Question

Write each of the following numbers in standard form:
(i) 0.0006
(ii) 0.00000083
(iii) 0.0000000534
(iv) 0.0027
(v) 0.00000165
(vi) 0.00000000689

Answer 1

(i) $0.0006=\frac{6}{{10}^4}=6\times {10}^{-4}$

(ii) $0.00000083=\frac{83}{{10}^8}=\frac{8.3\times 10}{{10}^8}=8.3\times {10}^{(1-8)}=8.3\times {10}^{-7}$

(iii) $0.0000000534=\frac{534}{{10}^{10}}=\frac{5.34\times {10}^2}{{10}^{10}}=5.34\times {10}^{(2-10)}=5.34\times {10}^{-8}$

(iv) $0.0027=\frac{27}{{10}^4}=\frac{2.7\times 10}{{10}^4}=2.7\times {10}^{(1-4)}=2.7\times {10}^{-3}$

(v) 0.00000165 = $\frac{165}{{10}^8}=\frac{1.65\times {10}^2}{{10}^8}=1.65\times 10$^(2-8) = 1.65×10^-6

(vi) 0.00000000689 = $\frac{689}{{10}^{11}}=\frac{6.89\times {10}^2}{{10}^{11}}=6.89\times 10$^(2-11)= 6.89×10^-9