A number, 𝑥, is rounded to two decimal places. The result is 9.24. Using inequalities, write down the error interval for 𝑥.
It’s important to note that whilst this question does ask us to use inequalities,
they won’t always. We should know that when we are asked to find the error interval, we do use
inequalities no matter what. In order to answer this question, we first need to calculate the upper and lower
bound of the rounded number 9.24. Now, it’s been rounded to two decimal places. It can be useful to write down the next rounded number up from this one. If the number had been rounded to the one above 9.24, it would have been 9.25. Similarly, the next one down from 9.24 is 9.23.
To find the upper and lower bound, we find the halfway point between our rounded
number and the two we’ve written down. The smallest possible value our number could have been — the lower bound — is,
therefore, 9.235. The upper bound of our number is 9.245. Remember though it gets really close to 9.245, but never quite reaches it since 9.245
itself would actually round up to 9.25.
In inequality form then, we write that 𝑥 is greater than or equal to 9.235, but that
it’s smaller than 9.245 because it never actually reaches it.