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.

Problem solving with standard form calculations

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

Which of the following is described here:  The middle (or average middle) value in an ordered data set.

What is the mode of the following? $$4.5\times10^3$$, $$4.5\times10^{-2}$$, $$4.5\times10^2$$, $$4.5\times10^3$$, $$4.2\times10^4$$.

Starting with the smallest number, put these numbers in ascending order.

Find the median of: $$4.5\times10^5$$, $$4.5\times10^3$$. $$4.2\times10^5$$, $$5.4\times10^3$$ and $$4.5\times10^4$$.

Convert $$4\times10^6 $$ m$$^3$$ into cm$$^3$$.

The volume of a football is $$4200$$ cm$$^3$$.  The volume of Wembley is $$4\times10^6 $$ m$$^3$$.  Assuming no gaps, approximately how many footballs will fit into Wembley stadium?

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 {{ }} and less than 10.

Calculate $$(4.6\times10^6)\div(2\times10^2)$$.

Calculate $$(5.4\times10^{5})\div(3\times10^{-2})$$.

Calculate $$480\text{ } 000\div(4\times10^{-2})$$.

Calculate $${(1.6\times10^4)\times(2\times10^{-5})}\over(6.4\times10^2)$$.  Give your answer in standard form.

A grain of sand has a mass of $$1.6\times10^{-5}$$ g.  How many grains of sand are there in $$5$$ kg?  Give you answer as an ordinary number.

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