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Year 9

Multiples of 10 involving negative exponents

I can write any integer in a range of forms.

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New
New
Year 9

Multiples of 10 involving negative exponents

I can write any integer in a range of forms.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. A positive exponent tells you how many identical values must be multiplied together.
  2. Dividing by 10^n is the same as multiplying by its reciprocal.
  3. A negative exponent tells you how many reciprocals of the base must be multiplied together.
  4. a^(−3) = 1/a^3

Keywords

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

Common misconception

A negative exponent implies that the entire value is negative.

Refer back to the table showing the structure of how the negative exponents occur and highlight that none of the decimal values are negative.

Ensure that you have place value grids accessible with the exponents of 10 included.
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 prime number is an integer greater than one with exactly factors.
Correct Answer: 2, two
Q2.
Which of the following products only use prime numbers?
Correct answer: 2 × 2 × 13
2 × 6 × 13
2 × 9 × 13
Correct answer: 2 × 3 × 5 × 17
Q3.
Write 300 as a product of its prime factors.
4 × 3 × 25
Correct answer: 2² × 3 × 5²
4 × 3 × 5²
2² × 3 × 25
2² × 3 × 5
Q4.
Use the fact that 60 = 2² × 3 × 5 to write 300 as a product of its prime factors.
2² × 3² × 5
Correct answer: 2² × 3 × 5²
2² × 3² × 5²
2 × 3 × 5²
Q5.
Use the fact that 60 = 2² × 3 × 5 to write 30 as a product of its prime factors.
2² × 3 × 5 ÷ 2
Correct answer: 2 × 3 × 5
2² × 5
2 × 3 × 5²
Q6.
If 52 = 2² × 13 and 175 = 5² × 7, which of the following is the most useful arrangement to calculate 175 × 52?
2 × 2 × 13 × 5 × 5 × 7
2 × 13 × 2 × 5 × 5 × 7
Correct answer: 2 × 5 × 2 × 5 × 13 × 7
2 × 7 × 2 × 5 × 13 × 5

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

$$10^{-4}$$

Correct Answer:$${1}\over{100 000}$$,$$10^{-5}$$

$$10^{-5}$$

Correct Answer:$${1}\over{1 000 000}$$,$$10^{-6}$$

$$10^{-6}$$

Q3.
Match each decimal to its equivalent exponential form.
Correct Answer:$$0.002$$,$$2\times10^{-3}$$

$$2\times10^{-3}$$

Correct Answer:$$0.00004$$,$$4\times10^{-5}$$

$$4\times10^{-5}$$

Correct Answer:$$0.2$$,$$2\times10^{-1}$$

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

Correct Answer:$$0.005$$,$$5\times10^{-3}$$

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

Correct Answer:$$0.000005$$,$$5\times10^{-6}$$

$$5\times10^{-6}$$

Correct Answer:$$0.0004$$,$$4\times10^{-4}$$

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

Q4.
$$3\times10^{-2}+2\times10^{-5}+8\times10^{-6}$$ represents the number
Correct Answer: 0.030028, 0.030 028
Q5.
Which of the following is not an alternative way of writing 2400?
$$24\times10^2$$
$$24 000\div10$$
Correct answer: $$240 000\div10^3$$
$$2.4\times10^3$$
$${{240}\over{10}}\times10^2$$
Q6.
Which of the following is not an alternative way of writing 12 000?
Correct answer: $$1.2\times10^3$$
$${{1200}\over{10^2}}\times10^3$$
$$120 000\times10^{-1}$$
$$1.2\times10^4$$
Correct answer: $${{120}\over{10^3}}\times10^4$$