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Year 10
Higher

Checking and securing understanding of writing large numbers in standard form

I can write very large 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 large numbers in standard form

I can write very large 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 large numbers, due to the number of digits involved.
  2. It can be more efficient to write these very large 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 astronomy, engineering, populations, etc.
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.
Standard form is when a number is written in the form $$A \times 10^n$$, (where ___________ and $$n$$ is an integer).
$$A < 10$$
$$1 ≤ A ≤ 10$$
Correct answer: $$1 ≤ A < 10$$
$$1 < A < 10$$
Q2.
Which of the following numbers are written in standard form?
$$287546\times10^{12}$$
Correct answer: $$9.8\times10^{-5}$$
Correct answer: $$9.4\times10^5$$
Correct answer: $$1\times10^9$$
$$9.4\div10^5$$
Q3.
Match each number written in exponent form with its place value.
Correct Answer:$$10^5$$,Hundred thousands

Hundred thousands

Correct Answer:$$10^4$$,Ten thousands

Ten thousands

Correct Answer:$$10^3$$,Thousands

Thousands

Correct Answer:$$10^2$$,Hundreds

Hundreds

Correct Answer:$$10^0$$,Ones

Ones

Q4.
Match each measurement to an equivalent measurement.
Correct Answer:4 km,4000 m

4000 m

Correct Answer:4 cm ,40 mm

40 mm

Correct Answer:4 mm,0.4 cm

0.4 cm

Correct Answer:4 m,400 cm

400 cm

Q5.
Starting with the smallest, put these measurements in order of size.
1 - 3 cm
2 - 3000 mm
3 - 30 m
4 - 3 km
Q6.
0.03 km + 4.9 m + 560 mm is equal to centimetres.
Correct Answer: 3546, 3546 cm

Exit quiz

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6 Questions

Q1.
Match each number to its standard form equivalent.
Correct Answer:340 000 ,$$3.4\times10^5$$

$$3.4\times10^5$$

Correct Answer:3400,$$3.4\times10^3$$

$$3.4\times10^3$$

Correct Answer:430 000 ,$$4.3\times10^5$$

$$4.3\times10^5$$

Correct Answer:4 300 000 ,$$4.3\times10^6$$

$$4.3\times10^6$$

Q2.
Which of the following numbers have not been written in standard form?
Correct answer: $$44.4\times10^5$$
$$4.4\times10^5$$
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:$$44\times10^5$$ ,$$4.4\times10^6$$

$$4.4\times10^6$$

Correct Answer:$$0.4\times10^5$$ ,$$4\times10^4$$

$$4\times10^4$$

Correct Answer:$$0.34\times10^5$$,$$3.4\times10^4$$

$$3.4\times10^4$$

Correct Answer:$$340\times10^5$$ ,$$3.4\times10^7$$

$$3.4\times10^7$$

Correct Answer:$$34\times10^5$$ ,$$3.4\times10^6$$

$$3.4\times10^6$$

Q4.
Starting with the smallest, put these numbers into ascending order.
1 - $$13 \text{ }400$$
2 - $$49\text{ } 000$$
3 - $$3.9\times10^{5}$$
4 - $$78.2\times10^{4}$$
5 - $$9.9\times10^{5}$$
Q5.
Starting with the place with the smallest population, put these towns and cities in ascending order of population size.
1 - Bath: $$0.95\times10^5$$
2 - Preston: $$313\times10^3$$
3 - Leeds: $$4600\times10^2$$
4 - Nottingham: $$7.3\times10^5$$
Q6.
Saturn is $$1.43\times10^9$$ km from the Sun. Neptune is further from the Sun than Saturn. Which of these lengths could show the distance from the Sun to Neptune?
Correct answer: $$4\text{ } 500\text{ }000\text{ }000$$ km
$$22\text{ }800\text{ }000\text{ }000\text{ }000$$ cm
$$1.43\times10^{12}$$ m
$$150\text{ } 000 \text{ }000\text{ }000$$ m