Question

How do you write \[0.005\] in scientific notation?

Answer 1

Hint:
In the scientific notation, a number is written in the form of a product of a whole number and 10 raised to a suitable power. The number \[0.005\] can be converted into the scientific notation by repeatedly multiplying it by \[10\] until it becomes equal to \[5\].

Complete step by step solution:
In the scientific notation, a number is written in the form of \[a \times {10^b}\], where \[1 \le a < 10\] and \[b\] is an integer. This means that the scientific notation is a way to write a number as a product of a ten raised to an integral power and a number between one and ten. So for converting a number into the scientific notation, we have to multiply it repeatedly by \[10\] until we obtain a number greater than or equal to one, and less than ten.
Let us write the number given in the question as
\[x = 0.005\]
Multiplying the above equation by \[10\] we get
\[\begin{array}{l} \Rightarrow 10x = 0.005 \times 10\\ \Rightarrow 10x = 0.05\end{array}\]
The number obtained is \[0.05\], which is less than one. So we again multiply the above equation by \[10\] to get
\[\begin{array}{l} \Rightarrow 100x = 0.05 \times 10\\ \Rightarrow 100x = 0.5\end{array}\]
Still the number \[0.5\] is less than one. So we once again multiply the above equation by \[10\] to get
\[\begin{array}{l} \Rightarrow 1000x = 0.5 \times 10\\ \Rightarrow 1000x = 5\end{array}\]
So finally, we have obtained \[5\] which is greater than one. Now, for the scientific notation, we divide the above equation by \[1000\] to get
\[\begin{array}{l} \Rightarrow x = \dfrac{5}{{1000}}\\ \Rightarrow x = 5 \times {10^{ - 3}}\end{array}\]

Hence, the given number \[0.005\] is written in the scientific notation as \[5 \times {10^{ - 3}}\].

Note:
We can observe that the magnitude of the power of ten in the scientific notation obtained above is equal to the number of zeroes in \[0.005\]. The power of 10 is equal to the number of zeros after the decimal point. An expression that represents the repeated multiplication of a same number is known as power. Whereas, when a number is written with a power then the power becomes the exponent of that particular number. It shows how many times that particular number will be multiplied by itself. Hence, whenever we are given the multiplication of the same numbers then, we can express that number with an exponent.