I can write very small numbers in the form A × 10^n, (where 1 ≤ A < 10) and appreciate the real-life contexts where this format is usefully used.
I can write very small numbers in the form A × 10^n, (where 1 ≤ A < 10) and appreciate the real-life contexts where this format is usefully used.
Exponential form - When a number is multiplied by itself multiple times, it can be written more simply in exponential form.
Associative law - The associative law states that a repeated application of the operation produces the same result regardless of how pairs of values are grouped. We can group using brackets.
Standard form - Standard form is when a number is written in the form A × 10^n, (where 1 ≤ A < 10 and n is an integer).
Pupils can incorrectly write a number in standard form or use a number in incorrect standard form whereby the number A does not satisfy 1 ≤ A < 10 or pupils use division of positive powers of 10.
Standard form represents a multiplicative relationship, so there should always be a multiplication. Embedding the understanding that negative exponents refer to 1/10^n is important. Using the place value chart with fractional and exponent form helps.
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$$60 300$$ - $${6.03}\times10^{4}$$
$$6 300 000$$ - $${6.3}\times10^{6}$$
$$603$$ - $${6.03}\times10^{2}$$
$$603 000$$ - $${6.03}\times10^{5}$$
$$6300$$ - $${6.3}\times10^{3}$$
$$63 000$$ - $${6.3}\times10^{4}$$
$$0.000402$$ - $${4.02}\times10^{-4}$$
$$42 000$$ - $${4.2}\times10^{4}$$
$$0.00042$$ - $${4.2}\times10^{-4}$$
$$4020$$ - $${4.02}\times10^{3}$$
$$0.00402$$ - $${4.02}\times10^{-3}$$
$$4200$$ - $${4.2}\times10^{3}$$
