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 for 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.

Dividing 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.

Standard form calculations

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 {{ }}.

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

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

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

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

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.

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

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

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

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

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

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

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

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?

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

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

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