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      Writing large numbers in standard form

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      Lesson details

      Learning outcome

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

      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.

      Teacher tip

      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.

      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

      Download starter quiz questions (PDF)

      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

      Assessment exit quiz

      Download exit quiz questions (PDF)

      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: $$\times10^{14}$$
      $$\div10^{13}$$
      $$\times10^{15}$$
      $$\div10^{14}$$

      To help you plan your 9 maths lesson on: Writing large numbers in standard form, download all teaching resources for free and adapt to suit your pupils' needs...