Question

In this question we need to convert the decimal number $0.0036$ into scientific notation. In mathematics scientific notation is used to write very big and small numbers in an efficient way, so that performing calculations becomes easier. To convert a given number to scientific notation, multiply and divide it with a power of 10.

Answer 1

Hint: Let us try to solve this question of converting $0.0036$ into scientific notation. The given decimal number is in standard notation and we need to convert it to scientific notation. Here are the steps of converting a decimal number from standard notation to scientific notation.
1) Find the first non-zero digit after the decimal place.
2) Count the number of zeros after the decimal place and unto the first non-zero digit.
3) Now multiply and divide the decimal number by the power of $10$. Power of $10$ is an equal number of zeros after decimal place more than 1.
Now, let us apply the given steps to convert $0.0036$ into scientific notation.
In $0.0036$ we have two zeros after the decimal place and its first non-zero digit is $3$.
So the power of $10$ which we have to multiply and divide is ${10^3}$. So the decimal number
$0.0036$ in scientific notation can be written as,
$0.0036\, = \,\dfrac{{0.0036 \times {{10}^3}}}{{{{10}^3}}}$
And as we know from the rule of exponent that ${a^{ - b}} = \dfrac{1}{{{a^b}}}$. Using this we get,
$0.0036\, = \,3.6 \times {10^{ - 3}}$

Hence the decimal number $0.0036$ can be written into scientific notation as $3.6 \times {10^{ - 3}}$.

Note: This type of questions are easy to do and are asked in exams as short type answer questions. If the given number is not a decimal number and is like 345 then we multiply and divide this number by negative power of $10$ instead of positive power of $10$.