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Subtracting numbers in standard form

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Lesson details

Learning outcome

I can appreciate the mathematical structures that underpin subtraction of numbers represented in standard form.

Key learning points

  1. When subtracting numbers represented in standard form, place value is an important consideration.
  2. If the power of 10 is the same for both numbers, it is easy to subtract.
  3. Standard form calculations can be done using a calculator.

Keywords

  • Standard form - 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

When subtracting numbers in standard form, pupils can also add the exponents of 10.

The use of the place value chart shows how the magnitude does not change to the sum of the powers of 10. The place value chart can support pupils to make the correct addition or subtraction of large or small numbers.

Teacher tip

Using MWB, ask pupils to write two numbers with different exponents to make 5 x 10^5. To support some pupils, they can convert to an ordinary number and write calculations. For more advanced, more use more significant figures. Extend further with the question 5 x 10^-5

Licence

This content is © Oak National Academy Limited (2025), 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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Prior knowledge starter quiz

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6 Questions

Q1.
Match each number in standard form to its equivalent ordinary number.

Correct Answer:$$7.5\times10^{-4}$$ ,0.00075

0.00075

Correct Answer:$$5.7\times10^{4}$$ ,57000

57000

Correct Answer:$$5.5\times10^{4}$$ ,55000

55000

Correct Answer:$$5.7\times10^{8}$$ , 570000000

570000000

Correct Answer:$$7\times10^{4}$$ ,70000

70000

Q2.
Without a calculator, work out 3.42 – 1.23.

Correct Answer: 2.19

Q3.
Without a calculator, work out 28.48 – 3.203.

Correct Answer: 25.277

Q4.
Without a calculator, work out 12.4 – 2.42 + 4.64.

Correct Answer: 14.62

Q5.
$$5^3 – 5^2 + \sqrt{25}$$ =

Correct Answer: 105

Q6.
Match each number to a correct statement about that number.

Correct Answer:$$-9\times10^2$$ ,is negative

is negative

Correct Answer:$$9\times10^2$$ ,is positive and less than 1000

is positive and less than 1000

Correct Answer:$$9\times10^{-2}$$ ,is less than 1

is less than 1

Correct Answer:$$2\times10^{9}$$ ,is even and greater than 1000

is even and greater than 1000

Assessment exit quiz

Download exit quiz questions (PDF)

6 Questions

Q1.
Work out $$9.8\times10^5 - 6.8\times10^5 $$, giving your answer in standard form.

Correct answer: $$3\times10^5$$
$$3\times10^7$$
$$3\times10^{9}$$
$$3\times10^{10}$$

Q2.
Work out $$3\times10^{-8} - 1.8\times10^{-8} $$, giving your answer in standard form.

$$1.2\times10^{-16} $$
$$1.2\times10^{-9} $$
Correct answer: $$1.2\times10^{-8} $$
$$1.2\times10^{0} $$

Q3.
Work out $$2.4\times10^7 - 3\text{ } 700\text{ }000$$, giving your answer in standard form.

$$2.03\times10^4$$
Correct answer: $$2.03\times10^7$$
$$2.03\times10^9$$
$$2.03\times10^{11}$$

Q4.
Work out $$4.9\times10^6- 280\text{ }000$$, giving your answer in standard form.

$$4.62\times10^2$$
$$4.62\times10^3$$
$$4.62\times10^4$$
$$4.62\times10^5$$
Correct answer: $$4.62\times10^6$$

Q5.
Work out $$9.38 \times 10^{10} - 1 \text{ } 300 \text{ } 000 \text{ } 000$$. Give your answer in standard form.

$$92.5\times10^{10}$$
Correct answer: $$9.25\times10^{10}$$
$$0.925\times10^{9}$$
$$92.5\times10^{9}$$
$$9.25\times10^{9}$$

Q6.
$$9$$ mm − $$ 0.5$$ cm − $$2\times10^{-3}$$ m = metres.

$$2\times10^{-4}$$ m
$$3\times10^{-3}$$ m
Correct answer: $$2\times10^{-3}$$ m
$$3\times10^{-4}$$ m
$$1\times10^{-3}$$ m

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