Question

How do you write 673.5 in scientific notation?

Answer 1

Hint: Here the basic concept which is going to be used is that we must know the general scientific notation form. Then, firstly, we will multiply and divide the given number by suitable ${10^n}$ where n is an integer and then convert it into scientific notation.

Complete Step by Step Solution:
As we know that, scientific notation is expressed in a form of $a.bcd \times {10^n}$ where $10 > a,b,c,d > 1$ (i.e. a,b,c,d must be between 1 and 10) and n is an integer
General scientific notation = $abcd \times {10^n}$
Here we have 673.5 which we have to convert into scientific notation
Now, we have to make 6.735 from 673.5. For that, we have to multiply and divide the given number by 100. We are multiplying and dividing the given number by 100 because decimal is present after three digits and we want it after the first digit so that it gets converted into scientific notation
$= 673.5 \times \dfrac{{100}}{{100}}$
We can also write it as
$=\dfrac{{673.5}}{{100}} \times 100$
$= 6.735 \times 100$
Now, we can write 100 as ${10^2}$
So, we get
$= 6.735 \times {10^2}$

Hence, the scientific notation of 673.5 is $6.735 \times {10^2}$

Note:
We should take care that decimal should be after the first digit in scientific notation. Whenever you are converting a number in scientific notation, focus on the place of decimal after how many digits it is, and then multiply it suitably. One more thing that when you are converting a number in the scientific notation form, multiply the given number only by ${10^n}$, where n is an integer, not by any other number.