Question:
Express each of the following in standard form:
(i) 345
(ii) 180000
(iii) 0.000003
(iv) 0.000027
Solution:
(i) $345=3.45 \times 100=3.45 \times 10^{2}$
(ii) $180000=18 \times 10000=18 \times 10^{4}=1.8 \times 10 \times 10^{4}=1.8 \times 10^{(1+4)}=1.8 \times 10^{5}$
(iii) $0.000003=\frac{3}{1000000}=3 \times 10^{-6}$
(iv) $0.000027=\frac{27}{100000}=\frac{27}{10^{6}}=\frac{2.7 \times 10}{10^{6}}=2.7 \times 10^{(1-6)}=2.7 \times 10^{-5}$