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Year 9

Writing large numbers in standard form

I can write very large numbers in standard form and appreciate the real-life contexts where this format is usefully used.

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New
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Year 9

Writing large numbers in standard form

I can write very large numbers in standard form 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).

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 big numbers allows pupils to explore real life examples of very big numbers. Discuss with pupils which careers, industries, etc. will use large 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.
A number written in __________ form represents a repeated multiplication.
Correct answer: exponential
factorial
product
reciprocal
Q2.
Which of the following are equivalent to $$8000\times8000$$?
Correct answer: $$8\times1000\times8\times1000$$
Correct answer: $$64\times 10^6$$
Correct answer: $$6.4\times 10^7$$
$$6.4\times 10^6$$
$$64\times 10^7$$
Q3.
Which of the following are equivalent to $$3.5\times0.03$$?
$$\frac{35\times3}{10^2}$$
Correct answer: $$\frac{35\times3}{1000}$$
$$\frac{35\times3}{10000}$$
Correct answer: $$\frac{35\times3}{10^3}$$
Correct answer: $$\frac{105}{10^3}$$
Q4.
Match each number written in exponent form with its value.
Correct Answer:$$10^4$$,$$10 000$$

$$10 000$$

Correct Answer:$$10^5$$,$$100 000$$

$$100 000$$

Correct Answer:$${1} \over {10^2}$$ ,$$0.01$$

$$0.01$$

Correct Answer:$$10^0$$,$$1$$

$$1$$

Correct Answer:$$10^1$$,$$10$$

$$10$$

Correct Answer:$${1} \over {10^4}$$ ,$$0.0001$$

$$0.0001$$

Q5.
Which of the following calculations are equivalent to 400 × 700?
Correct answer: 4 × 100 × 7 × 100
4 × 100 × 7 × 1000
Correct answer: 2.8 × 100 000
28 000
Correct answer: 28 × 10 000
Q6.
Without using a calculator, work out 3.4 × 2.5.
Correct Answer: 8.5, 8.50

Exit quiz

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6 Questions

Q1.
Which of the following are written in exponential form?
Correct answer: $$2^4$$
$$5\times5\times5\times 5$$
Correct answer: $$3^6$$
Correct answer: $${4}^{-2}$$
$$(-3)\times( -3) \times( -3)$$
Q2.
Which of the following are written in standard form?
Correct answer: $${2.6}\times10^{4}$$
Correct answer: $${3.9}\times10^{2}$$
$${24}\times10^{3}$$
Correct answer: $${1.05}\times10^{7}$$
$${0.48}\times10^{5}$$
Q3.
Write $$34 000 000$$ in standard form.
$$34\times10^{6}$$
$$3.4\times10^{6}$$
$$0.34\times10^{8}$$
Correct answer: $$3.4\times10^{7}$$
$$3\times10^{7}$$
Q4.
Match each ordinary number to the equivalent number written in standard form.
Correct Answer:$$303 000$$,$${3.03}\times10^{5}$$

$${3.03}\times10^{5}$$

Correct Answer:$$33 000$$,$${3.3}\times10^{4}$$

$${3.3}\times10^{4}$$

Correct Answer:$$30 300$$,$${3.03}\times10^{4}$$

$${3.03}\times10^{4}$$

Correct Answer:$$303 $$,$${3.03}\times10^{2}$$

$${3.03}\times10^{2}$$

Correct Answer:$$3 300 000$$,$${3.3}\times10^{6}$$

$${3.3}\times10^{6}$$

Correct Answer:$$3300$$,$${3.3}\times10^{3}$$

$${3.3}\times10^{3}$$

Q5.
$${1.8}\times10^{4}$$ as an ordinary number is .
Correct Answer: 18000, 18 000, 18,000
Q6.
What is covered up on the calculator display?
An image in a quiz
$$\times10^{13}$$
Correct answer: $$\times10^{14}$$
$$\div10^{13}$$
$$\times10^{15}$$
$$\div10^{14}$$