Question

How do you write 7.4 nm in scientific notation?

Answer 1

Hint: Scientific notation is a means of expressing very large or small numbers by powers of ten so that the values are more easily understood. A number in scientific notation form is in the form \[A\times {{10}^{b}}\] where A is a rational number in decimal form. It helps to use the given number easily for bigger calculations.

Complete step by ste answer:
As per the given question, we need to express the given number in scientific notation. And, we are provided with the number 7.4nm.
We know that nm means nano meter and one nano meter is equal to 0.000000001 m, then
\[\Rightarrow 7.4nm=7.4\times 0.000000001m=0.0000000074m\]
To convert a n-digit number into scientific form by moving the decimal point at the right most point of the number by (n-1) times to the left side and multiplied by (n-1) powers of 10. If the number is a decimal number then we have to write it as a power of 10 such that there is only one digit in the decimal part.
When we write numbers in scientific notation, we want one digit after the decimal. This means we need to loop it only nine times to the right.
The number of times we looped it is our exponent, and since we looped right side, it is negative. If we loop it to the left side, then the power will be positive.
Here, for looping means we need to move the decimal point by \[{{9}^{th}}\] place to the right and multiply by 10 to the power -9. Thus, we get
\[\Rightarrow 0.0000000074=\dfrac{74}{10000000000}=\dfrac{7.4}{1000000000}=7.4\times {{10}^{-9}}\]
\[\therefore 7.4\times {{10}^{-9}}\] is the scientific notation of 7.4 nm.

Note:
In order to solve these types of problems, we should have enough knowledge about the scientific notation. We can find the scientific form of 7.4 nm by simply writing the digit 4 to the right of decimal and 7 to the left side of the decimal and multiplying with \[{{10}^{-9}}\](\[\because \]\[1nm={{10}^{-9}}m\]). We should avoid calculation mistakes while dividing with multiples of 10.