Answer: 2 450 000, 2450000, 2,450,000, 2450 000
Q6.
What should go in the box to make this statement correct? $$240 000 000 000 000 = 2.4 \square$$
$$\times10^{13}$$
$$\times10^{15}$$
$$\div10^{14}$$
Correct answer: $$\times10^{14}$$
$$\div10^{13}$$

Exit quiz

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6 Questions

Q1.
Standard form follows this convention: $$A \times 10^B$$ and $$1 ≤ A < 10$$ and $$B$$ is an .
Correct Answer: integer, whole number
Q2.
Which of the following are written in standard form?
$${0.26}\times10^{-4}$$
Correct answer: $${3.04}\times10^{-5}$$
$${4.3}\div10^{3}$$
Correct answer: $${7.2}\times10^{-3}$$
$${5.23}\div10^{-2}$$
Q3.
Use a place value grid to write $$0.00506$$ in standard form.
$${5}\div10^{-3}$$
$${5.06}\times10^{-2}$$
Correct answer: $${5.06}\times10^{-3}$$
$${5.06}\div10^{-3}$$
$${5}\times10^{-3}$$
Q4.
Write $$0.00047$$ in standard form.
$${4.7}\times10^{-3}$$
$${4.7}\times10^{3}$$
Correct answer: $${4.7}\times10^{-4}$$
$${4.7}\div10^{-4}$$
$${4.7}\times10^{4}$$
Q5.
$${4.08}\times10^{-4}$$ as an ordinary number is .
Correct Answer: 0.000408, 0.000 408
Q6.
Match each ordinary number to the equivalent number written in standard form.
Correct Answer:$$0.000402$$,$${4.02}\times10^{-4}$$

$${4.02}\times10^{-4}$$

Correct Answer:$$42 000$$,$${4.2}\times10^{4}$$

$${4.2}\times10^{4}$$

Correct Answer:$$0.00042$$,$${4.2}\times10^{-4}$$

$${4.2}\times10^{-4}$$

Correct Answer:$$4020$$,$${4.02}\times10^{3}$$

$${4.02}\times10^{3}$$

Correct Answer:$$0.00402$$,$${4.02}\times10^{-3}$$

$${4.02}\times10^{-3}$$

Correct Answer:$$4200$$,$${4.2}\times10^{3}$$

$${4.2}\times10^{3}$$