Question

How do you write \[5.3\times {{10}^{-3}}\] in standard form?

Answer 1

Hint: In this problem, we have to convert the scientific notation to the normal or standard notation. We should know that in scientific notation, a number is written as \[a\times {{10}^{n}}\], where n is an integer. To convert the scientific notation to its standard form, we just need to multiply the power \[{{10}^{n}}\], this means moving the decimal point n digits to the right if multiplying or to the left if dividing. In this problem, we can multiply 0.001 to the number 5.3 by moving the decimal point left side, to get the standard form.

Complete step by step solution:
We know that, the given scientific notation to be converted into a standard notation is,
\[5.3\times {{10}^{-3}}\]
We know that, \[{{10}^{-3}}\] can be written as 0.001.
We can write 0.001 instead of \[{{10}^{-3}}\] in the given scientific notation, we get
\[\Rightarrow 5.3\times 0.001\]
Now we can multiply both the numbers, we get
\[\Rightarrow 0.0053\]
Here we have moved the decimal point 3 points to the left.
Therefore, the standard notation of \[5.3\times {{10}^{-3}}\] is \[0.0053\].

Note: Students make mistakes moving the decimal point, which should be concentrated. We should also know that, while converting the scientific notation to standard notation, if we multiply the decimal number with\[{{10}^{n}}\], we have to move the decimal point n digits to the right side, if we divide the decimal number with\[{{10}^{n}}\], we have to move the decimal point n digits to the left side.