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Question

Mathematics Question on Use of Exponents to Express Small Numbers in Standard Form

Express the number appearing in the following statements in standard form.
(i) 1 micron is equal to 11000000\frac{1}{1000000} m
(ii) Charge of an electron is 0.000,000,000,000,000,000,16 coulomb.
(iii) Size of a bacteria is 0.0000005 m
(iv) Size of a plant cell is 0.00001275 m
(v) Thickness of a thick paper is 0.07 mm

Answer

(i) 1 micron is equal to 11000000\frac{1}{1000000} m
11000000\frac{1}{1000000} = 0.000001 = 1 × 10−6m


(ii) 0.00000000000000000016

0.00000000000000000016 =16100000000000000000000\frac{16}{100000000000000000000}
= 1.6 × 101020\frac{10 }{ 10^{20}}
= 1.6 × 10−19 coulomb


(iii) 0.0000005 m
0.0000005 m = 510000000\frac{5}{10000000}
=5107= \frac{5}{10^7}
= 5 × 10−7m


(iv) 0.00001275 m

0.00001275 m = 1275100000000\frac{1275}{100000000}
= 1.275 × 103108\frac{10^3}{10^8}
= 1.275 × 10−5m


(v) 0.07 mm
0.07 mm =7100\frac{ 7}{100}
=7102= \frac{7}{10^2}
= 7 × 10−2mm