An electron travels through a small hole at about 143000 miles per second. Approximately how many miles will the electron travel in one day?
We could write this miles per second as a fraction of 143000 miles in the numerator per, or every, one second in the denominator. We want to know how far the electron will go in one day. This means we’re looking for how many miles he’ll go in one day. But most people don’t memorize how many seconds are in one day. And so, we’ll need to take a few steps to get from seconds to days.
We can start by converting from seconds to minutes. We know that there are 60 seconds in one minute. If we multiplied the miles per second times seconds per minute, we would find out how many miles the electron would go in one minute. From there, we’ll need to convert our one minute to one hour. We know there are 60 minutes in one hour. After that, we’ll convert from hours to days and we’ll have 24 hours in every day.
With this, we can cancel out our units. We have seconds in the numerator and the denominator, minutes in the numerator and the denominator, hours in the numerator and the denominator. We’re left with miles in our numerator and day in our denominator. The electron would travel 143000 times 60 times 60 times 24 miles per day, or in one day. At this point, we can use the calculator to do this calculation. We’ll plug in 143000 times 60 times 60 times 24 into our calculator.
Your calculator screen might return something like this. This E10 tells us we’re dealing with 10 to the 10th power. And for our significant figures, we could round to the first decimal place. Instead of having 1.23552, we see the three in the second decimal place and know that this 1.23552 will round down to 1.2. It would be 1.2 times 10 to the 10th power. This electron would travel 1.2 times 10 to the 10th power miles per day. And so, the approximate distance the electron travels in one day is 1.2 times 10 to the 10th miles.