Question

How do you write $0.0025 \times 111.09$ in scientific notation?

Answer 1

Hint: A scientific notation means of expressing very large or small numbers by powers of ten so that the values are more easily understood.
For example: 1000 can be represented in scientific notation as \[1 \times {10^3}\].
In solving the question convert both the decimals and then multiply to get the required scientific notation.

Complete step-by-step answer:
A scientific notation is a method of expressing numbers that are too big and too small to be conveniently written in decimal form. The general form to write in scientific notation is,\[N \times {10^m}\],
Where N is the number between 1 and 10, but not 10 itself, and m is any integer.
Now given number is $0.0025 \times 111.09$,
Let’s convert both the decimals and then multiply.
First step is to move the decimal place to the left to create a new number from 1 to 10. For 0.0025 move the decimal 3 places so, we get N= 2.5 and for the second number i.e.,111.09 move the decimal 2 places so we get, N= 1.1109.
Now determine the exponent it will be the number of times we moved the decimal, now we moved the decimal 3 times for the first number and because we moved the decimal to the right, the exponent is negative, therefore, here \[m = - 3\], so we get, \[{10^{ - 3}}\], we moved the decimal, now we moved the decimal 2 times for the second number and because we moved the decimal to the right, the exponent is positive, therefore, here \[m = 2\], so we get, \[{10^2}\],
Now substitute the value of N and m in the general form of scientific notation \[N \times {10^m}\]for both the numbers, we get,\[2.5 \times {10^{ - 3}} \times 1.1109 \times {10^2}\],
Now simplifying we get, \[2.5 \times 1.1109 \times {10^{ - 1}}\],

\[\therefore \]The scientific notation of $0.0025 \times 111.09$ will be equal to \[2.5 \times 1.1109 \times {10^{ - 1}}\].

Note:
While writing the numbers in scientific notation we have to follow some rules and they are:
The scientific notations are written in two parts one is just the digits with the decimal point placed after the first digit, followed by multiplication with 10 to a power number of decimal point that puts the decimal point where it should be.
If the number is greater than 1 and multiplies by 10 then the decimal point has to move to the left and the power of 10 will be positive.
If the number is smaller than 1 means in the form of decimal numbers, then the decimal point has to move to the right and the power of 10 will be negative.