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Question: 1 micrometer is _________ kilometer. A. \({10^{ - 9}}\) B. \({10^{ - 8}}\) C. \({10^{ - 10}}\)...

1 micrometer is _________ kilometer.
A. 10−9{10^{ - 9}}
B. 10−8{10^{ - 8}}
C. 10−10{10^{ - 10}}
D. 108{10^8}

Explanation

Solution

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:
⇒\Rightarrow1 km = 1000 m.
1 micrometer is equal to 1106\dfrac{1}{{{{10}^6}}} of a meter, as given below;
⇒\Rightarrow1 μ\mu m = 10−6{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 106{10^6}micrometers.
Here we know that as already discussed before one micrometer is equal to 10−6{10^{ - 6}}of a meter, as given below:
⇒1μ\Rightarrow 1\mum = 10−6{10^{ - 6}}m
But we know that a thousand meters makes one kilometer.
⇒1\Rightarrow 1km = 103{10^3}m.
⇒10−3\Rightarrow {10^{ - 3}}km = 1 m.
∴1\therefore 1m = 10−3{10^{ - 3}}km.
Now converting one micrometer to kilometer, as given below:
Substitute the 1 m expression in the equation 1μ1\mu m = 10−6{10^{ - 6}}m, as given below:
⇒1μ\Rightarrow 1\mum = 10−6(10−3){10^{ - 6}}({10^{ - 3}})km
⇒1μ\Rightarrow 1\mum = 10−9{10^{ - 9}}km
Thus 1 micrometer is 10−9{10^{ - 9}}kilometer.

1 micrometer is 10−9{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:
⇒1\Rightarrow 1km = 1000 m , and hence 1 m = 10−3{10^{ - 3}}km.
⇒1\Rightarrow 1m = 100 cm, and hence 1 cm = 10−2{10^{ - 2}}m.
⇒1\Rightarrow 1cm = 10 mm and hence 1 mm = 10−1{10^{ - 1}}cm.
⇒1\Rightarrow 1 μ\mu m = 10−6{10^{ - 6}} m.