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Question: The ratio of one micron to one nanometre is \( {\text{A}}{\text{. 1}}{{\text{0}}^3} \\\ {...

The ratio of one micron to one nanometre is
A. 103 B. 10−3 C. 10−6 D. 10−1  {\text{A}}{\text{. 1}}{{\text{0}}^3} \\\ {\text{B}}{\text{. 1}}{{\text{0}}^{ - 3}} \\\ {\text{C}}{\text{. 1}}{{\text{0}}^{ - 6}} \\\ {\text{D}}{\text{. 1}}{{\text{0}}^{ - 1}} \\\

Explanation

Solution

One micron is equal to one micrometre which is 106{10^6} times smaller than one metre. One nanometer is 109{10^9} times smaller than one metre. By taking the ratio of these values we can obtain the required solution.

Complete step by step answer:
To measure shorter lengths than cm, there are units defined as given below. Since metre is the S.I. unit of length, all these lengths are related to metre as follows.
Micrometre: 1μm=10−6m1\mu m = {10^{ - 6}}m
Nanometre: 1nm=10−9m1nm = {10^{ - 9}}m
We also call micrometre as one micron. The ratio of one micron to one nanometre is given as
1μm1nm=10−610−9=103\dfrac{{1\mu m}}{{1nm}} = \dfrac{{{{10}^{ - 6}}}}{{{{10}^{ - 9}}}} = {10^3}
This is the required answer.

So, the correct answer is “Option A”.

Additional Information: The unit of length refers to an internationally accepted standard unit used for measuring length. The most commonly used system is the S.I. system of units. In this system, the unit of length is metre (m). There is another system which is used for units called the C.G.S. system of units. In the C.G.S. system the unit of length is centimetre (cm). The unit metre and centimetre is related to each other as follows:
1m=100cm1m = 100cm Or 1cm=10−2m1cm = {10^{ - 2}}m
The other units for measuring distances shorter than a centimetre are given as
Millimetre: 1mm=10−3m1mm = {10^{ - 3}}m
Picometre: 1pm=10−12m1pm = {10^{ - 12}}m
Femtometre: 1fm=10−15m1fm = {10^{ - 15}}m
We can also define bigger units of length as follows:
Kilometre: 1km=103m1km = {10^3}m
We can go beyond this in units of million (106{10^6}), billion (109{10^9}) and trillion (1012{10^{12}}) and so on.
For very large or astronomical distances, we have units like light year, Astronomical units defined as follows:
Light year: It is the distance travelled by light in one year.
1ly=1013km=1016m1ly = {10^{13}}km = {10^{16}}m
Astronomical unit: It is the distance between earth and sun.
1AU=149.6×106km=149.6×109m1AU = 149.6 \times {10^6}km = 149.6 \times {10^9}m

Note: We may go beyond femtometre also but with present scientific technology, length smaller than 10−15m{10^{ - 15}}m has not been observed or measured yet. All the lengths between these units are not officially named, instead they are expressed in terms of given units.