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Question: 100m=_______nm. (A)\({10^{11}}\) (B)\({10^{ - 7}}\) (C)\({10^{ - 8}}\) (D) None of the ab...

100m=_______nm.
(A)1011{10^{11}}
(B)10−7{10^{ - 7}}
(C)10−8{10^{ - 8}}
(D) None of the above

Explanation

Solution

We know the relation between nanometer and meter. The nanometer is equal to one billionth or one thousand millionth of the meter. It is a unit of length. The relation between the nanometer and the meter is as shown below,
1nm=1×10−9m1nm = 1 \times {10^{ - 9}}m

Complete Answer:
We know the relationship between meter and nanometer. According to which nanometer is the 1109th\dfrac{{\text{1}}}{{{\text{1}}{{\text{0}}^{\text{9}}}}}^{\text{th}} part of the meter. Thus,
The relation between the meter and the nano-meter is given below.
1nm=1×10−9m or 109nm=1m1nm = 1 \times {10^{ - 9}}m{\text{ or }}{10^9}nm = 1m …..equation (1)
We want to find out the 100m into its corresponding nm. Let us use the above relation to find 100 meters in terms of nano-meter.
Let us multiply the equation (1) by multiplying both the sides with 100, we get the following.
1×10−9m×100m=1nm×100m1 \times {10^{ - 9}}m \times 100m = 1nm \times 100m
Let us simplify it. On simplification we get,

⇒100m=1nm×100m1×10−9m ⇒100m=1nm×100×1×109 ⇒100m=102×1×109nm ⇒100m=1×1011nm  \Rightarrow 100m = \dfrac{{1nm \times 100m}}{{1 \times {{10}^{ - 9}}m}} \\\ \Rightarrow 100m = 1nm \times 100 \times 1 \times {10^9} \\\ \Rightarrow 100m = {10^2} \times 1 \times {10^9}nm \\\ \Rightarrow 100m = 1 \times {10^{11}}nm \\\

Thus, 100m=1×1011nm100m = 1 \times {10^{11}}nm

∴\therefore The required answer 100m=1×1011nm100m = 1 \times {10^{11}}nm. Hence, option (A) is the correct option.

Additional information:
A nanometer is a unit of length in the metric system which is equal to one billionth of a meter (0.000000001m{\text{0}}{\text{.000000001m}}). One nanometer is equal to 1×10 - 9m{\text{1}} \times 1{{\text{0}}^{{\text{ - 9}}}}{\text{m}}. It is represented by nm. 1nm = 11000000000metres{\text{1nm = }}\dfrac{1}{{{\text{1000000000}}}}{\text{metres}}
A nanometer is used to express dimensions on an atomic scale, to specify the wavelength of electromagnetic radiation near the visible part of the spectrum.
Other units are the following.
Pico-meter (represented by p) is equal to1×10−121 \times {10^{ - 12}} .
Micrometer (represented by μ) is equal to1×10−61 \times {10^{ - 6}} .
Millimeter (represented by m) is equal to1×10−31 \times {10^{ - 3}} .
It should be noted that one nm is 80000 times finer/ thinner than the hair of a human being. The nano-meter was also known as the milli-micro-meter.

Note:
The conversion unit changes the units of one quantity to the other without affecting the value. A Student should use the conversion factor to change the units of quantity without any change in value.
Whenever we are asked to find out the unit and its conversions always look for the requirements and remember the unit conversions. For example meter to picometer, microcomputer, etc.