Question

How do you write $3\times {{10}^{3}}$ in decimal notation?

Answer 1

Hint: Here in this question, decimal notation means representing the numbers in decimal form. In question, it is given in scientific notation. This notation is used to represent numbers which are very huge or very tiny in a form of multiplication of a single-digit number and 10 raised to the power of the respective exponent. The exponent here is 3 that means the number is very large.

Complete step by step answer:
Now, let’s discuss the question.
As we know that scientific notation is a form of presenting very large numbers or very small numbers in a simpler form. It helps us to represent the numbers which are very huge or very tiny in a form of multiplication of a single-digit number and 10 raised to the power of the respective exponent. We can also say that the exponent is positive if the number is very large and it is negative if the number is very small. There is a specific way to represent the scientific notation. It is represented as:
$\Rightarrow a\times {{10}^{b}};1\le a<10$
Here, a can be any number in the range of 1 to 10 including 1 but excluding 10. The reason for excluding 10 is that it is used in the formation of exponent. And b is the power. Just like it is given in question, 3 is the power of 10.
Basically we will expand the number to convert from scientific notation to decimal notation.
In this question, $3\times {{10}^{3}}$is given. ${{10}^{3}}$ means 10 is multiplied 3 times. So when we expand, the power becomes the number of zeros which we will write after 1 and simultaneously we multiply 1 by 3. So when 1 is multiplied to 3 it will be 3 and after that we will put 3 zeros because we have the power of 3 on 10.
$\Rightarrow 3\times {{10}^{3}}\Leftrightarrow 3000$
So, this is the decimal notation.

Note: Students should take care that if the ‘a’ in $a\times {{10}^{b}};1\le a<10$ given in decimal, then it depends on the power of 10 that where the decimal gets shifted. It will shift to the right if the power is positive, for example:$4.9\times {{10}^{4}}=49000$, the power is positive so the decimal is shifted 4 times in right from its position. But if the power is negative, the decimal will shift to its left. For example: 0.000000097 = $9.7\times {{10}^{-8}}$, the power is negative, so decimal gets shifted to the left.