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Year 7

Exponential and fractional column headings

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

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New
New
Year 7

Exponential and fractional column headings

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

Download all resources
Share activities with pupils

Lesson details

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.

Common misconception

10^3 means 10 x 3

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

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.

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.
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).

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Starter quiz

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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

Exit quiz

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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: $$0.3059$$