Question

What is the scientific notation of $ 0.01 $ ?

Answer 1

Hint: To convert the given decimal value into their scientific notation, write the term as a product of two numbers in which the first term is an integer/real number and the second one is an exponential term (power of ten). For this, first convert the value in terms of fraction and write the denominator in power of ten, or the exponential term.

Complete step by step solution:
We are given a decimal number, $ 0.01 $.
Since, we can see that the number of digits after the decimal is $ 2 $. So, divide only the real number value with no zero before decimal and no decimal point by $ 10 $ to the power of $ 2 $ and we get:
 $
  0.01 \\
   = \dfrac{1}{{{{10}^2}}} \;
  $
For scientific notation, we know that the term should be written in two terms first is the decimal/real value that we already have that is $ 1 $ , second, we need the exponential term for that multiply the numerator and denominator by $ {10^{ - 2}} $ .
 $ \dfrac{1}{{{{10}^2}}} \times \dfrac{{{{10}^{ - 2}}}}{{{{10}^{ - 2}}}} = \dfrac{{1 \times {{10}^{ - 2}}}}{{{{10}^2} \times {{10}^{ - 2}}}} $
Since, the base is the same in the denominator, that is $ 10 $ so, from the Law of radicals, we know that if the base is the same for some values in a multiplication, then their powers are added. For example- $ {p^a}.{p^b} = {p^{a + b}} $ .
Applying this in our equation obtained above for our denominator, we get:
 $ \dfrac{{1 \times {{10}^{ - 2}}}}{{{{10}^2} \times {{10}^{ - 2}}}} = \dfrac{{1 \times {{10}^{ - 2}}}}{{{{10}^{2 + \left( { - 2} \right)}}}} = \dfrac{{1 \times {{10}^{ - 2}}}}{{{{10}^0}}} = 1 \times {10^{ - 2}} $ .
And, we obtained the first term a real number and second part an exponential term, which represents that it is the scientific notation.
Therefore, the scientific notation of $ 0.01 $ is $ 1 \times {10^{ - 2}} $ .
So, the correct answer is “ $ 1 \times {10^{ - 2}} $ ”.

Note: Scientific notation is the way which is used to handle a very large number or very small number. It is represented as two terms in which the first is decimal/real number value and the second term is the exponential term.