Question

When multiplying a number by 10, move the decimal to the right. When multiplying a number by 0.1, move the decimal to the left. Why?

Answer 1

Answer:

When multiplying a number by 10, move the decimal to the right. Whenever a number is multiplied by 10, the decimal is shifted to one place in the right.

Like : $7.36\times10=73.6$

When multiplying a number by 0.1, move the decimal to the left. This means the number is multiplied by $\frac{1}{10}$ or we can say the number is simply divided by 10.

So, when a number is divided by 10, the decimal is shifted to one place on the left.

Like : $44.56\times0.1=4.456$

or $\frac{44.56}{10}=4.456$

Answer 2

The reasons are:

1. Moving a decimal to the right implies a product of 10
2. Moving a decimal to the left implies a division by 10

How to determine the places of the decimals

The product of two numbers is represented as:

a * b

Assume that:

a = 5.73 and b = 10.

The expression becomes

5.73 * 10 = 57.3

Notice that, the decimal moved from the ten place to the hundred place after the numbers are multiplied.

This implies a product of 10

However, assume b = 0.1

The expression becomes

5.73 * 0.1 = 0.573

Notice that, the decimal moved from the ten place to the tenth place after the numbers are multiplied.

This implies a division by 10

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