Question

How do you write \[2.7\times {{10}^{7}}\] in decimal form?

Answer 1

Hint: Multiply the decimal number 2.7 with \[{{10}^{7}}\] and move the decimal point 7 places to the right from its original position to get the answer. But first understand the meaning of scientific notation of a number.

Complete step by step answer:
Here, we have been provided with the exponential form of a number given as \[2.7\times {{10}^{7}}\] and we are asked to write it in the decimal form. But first we need to understand about the term ‘scientific notation’.
A scientific form is a way of writing down a very large or a very small number easily. For example: - let us consider a very large number like: - 50000000, so we can write this number in scientific form by considering a decimal point after the digit 5 and writing the number of places we have jumped as the positive exponent of 10. So, we have,
\[\Rightarrow 50000000=5.0\times {{10}^{7}}\]
Here, exponent is 7 because we jumped 7 places to the left to move the decimal point.
Small numbers are also written in scientific form. However, instead of the index being positive, it will be negative. This is because here the number will be very small in comparison to 1 and we will jump the decimal point to the right. For example: - let us consider the number 0.0000006, so it can be represented in scientific form as: -
\[\Rightarrow 0.0000006=6.0\times {{10}^{-7}}\]
Here, the exponent is -7 because we jumped 7 places to the right to move the decimal point.
Let us come to the question, here we have to change \[2.7\times {{10}^{7}}\] into decimal form. So, we need to apply the reverse process of writing a large number into scientific notation. As we can see that the exponent is 7 so it means we have moved the decimal point to the left while writing the scientific form. That means to change it into the decimal form again we need to move the decimal point to the right while multiplying 2.7 with \[{{10}^{7}}\]. So, moving 7 places to the right from the original position of the decimal point, we get,
\[\Rightarrow 2.7\times {{10}^{7}}=27000000\]
Hence, 27000000 is our answer.

Note:
One may note that the scientific form of a number is also known as standard form or standard index form. We generally use these representations to make our calculations easy. Certain formulas of exponents and powers are used in scientific calculations and the concept of rounding off is introduced.