Choose exam board for KS4 Computer Science (GCSE)
Choose exam board for KS4 English
Choose exam board for KS4 French
Choose exam board for KS4 Geography
Choose exam board for KS4 German
Choose exam board for KS4 History
Choose tier for KS4 Maths
Choose exam board for KS4 Music
Choose exam board for KS4 Physical education (GCSE)
Choose exam board for KS4 Religious education (GCSE)
Choose exam board for KS4 Spanish

      Exponential and fractional column headings

      Lesson details

      Learning outcome

      I can express place value column headings using both exponential and fractional representations.

      Key learning points

      1. The column headings for integer values can be expressed in different ways.
      2. The column headings for integer values can be expressed in exponential form.
      3. The column headings for non-integer values can be represented with fractions.

      Keywords

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

      • Fractional form - A number is in fractional form when it is displayed as one integer divided by another integer.

      Common misconception

      10^3 means 10 x 3

      10 x 3 = 30. 10^3 = 10 x 10 x 10 = 1000.

      Teacher tip

      By having ready to fill place value charts with headings expressed in different forms it will save pupils repeatedly copying the tables out. It will also provide potential scaffolding where needed.

      Licence

      This content is © Oak National Academy Limited (2026), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

      Loading...

      Prior knowledge starter quiz

      6 Questions

      Q1.
      __________ are all of the positive and negative whole numbers, and zero.

      Correct Answer: Integers

      Q2.
      Which of these is not a number?

      8
      0.8
      Correct answer: $$\div$$
      $$3\over8$$
      -83

      Q3.
      Which of these numbers are integers?

      Correct answer: 8
      0.8
      $$3\over8$$
      Correct answer: -83

      Q4.
      What is the value of the digit 3 in the number 8352?

      3
      8300
      350
      Correct answer: 300

      Q5.
      Starting with the smallest, put these numbers in order of size.

      1 - 83
      2 - 308
      3 - 380
      4 - 803
      5 - 3800
      6 - 8003

      Q6.
      Match the numbers with the correct expression for the value of their digit 3

      Correct Answer:8 300 000,3 x 100 000

      3 x 100 000

      Correct Answer:3 000 000,3 x 1 000 000

      3 x 1 000 000

      Correct Answer:8 003 000,3 x 1000

      3 x 1000

      Correct Answer:8 003,3 x 1

      3 x 1

      Correct Answer:38 000,3 x 10 000

      3 x 10 000

      6 Questions

      Q1.
      1, 10, 100, 1000, 10 000, 100 000, and 1 000 000 are all __________ of 10

      Correct Answer: powers

      Q2.
      Which of these represent the thousands column heading in exponential form?

      $$1\;000$$
      $$10\times10\times10$$
      $$10\times3$$
      Correct answer: $$10^3$$
      $$3^{10}$$

      Q3.
      Match the powers of ten from our place value chart to their correct exponential form.

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

      $$10^0$$

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

      $$10^1$$

      Correct Answer:100,$$10^2$$

      $$10^2$$

      Correct Answer:1000,$$10^3$$

      $$10^3$$

      Correct Answer:1 000 000,$$10^6$$

      $$10^6$$

      Correct Answer:1 000 000 000,$$10^9$$

      $$10^9$$

      Q4.
      What is this number? $$7\times10^5+2\times10^4+9\times10^3$$

      $$729$$
      $$702\;090$$
      Correct answer: $$729\;000$$
      $$752\;493$$
      $$729\times10$$

      Q5.
      In the number 0.78952 the 5 is in which place value column? Give your answer in fractional form.

      Correct answer: $$1\over10\space000$$
      $$1\over1000$$
      $$0.0001$$
      $$0.0005$$

      Q6.
      Write this number in decimal form. $${3\times{1\over10}}+{5\times{1\over1000}}+{9\times{1\over10\space000}}$$

      $$0.359$$
      $$0.3590$$
      $$95\;030$$
      $$0.3509$$
      Correct answer: $$0.3059$$

      To help you plan your 7 maths lesson on: Exponential and fractional column headings, download all teaching resources for free and adapt to suit your pupils' needs...