Question

How do you write 0.0173 in scientific notation?

Answer 1

Hint: First convert the decimal to fraction by dividing ${{10}^{4}}$. Then bring it to the multiplication form by taking the power as negative. Write 173 as $1.73\times {{10}^{2}}$ and do the necessary calculation to obtain the required result.

Complete step by step solution:
As we know, if there is ‘n’ number of digits after the decimal, then the denominator of fraction will be ${{10}^{n}}$
So, 0.0173 can be written in fraction as
\[0.0173=\dfrac{173}{{{10}^{4}}}\]
Again as we know if there is any power in division from, it becomes negative in multiplication form.
So, \[\dfrac{173}{{{10}^{4}}}\] can also be written as
$=173\times {{10}^{-4}}$
Scientific notation: In scientific notation, we have to place the decimal in such a way that there is one non-zero digit to the left of the decimal point.
So, $173\times {{10}^{-4}}$ can be written in scientific notation as
$=1.73\times {{10}^{2}}\times {{10}^{-4}}$ (Since 173 can be written as $1.73\times {{10}^{2}}$)
As we know ${{a}^{m}}\times {{a}^{n}}={{a}^{m+n}}$
So, ${{10}^{2}}\times {{10}^{-4}}={{10}^{2-4}}={{10}^{-2}}$
Now, our expression becomes
$=1.73\times {{10}^{-2}}$
Hence, the scientific notation of $0.0173=1.73\times {{10}^{-2}}$.
This is the required solution.

Note: We can directly write in scientific notation by moving the decimal only. The number of decimal places moved will be the exponent on 10. If we move the decimal to right then the exponent will be negative and if we move the decimal to left then the exponent will be positive. For example, for the scientific notation of 0.0173, we have to move 2 decimal places to the right. So, the exponent on 10 will be $-2$. Hence the scientific notation$=1.73\times {{10}^{-2}}$.