Question

How do you convert \[2.14\times {{10}^{-4}}\] into standard form?

Answer 1

Hint: The scientific form of a number is a special notation in which the number can be written without changing its value. In scientific notation, the number is written with one digit to the left of the decimal and the remaining digits written to the right of the decimal. The number is then multiplied by a power of ten.
The standard form of a number can be written using the scientific form.

Complete step by step solution:
In this question, we are asked to write \[2.14\times {{10}^{-4}}\] in its standard form.
First, let’s write it in its scientific form. We know that the scientific form of a number is a special notation for a number of the form \[a\times {{10}^{n}}\], here a is a decimal number and n is an integer. The decimal number a has only 1 digit on the left side of the decimal point and the remaining digits on the right-hand side of the decimal point. It should be noted that the last digit on the right-hand side of the decimal should be non-zero.
Here the given number is \[2.14\times {{10}^{-4}}\] as we can see this number is already in the form
Multiplying and dividing the above number by 100, we get, \[a\times {{10}^{n}}\]. It satisfies all the conditions of scientific form.
Hence, \[2.14\times {{10}^{-4}}\] is a number written in scientific form.
To express it in standard form, we just have to multiply it by \[{{10}^{-4}}\].
We know that multiplying by \[{{10}^{-4}}\] means shifting the decimal point to left by four digits. We get \[0.000214\].
Thus, the standard form is \[0.000214\]

Note: Numbers that are in the range of \[\left( 0,1 \right)\] can also be written in scientific notation, but the scientific notation for these numbers is of form \[a\times {{10}^{-n}}\], here \[n\] is a positive integer. Similarly, negative numbers can also be written in scientific notation with a negative sign before it.