Question

1 micrometer is _________ kilometer.
A. ${10}^{-9}$
B. ${10}^{-8}$
C. ${10}^{-10}$
D. ${10}^8$

Answer 1

Hint: First of all this is a very simple and a very easy problem. This problem deals with meter to kilometer conversion and micrometer to meter conversion and at last micrometer into kilometer conversion.
The meter conversion is as given below:
1 kilometer is equal to a thousand meters, as given below:
$\Rightarrow$1 km = 1000 m.
1 micrometer is equal to ${\displaystyle \frac{1}{{10}^6}}$ of a meter, as given below;
$\Rightarrow$1 $\mu$m = ${10}^{-6}$ m.

Complete step-by-step answer:
Given 1 micrometer, we have to convert it into kilometers.
We know that one kilometer is a thousand meters.
One meter is equal to a hundred centimeters.
And one centimeter is equal to ten millimeters.
One meter is also equal to ${10}^6$micrometers.
Here we know that as already discussed before one micrometer is equal to ${10}^{-6}$of a meter, as given below:
$\Rightarrow 1\mu$m = ${10}^{-6}$m
But we know that a thousand meters makes one kilometer.
$\Rightarrow 1$km = ${10}^3$m.
$\Rightarrow {10}^{-3}$km = 1 m.
$\therefore 1$m = ${10}^{-3}$km.
Now converting one micrometer to kilometer, as given below:
Substitute the 1 m expression in the equation $1\mu$m = ${10}^{-6}$m, as given below:
$\Rightarrow 1\mu$m = ${10}^{-6}({10}^{-3})$km
$\Rightarrow 1\mu$m = ${10}^{-9}$km
Thus 1 micrometer is ${10}^{-9}$kilometer.

1 micrometer is ${10}^{-9}$kilometer.

Note:
While solving this problem we need to understand that the meter conversion is very important and is very crucial in real life applications. Here are some conversions that we need to remember always, which are given below:
$\Rightarrow 1$km = 1000 m , and hence 1 m = ${10}^{-3}$km.
$\Rightarrow 1$m = 100 cm, and hence 1 cm = ${10}^{-2}$m.
$\Rightarrow 1$cm = 10 mm and hence 1 mm = ${10}^{-1}$cm.
$\Rightarrow 1$$\mu$m = ${10}^{-6}$ m.