Question

How do you write each number as a scientific notation 4100?

Answer 1

Hint: In this question, we are given a number in standard form and we need to change it in scientific notation. For this we need to change it in scientific notation. For this we need to change the number in $N\times {{10}^{a}}$ form where N is a number less than 10 i.e. it should lie between 0 to 9, a is the power to the 10 raised. The sign ‘a’ is determined if while changing to scientific notation we moved the decimal point to the right or to the left. If we move the decimal to the left, then ‘a’ is positive and if decimal is moved to the right, a is negative. Value of ‘a’ is given by the number of steps taken by decimal.

Complete step-by-step answer:
Here we are given the number in standard form as 4100. We need to change it in the scientific notation. For changing it into scientific notation we need it in the form as $N\times {{10}^{a}}$ where N lies between 0 and 9. For this, we will try to move the decimal point. As we know, every integer can be considered as having a decimal point after one's place. So we have 4100.0 actually. Let us change it to $N\times {{10}^{a}}$. For N first, let us move the decimal to the left by 3 places so the value of N becomes 4.1000 or 4.1 which lies between 0 and 9. Now for the exponential part. We need to learn rules to determine the value of a. If we move the decimal point to the right, the value of ‘a’ becomes negative and if we move the decimal point to the left value of ‘a’ becomes positive. The value of ‘a’ is determined by the number of places it has moved.
Since here we have moved the decimal point to the left by 3 digits so the value of a will be 3. Hence the overall number becomes $4.1\times {{10}^{3}}$.
Therefore the scientific notation of 4100 is given by $4.1\times {{10}^{3}}$.

Note: Students should note that, after decimal points the zeroes at last can be ignored i.e. we can write 4.1000 as 4.1 only. Make sure to check that N lies between 0 and 9. Take care of the sign of ‘a’ as well.