Write each of the following numbers in standard form:

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

Solution:

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

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

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