Question

How do you write \[0.000223 \times {10^{ - 2}}\] in scientific notation?

Answer 1

Hint: In this problem, we will first convert the number \[0.000223\] to scientific notation and then add the powers of 10. We know that the scientific notation is a method of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

Complete step by step solution:
We know that all numbers in scientific notation or standard form are written in the form \[m \times {10^n}\], where \[m\] is a number between 1 and 10 which means that \[1 \leqslant \left| m \right| < 10{\text{ }}\] and the exponent n is a positive or negative integer. First we will convert the number \[0.000223\] to scientific notation. We can convert \[0.000223\] into scientific notation by using the following steps:
-We will first move the decimal four times to right in the number so that the resulting number will be \[m = 2.23\] which is greater than 1 but less than 10.
-Here, we have moved the decimal to the right, as a result the exponent \[n\] is negative.
\[n = - 4\]
-Now, if we will write in the scientific notation form \[m \times {10^n}\], we get
$2.23 \times {10^{ - 4}}$
\[ \Rightarrow 0.000223 \times {10^{ - 2}} = 2.23 \times {10^{ - 4}} \times {10^{ - 2}} \\
\therefore 0.000223 \times {10^{ - 2}}= 2.23 \times {10^{ - 6}}\]

Thus, $2.23 \times {10^{ - 6}}$ is our final answer.

Note:While solving this type of problem, one important thing to keep in mind is the direction in which we move the decimal. If we move the decimal in the right direction, the exponent value will be negative. And when we move the decimal in the left direction the exponent value will be positive. If we forget to consider this, the answer obtained will be wrong.