Question

How many times smaller is 2 × 10-3 than 4 × 10-2? PLEASE HELP

A.
20
B.
200
C.
2,000
D.
0.2

Answer 1

The required "option A) 20" is correct.

Explanation:

Let x be the smaller than 4 ×
`10^(-2)`.

To find, the number of times smaller is 2 ×
`10^(-3)` than 4 ×
`10^(-2)` = ?

∴ x =
`(4* 10^(-2))/(2* 10^(-3))`

= 2 ×
`10^(-2)` ×
`10^(3)`

Using the identity,

`a^(m)=(1)/(a^(-m))`

= 2 ×
`10^(-2+3)`

Using the identity,

`a^(m) *a^(n)=a^(m+n)`

= 2 ×
`10^(1)`

= 2 × 10

= 20

Thus, the required "option A) 20" is correct.