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 = \(\frac{6}{10^4}=6\,\times10^{-4}\)

(ii) 0.00000083 = \(\frac{8^3}{10^3}\) = \(\frac{8.3\times10}{10^3}\) = 8.3 x 10^(1-8) = 8.3 x 10^-7

(iii) 0.0000000534 = \(\frac{534}{10^{10}}\) = \(\frac{5.34\times10^2}{10^{10}}\) = 5.34 x 10^(2-10) = 5.34 x 10^-8

(iv) 0.0027 = \(\frac{27}{10^4}\) = \(\frac{27\times10}{10^4}\) = 2.7 x 10^(1-4) = 2.7 x 10^-3

(v) 0.00000165 = \(\frac{165}{10^3}=\frac{1.65\times10^2}{10^3}\) = 1.65 x 10^(2-8) = 1.65 x 10^-6

(vi) 0.00000000689 = \(\frac{689}{10^{11}}=\frac{6.89\times10^2}{10^{11}}\) = 6.89 x 10^(2-11) = 6.89 x 10^-9