Question

How do you write $ 213 $ in scientific notation?

Answer 1

Hint: Scientific notation can be expressed as the means of expressing very large numbers by powers of ten so that the values are more easily understood. The standard form for the scientific notation can be expressed as $ a \times {10^b} $ where $ \left| a \right| < 10 $ here we will convert the given number in scientific notation by framing the number for “a” by taking every number from the first non-zero number to the last non zero number.

Complete step by step solution:
Take the given number: $ 213 $
Since we have to frame “a” such that it is less than $ 10 $ . So we move the decimal point right of $ 213 $ up to 2 places.
Therefore, $ a = 2.13 $
Since we moved the decimal point up to 2 places we have,
 $ b = 2 $
Now, placing the values of “a” and “b” in the standard form: $ a \times {10^b} $
 $ \Rightarrow 2.13 \times {10^2} $
Hence, the scientific notation of $ 213 $ is $ 2.13 \times {10^2} $
So, the correct answer is “ $ 2.13 \times {10^2} $ ”.

Note: Be careful in shifting the decimal point. Always remember there will be only one single digit before the decimal point and product of ten which can have any number of powers. Power can be positive or negative. Also, the above solution can be done in single step using the concepts that when you move decimal point from right hand to left hand side the power to ten is positive while when you move decimal from left hand side to the right hand side the power will become negative, you can cross check for it which gives us the original value only.