Question

How do you convert $0.0017$ to scientific notation?

Answer 1

Hint: We are given a number in decimal form. We have to write the equivalent number in scientific form. First, we will place the decimal after the first number to the right. Then, we will count the number of digits on the left of the decimal place. Then, write the value of count as a power of ten multiplied by the decimal number.
The number in scientific notation can be represented as:
$a \times {10^b}$

Complete step by step solution:
Given number is $0.0017$
For converting the number into scientific notation, move the decimal after the first whole number that is 1.
$ \Rightarrow 001.7$
Now, we will count the number of digits before the decimal in the number.
$ \Rightarrow b = 3$
Now, we will remove the zero before the decimal digit in the number to calculate the value of $a$
$ \Rightarrow a = 1.7$
Now, write the number in scientific form by substituting the values of $a$ and $b$.
$ \Rightarrow 1.7 \times {10^{ - 3}}$

Note: The students must remember that the exponent of the scientific number expresses the number of placeholders present, which means the number of places the decimal will move either to the left or right to the value of base. Also, the students please note that if the power of 10 is negative, then it represents the small number in standard form whereas if the power of 10 is positive, it will represent the large number.
The students please note that the question can be solved using an alternate method also which is described here.
Alternate method:
Another method to write the number in scientific form is by assuming that the decimal number is placed at the end of the number $0.0017$
Then, we will move the decimal to the right by $3$ places such that the decimal is placed after the first digit of the number.
$ \Rightarrow 001.7$
Now, we will remove the zero before the decimal digit in the number to calculate the value of $a$.
$ \Rightarrow a = 1.7$
Now, write the number in scientific form by substituting the values of $a$ and $b$.
$ \Rightarrow 1.7 \times {10^{ - 3}}$