Approximate this fraction (simple arithmetic)

Question

If I have $1.5\cdot10^{-5}=\frac{1.5}{10^5}$ , how can I rewrite (approximate) this fraction as $$ \approx \frac{1}{66.7\cdot 10^3}\quad ? $$ My calculator gives the exact answer $\frac{3}{200000}$, but how to approximate it as $\approx \frac{1}{66.7\cdot 10^3}$?

Answer 1

Note that $1.5=\frac{15}{10}=\frac{3}{2}$ .. So$$1.5\cdot10^{-5}=\frac32\cdot\frac{1}{100000}=\frac{3}{200000}=0.000015$$ So..This is in a sense the most accurate approximation.. What you have done $$\frac32=\frac{1}{\frac23}\approx\frac{1}{0.6666667}$$ You can also write this as $$\frac{1}{0.\overline6}$$

Answer 2

\begin{align}1.5\cdot10^{-5}&=\frac{1.5}{10^5}\\\\ &=\frac{15}{10^6}\\\\ &=\frac{15}{10 \times 100000}\\\\ &=\frac{3}{2 \times 100000}\\\\ &=\frac{3}{200000}\end{align}

This is what your calculator giving.

Now $$\frac 32 = 1.5$$

Then $$\frac {1.5}{100000} = 0.000015$$