Question

How do you convert $584\mu \text{s}$ to seconds?

Answer 1

Hint: We have the relation of $1\mu \text{s}$ being equal to ${10}^{-6}$ seconds. Then we explain the process of expressing indices in their scientific form of decimal. We start with taking the decimal number at the end and move it leftwards to multiply the new number 10 with ${10}^{-6}$. We stop when the decimal has only one digit to cross.

Complete step-by-step answer:
We have the relation of $1\mu \text{s}$ being equal to ${10}^{-6}$ seconds. Therefore, we convert $584\mu \text{s}$ to $584\times {10}^{-6}$ seconds. Now we express it in its scientific form.
For the given number we move the decimal to the left side one position. The decimal keeps going towards the left till the decimal has only one digit to cross after decimal. The more we move to the left, the more we multiply with 10 to ${10}^{-6}$.
We bring decimal in the form of $584\times {10}^{-6}=584.0\times {10}^{-6}$.
We explain the first two steps. The decimal starts from its actual position in $584.0$.
Now it crosses the 4 in $584.0$ which means we have to multiply 10.
So, $584.0$ becomes $58.4$ and ${10}^{-6}$ becomes ${10}^{-6}\times 10={10}^{-5}$
Now in the second step the point crosses 8. So, $58.4$ becomes $5.84$ and ${10}^{-5}$ becomes ${10}^{-5}\times 10={10}^{-4}$.
Now we have only one digit as 5 left in $5.84$ to cross. Here we stop the process.
Therefore, the scientific form of $584\times {10}^{-6}$ is $5.84\times {10}^{-4}$. We get $584\mu \text{s}$ is equal to $5.84\times {10}^{-4}$ seconds.

Note: We also can add the zeros after decimal of $5.84$. The use of zeroes is unnecessary. But in cases where we have digits other than 0 after decimal, we can’t ignore those digits. The final form will be $584\times {10}^{-6}=5.84\times {10}^{-4}$.