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Year 10
Higher

Checking and securing understanding of 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 10
Higher

Checking and securing understanding of 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

  • 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.

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.

When ordering, encourage students to use the approach where all numbers are correctly converted to standard form rather than writing out the ordinary number. Discuss why this approach is used in microbiology, nanotechnology, medicine.
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.
A number written in exponential form represents a repeated __________.
addition
division
Correct answer: multiplication
subtraction
Q2.
Match each fraction to its equivalent exponential form.
Correct Answer:$${1}\over{10}$$ ,$$10^{-1}$$

$$10^{-1}$$

Correct Answer:$${1}\over{100}$$ ,$$10^{-2}$$

$$10^{-2}$$

Correct Answer:$${1}\over{1000}$$ ,$$10^{-3}$$

$$10^{-3}$$

Correct Answer:$${1}\over{10 000}$$ ,$$10^{-4}$$

$$10^{-4}$$

Q3.
$$3\times10^{-2}+2\times10^{-5}+8\times10^{-6}$$ represents the number .
Correct Answer: 0.030028, 0.030 028
Q4.
Why is standard form important?
Correct answer: It helps concisely write very big or very small numbers.
Correct answer: It saves time.
Correct answer: It minimises errors.
It guarantees no errors when calculating with big or small numbers.
Q5.
$${2.45}\times10^{6}$$ as an ordinary number is .
Correct Answer: 2 450 000 , 2450000 , 2,450,000
Q6.
Work out $$\frac{1}{10} + 10^{-1} + \frac{1}{100} + 10^{-2} + \frac{1}{1000}+ 10^{-3}$$. The answer as a decimal is .
Correct Answer: 0.222

Exit quiz

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6 Questions

Q1.
Match each ordinary number to its standard form equivalent.
Correct Answer:$$0.000034$$ ,$$3.4\times10^{-5}$$

$$3.4\times10^{-5}$$

Correct Answer:$$0.0034$$,$$3.4\times10^{-3}$$

$$3.4\times10^{-3}$$

Correct Answer:$$0.000043$$ ,$$4.3\times10^{-5}$$

$$4.3\times10^{-5}$$

Correct Answer:$$0.0000043$$ ,$$4.3\times10^{-6}$$

$$4.3\times10^{-6}$$

Q2.
Which of the following have not been written in standard form?
$$4\times10^{-5}$$
$$0.4\times10^{-5}$$
Correct answer: $$0.34\times10^{-5}$$
Correct answer: $$340\times10^{-5}$$
Correct answer: $$34\times10^{-5}$$
Q3.
Match each number to its correct standard form equivalent.
Correct Answer:$$44.4\times10^{-5}$$ ,$$4.44\times10^{-4}$$

$$4.44\times10^{-4}$$

Correct Answer:$$0.34\times10^{-5}$$ ,$$3.4\times10^{-6}$$

$$3.4\times10^{-6}$$

Correct Answer:$$340\times10^{-5}$$ ,$$3.4\times10^{-3}$$

$$3.4\times10^{-3}$$

Correct Answer:$$34\times10^{-5}$$ ,$$3.4\times10^{-4}$$

$$3.4\times10^{-4}$$

Q4.
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 - $$9.9\times10^{-3}$$
Q5.
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?
Correct 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
Q6.
Match each living creature to its length.
Correct Answer:Tick,$$5\times10^{-3}$$ m

$$5\times10^{-3}$$ m

Correct Answer:Ant,$$0.2\times10^{1}$$ mm

$$0.2\times10^{1}$$ mm

Correct Answer:Ladybird ,$$1.1\times10^{-2}$$ m

$$1.1\times10^{-2}$$ m

Correct Answer:Tarantula ,$$13\times10^{-2}$$ m

$$13\times10^{-2}$$ m

Correct Answer:Snake,$$1\times10^{2}$$ cm

$$1\times10^{2}$$ cm