Question

What is the number $0.00125$ expressed in scientific notation?

Answer 1

Hint: To express the numbers in a scientific notation, you need to convert this value from a fraction into a decimal. A number expressed in scientific notation is in the form \[a \times {10^n}\]. where, \[1 \leqslant a < 10\] and \[n\] is an integer. The number \[n\] is known as an order of magnitude. The number a is the coefficient of the scientific notation and is normally greater than or equal to \[1\] and less than \[10\].

Complete step-by-step solution:
The given number is \[0.00125\].
We have to express the given number as scientific notation.
This means we have to write \[0.00125\] as a number between one and ten.
In this step we move the first decimal point to the left side, so we have the denominator as \[{10^1}\].
\[0.00125 = 0.0125 \times \dfrac{1}{{10}}\].
In this step we move Second decimal point to left side, so we get the denominator as \[{10^2}\]
\[0.00125 = 0.125 \times \dfrac{1}{{10}} \times \dfrac{1}{{10}}\]
In this step we move the third decimal point to the left side, we get the denominator as\[{10^3}\]
\[0.00125 = 1.25 \times \dfrac{1}{{10}} \times \dfrac{1}{{10}} \times \dfrac{1}{{10}}\]
\[0.00125 = 1.25 \times \dfrac{1}{{10 \times 10 \times 10}}\]
$ = 1.25 \times \dfrac{1}{{1000}}$
We know that we should write the number between one and ten.
In the last step we get the expression as \[0.00125 = 1.25 \times \dfrac{1}{{1000}}\] between the value one and ten.
To obtain the actual numeric value we started with we need to move the decimal point three places to the left.
That is we get, \[0.00125 = 1.25 \times \dfrac{1}{{1000}}\]
Thus we write this as ,
\[0.00125 = 1.25 \times {10^{ - 3}}\] in scientific notation.
Therefore the solution for the expression is \[0.00125 = 1.25 \times {10^{ - 3}}\].

Note: Scientific notation does is it shifts your numbers. So the first non zero digit is a whole number and the rest are expressed as decimals. It then multiplies there by a power of ten, where the power represents the number of positions the decimal points moves.