Question

Express 0.0000000000085 In Standard Form.

Answer 1

Step 1: Calculating standard form

Given number is $0.0000000000085$

Write the decimal number in terms of fraction.

$\begin{array}{rcl}0.0000000000085& =& \frac{85}{10000000000000}(13zerosafter1)\\ Since,10000000000000& =& {10}^{13}\\ 0.0000000000085& =& \frac{85}{{10}^{13}}\\ or,0.0000000000085& =& 85\times {10}^{-13}\\ & & \end{array}$

$85$ is not a number between $1.0$ and $10.0$, So write, $85=8.5\times {10}^1$. Hence, we get,

$\begin{array}{rcl}0.0000000000085& =& 85\times {10}^{-13}\\ & =& 8.5\times {10}^1\times {10}^{-13}\\ & =& 8.5\times {10}^{1-13}(u\sin gformula,a^m\times a^n=a^{m+n})\\ & =& 8.5\times {10}^{-12}\end{array}$

Therefore, Standard Form of $0.0000000000085$is $8.5\times {10}^{-12}$.