Question

Multiplying and Dividing by Powers of 10 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:

Because we actually divide by 10 when a number is multiplied by 0.1.

Step-by-step explanation:

Let $a$ be a number.

When we multiply a number by 10:

$a \times 10 = 10 a$ (One '0' is increased in the number)

For example:

$23 \times 10 = 230$

Considering a decimal number:

$2.3 \times 10 = 23$

Multiplying a number with 0.1 (which is actually $\frac{1}{10}$) means dividing the number by 10.

$23\times 0.1 =23\times \frac{1}{10}=2.3$

Considering a decimal number:

$2.3 \times 0.1 = 2.3 \times \frac{1}{10} = 0.23$

Therefore, When multiplying a number by 0.1, move the decimal to the left.

Answer 2

Answer:

Sample Response: You move the decimal to the right when multiplying a number by 10 because you are making the number bigger. You move the decimal to the left when multiplying a number by 0.1 because you are making the number smaller.

Step-by-step explanation:

hope this helps