Question

How do you write \[0.034\] in scientific notation?

Answer 1

Hint: Here, we will convert the given decimal number in Scientific notation by using the formula of scientific notation. Scientific notation is a way of expressing a number that is either too large or too small in a simpler form or in the decimal form. As the given number is already a decimal number so we will convert it to a multiple of 10.

Formula Used:
We can express the number \[N\] in the form of \[N = a \times {10^n}\] where \[1 \le a < 10\] and \[n\] is an integer.

Complete step by step solution:
We are given a decimal number \[0.034\].
Let \[N\] be the given decimal number. So, we get
\[ N = 0.034\]
We can express the number \[N\] in the form of \[N = a \times {10^n}\] where \[1 \le a < 10\] and \[n\] is an integer
Since the decimal point has to be moved two places to the right to convert it in the form of scientific notation, so \[n = - 2\]
\[ \Rightarrow N = 3.4 \times {10^{ - 2}}\] where \[a\] is greater than \[1\] and less than\[10\].

Therefore, the scientific notation of \[0.034\] is \[3.4 \times {10^{ - 2}}\].

Note:
We will follow the following steps to write a decimal number in the form of scientific notation. First, we will move the decimal point such that there exists only one non-zero digit to the left of the decimal point and then we will count the number of digits between the old decimal point and the new decimal point. The number of digits gives the power of \[10\] that is equal to \[{10^n}\]. If the decimal point is moved to the left, then the exponent \[n\] is positive and if the decimal point is moved to the right, then the exponent \[n\] is negative. Thus we need to remember these rules whenever we are writing a decimal number in scientific notation.