Multiplying by a multiple of 10 is understood through place value: for example, means 6 groups of 3 tens, or tens, giving 18 tens, or 180. The factor 30 is decomposed as , so the resulting product has one additional place-value shift rather than a zero being appended mechanically; this reasoning supports multiplication of larger whole numbers and the standard algorithm.
To multiply by a multiple of , first think about the place value in the second factor.
For example, solve:
Rewrite as tens:
This means is groups of tens:
Since tens equal hundred, tens equal :
Therefore,
The factor has one ten, so the product shifts one place value to the left from , giving .
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