Equivalent fractions can be used to calculate the quotient when dividing with two numbers represented in standard form.
Using your knowledge of the index laws, you can combine powers with the same base.
Standard form calculations can be done using a calculator.

Common misconception

When the dividing numbers written in standard form changing the multiplication symbol between the number and power of ten to a division symbol.

Encourage pupils to write any division as a fraction. This makes the maintenance of the multiplication symbol easier to see.

Keywords

Standard form - Standard form is when a number is written in the form A × 10n, (where 1 ≤ A < 10 and n is an integer).
Exponential form - When a number is multiplied by itself multiple times, it can be written more simply in exponential form.
Commutative - The commutative law states you can write the values of a calculation in a different order without changing the calculation; the result is still the same. It applies for addition and multiplication.
Associative - The associative law states that it doesn't matter how you group or pair values (i.e. which we calculate first), the result is still the same. It applies for addition and multiplication.

Before starting on this lesson have some divisions of numbers in standard form on the board and ask the pupils to work out the answers on MWBs. The approaches by different pupils can be shared with the class which will allow for discussion about efficiency.

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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6 Questions

Q1.

form is when a number is written in the form $$A × 10^n$$, where $$1 ≤ A < 10$$ and $$n$$ is an integer.

Correct Answer: Standard, standard

Q2.

Calculate $$(2.3\times10^7)\times(3\times10^2)$$

$$5.3\times10^9$$

Correct answer: $$6.9\times10^9$$

$$5.3\times10^{14}$$

$$6.9\times10^{14}$$

Q3.

Calculate $$(2.6\times10)\times(2\times10^{-2})$$.

$$4.6\times10^{-3}$$

$$5.2\times10^{-3}$$

$$4.6\times10^{-1}$$

Correct answer: $$5.2\times10^{-1}$$

Q4.

Jacob correctly rewrites the calculation $$(2\times10^{-2})\times110\text{ }000\times(3\times10^4)$$ as an equivalent calculation using standard form. Which of these shows Jacob's calculation?

$$(2\times10^{-2})\times(11\times10^4)\times(3\times10^4)$$

$$(2\times10^{-2})\times(11\times10^3)\times(3\times10^4)$$

$$(2\times10^{-2})\times(1.1\times10^4)\times(3\times10^4)$$

Correct answer: $$(2\times10^{-2})\times(1.1\times10^5)\times(3\times10^4)$$

Q5.

Calculate $$(2\times10^{-2})\times110\text{ }000\times(3\times10^4)$$.

$$6.1\times10^2$$

$$6.1\times10^7$$

$$6.6\times10^2$$

Correct answer: $$6.6\times10^7$$

Q6.

The radius of Jupiter is $$7.1\times10^4$$ km. What is the diameter of Jupiter? Give your answer in standard form.

$$3.55\times10^2$$ km

$$3.55\times10^4$$ km

$$14.2\times10^4$$ km

Correct answer: $$1.42\times10^5$$ km

$$1.42\times10^8$$ km

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6 Questions

Q1.

Standard form is when a number is written in the form $$A × 10^n$$. When numbers are written in standard form the value of $$A$$ must be greater than or equal to one and less than .

Correct Answer: 10, ten

Q2.

Calculate $$(9\times10^6)\div(3\times10^2)$$.

$$6\times10^3$$

Correct answer: $$3\times10^4$$

$$3\times10^3$$

$$3\div10^4$$

$$6\div10^4$$

Q3.

Calculate $$(5.6\times10^{5})\div(2\times10^{-3})$$.

$$3.6\times10^2$$

$$3.6\times10^8$$

$$2.8\times10^2$$

Correct answer: $$2.8\times10^8$$

$$2.8\times10^5$$

Q4.

Calculate $$96\text{ } 000\div(3\times10^{-1})$$.

$$3.2\times10^2$$

$$3.2\times10^3$$

$$3.2\times10^4$$

Correct answer: $$3.2\times10^5$$

$$3.2\times10^6$$

Q5.

Calculate $${(1.4\times10^4)\times(3\times10^{-5})}\over(8.4\times10^2)$$. Give your answer in standard form.

$$0.5\times10^{-3}$$

$$0.5\times10^{-4}$$

$$5\times10^{-3}$$

Correct answer: $$5\times10^{-4}$$

Q6.

A grain of rice has a mass of $$3\times10^{-2}$$ g. How many grains of rice are there in $$12$$ kg? Give you answer as an ordinary number.

Correct Answer: 400 000, 400000, 400,000