Question

How do you convert $ 5.5 \times {10^{ - 3}} $ into standard notation?

Answer 1

Hint: The number given in the question is in scientific notation. As we know that, scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form while the standard notation is the normal way of writing numbers. So, to convert it in standard notation, we need to remove the multiplier $ {10^{ - 3}} $ and shift the decimal accordingly.

Complete step-by-step answer:
(i)
We are given,
 $ 5.5 \times {10^{ - 3}} $
As we know that, if the multiplier $ 10 $ has a positive exponent, it is a big number and the decimal should get shifted to the right. While if the exponent is a negative value, it is a small number so the decimal should get shifted to the left side.
So, in this question, $ 10 $ has a negative exponential power i.e., $ - 3 $ , therefore we know it is a small number and hence, decimal must move to the left side $ 3 $ times as the magnitude of the exponent is $ 3 $ .
Shifting the decimal one step towards left, we get:
 $ .55 \times {10^{ - 2}} $ [power of $ 10 $ became $ - 2 $ as we completed one out of three steps towards left]
If there is no digit before the decimal, we put $ 0 $ there. So, it will become:
 $ 0.55 \times {10^{ - 2}} $
(ii)
Now, we will shift the decimal one more step towards left and insert another $ 0 $ before the decimal
 $ 0.055 \times {10^{ - 1}} $
(iii)
As we can see, power of $ 10 $ has become $ - 1 $ , we need to shift the decimal for one last time.
So, we get:
 $ 0.0055 \times {10^0} $
i.e., $ 0.0055 $
Therefore, standard notation of $ 5.5 \times {10^{ - 3}} $ is $ 0.0055 $
So, the correct answer is “ $ 0.0055 $ ”.

Note: We could also have converted $ {10^{ - 3}} $ to $ \dfrac{1}{{1000}} $ and then we would divide $ 5.5 $ with $ \dfrac{1}{{1000}} $ to obtain the answer by shifting the decimal three times to left as the denominator as three zeroes in it. The answer obtained would be the same. Also, always remember if the power of $ 10 $ is negative, it is a small number and the decimal needs to be shifted to the left direction. Whereas, if the power is positive, it is a large number and the decimal needs to be shifted to the right direction.