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

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

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 in addition and multiplication.

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.

Multiplying numbers in standard form

Maths

In the prior unit, pupils formalised their understanding of the index laws. This understanding will allow them to perform calculations with values written in standard form more efficiently.

In this unit pupils will learn how to add, subtract, multiply and divide numbers written in standard form.

Standard form calculations

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

Calculate $$(4.6\times10^4)\times(2\times10^3)$$.

Calculate $$(3.8\times10^{-4})\times(2\times10)$$.

$$(2\times10^{-4})\times(23\times10^3)\times(2\times10^2)$$

$$(2\times10^{-4})\times(2.3\times10^3)\times(2\times10^2)$$

$$(2\times10^{-4})\times(2.3\times10^4)\times(2\times10^2)$$

$$(2\times10^{-4})\times(0.23\times10^5)\times(2\times10^2)$$

Aisha correctly rewrites the calculation $$(2\times10^{-4})\times23\text{ } 000\times(2\times10^2)$$ as an equivalent calculation using standard form. Which of these shows Aisha's calculation?

Calculate $$(2\times10^{-4})\times23\text{ } 000\times(2\times10^2)$$.

The radius of Saturn is $$6\times10^4$$ km.  What is the diameter of Saturn?  Give your answer in standard form.

Standard form is when a number is written in the form $$A\times10^n$$. Which of the following is true for $$A$$? 

Write $$456\text{ } 000$$ in standard form.

Write $$0.000\text{ } 023\text{ } 5$$ in standard form.

Simplify $${x^8\times x^{-3}}\over x^4$$.

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