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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

      To help you plan your 10 maths lesson on: Subtracting numbers in standard form, download all teaching resources for free and adapt to suit your pupils' needs...