Question

Express the number appearing in the following statements in the standard form:
I.Micron is equal to $ \dfrac{1}{{1000000}}{\text{m}} $
II.Charge of an electron is 0.000,000,000,000,000,000,16 coulomb
III.Size of bacteria is 0.0000005 m
IV.Size of plant cell is 0.00001275 m
V.Thickness of a thick paper is 0.07 mm

Answer 1

Hint: As, it is a question from exponent and power, here in these question the power of the base, i.e., 10 is to be taken into consideration, as whenever any base has power of negative number, then the reciprocal of the base is taken, as by taking the reciprocal of any number then its power sign is changed. We need to expand the base with the help of the power.

Complete step-by-step answer:
I.Given, 1 Micron is equal to $ \dfrac{1}{{1000000}}{\text{m}} $ .
We need to find a standard form of the given expression.
As, 1000000 can be written as $ {10^6} $ .
Therefore, $ \dfrac{1}{{1000000}}{\text{m}} $ can be written as $ \dfrac{1}{{{{10}^6}}} $ .
We know $ \dfrac{1}{{{a^n}}} = {a^{ - n}} $ .
So, we can write $ \dfrac{1}{{{{10}^6}}} $ as $ {10^ - }^6 $ .
Therefore, the standard form of $ \dfrac{1}{{1000000}}{\text{m}} $ will be $ {10^ - }^6 $ .

II.Given, charge of an electron is 0.000,000,000,000,000,000,16 coulomb
We need to find a standard form of the given expression.
As, 0.000,000,000,000,000,000,16 can be written as $ \dfrac{{16}}{{1000,00,000,000,000,000}} $ .
As, 1000,000,000,000,000,000 can be written as $ {10^{18}} $ .
Therefore, $ \dfrac{{16}}{{1000,00,000,000,000,000}} $ can be written as $ \dfrac{{16}}{{{{10}^{18}}}} $ .
We know $ \dfrac{1}{{{a^n}}} = {a^{ - n}} $ .
So, we can write $ \dfrac{{16}}{{{{10}^{18}}}} $ as $ 16 \times {10^{ - 18}} $ .
Charge of an electron is 0.000,000,000,000,000,000,16 coulomb can be written in standard form as $ 16 \times {10^{ - 18}} $ coulomb.

III.Given, Size of bacteria is 0.0000005 m
We need to find a standard form of the given expression.
As, 0.0000005 m can be written as $ \dfrac{5}{{10000000}} $ .
As, 10000000 can be written as $ {10^7} $ .
Therefore, $ \dfrac{5}{{10000000}} $ can be written as $ \dfrac{5}{{{{10}^7}}} $ .
We know $ \dfrac{1}{{{a^n}}} = {a^{ - n}} $ .
So, we can write $ \dfrac{5}{{{{10}^7}}} $ as $ 5 \times {10^{ - 7}} $ .
Therefore, the size of bacteria is 0.0000005 m and it can be written as $ 5 \times {10^{ - 7}} $ m.

IV.Given, Size of plant cell is 0.00001275 m
We need to find a standard form of the given expression.
As, 0.00001275 m can be written as $ \dfrac{{1275}}{{100000000}} $ .
As, 100000000 can be written as $ {10^8} $ .
Therefore, $ \dfrac{{1275}}{{100000000}} $ can be written as $ \dfrac{{1275}}{{{{10}^8}}} $ .
We know $ \dfrac{1}{{{a^n}}} = {a^{ - n}} $ .
So, we can write $ \dfrac{{1275}}{{{{10}^8}}} $ as $ 1275 \times {10^{ - 8}} $ .
Therefore, Size of the plant cell is 0.00001275 m which can be also written as $ 1275 \times {10^{ - 8}} $ m.

V.Given, Thickness of a thick paper is 0.07 mm
We need to find a standard form of the given expression.
As, 0.07 mm can be written as $ \dfrac{7}{{100}}{\text{mm}} $ .
As, 100 can be written as $ {10^2} $ .
Therefore, $ \dfrac{7}{{100}} $ can be written as $ \dfrac{7}{{{{10}^2}}} $ .
We know $ \dfrac{1}{{{a^n}}} = {a^{ - n}} $ .
So, we can write $ \dfrac{7}{{{{10}^2}}} $ as $ 7 \times {10^{ - 2}} $ .
Therefore, the thickness of a thick paper is 0.07 mm which can be written as $ 7 \times {10^{ - 2}} $ mm.

Note: Power or exponent of any number is the number of times any particular number is being multiplied by it. Whenever in any expression there is involvement of two things base and power that number is called an exponential number.