When you multiply a number by 10, you are essentially scaling the number up by a factor of ten. Each digit in the number shifts one place to the left in a decimal representation, which increases the value of the number. For example:
- \(5.3 \times 10 = 53.0\) (moving the decimal one place to the right)
This makes sense because multiplying by 10 increases the quantity tenfold.
Conversely, when you multiply a number by 0.1, you are scaling the number down or reducing it to one-tenth of its value. As a result, each digit shifts one place to the right in the decimal representation, reducing the value of the number. For example:
- \(5.3 \times 0.1 = 0.53\) (moving the decimal one place to the left)
In summary, moving the decimal place to the right when multiplying by 10 increases the value, while moving it to the left when multiplying by 0.1 decreases the value. This reflects the effect of scaling the number up or down according to the factor by which you are multiplying.
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