Video Transcript
Estimate the result of 1,378 divided by 232 by rounding each number to the nearest ten.
Sometimes, we don’t necessarily want to work out the exact answer to a calculation, and so we use estimation to help predict that answer. Estimation can also be really useful for helping us to check whether a calculation we’ve already performed is likely to be correct. When we estimate, we begin by rounding the numbers in our calculation to a given degree of accuracy. The degree of accuracy might vary. One significant figure, for example, is quite common. In this question, though, it’s telling us to round each number to the nearest ten.
So, let’s begin by rounding 1,378 to the nearest ten. We begin by identifying the tens column. The tens column has the number seven in it. The digit immediately to the right of this number is called the deciding digit. This digit tells us whether we round up or round down. If the deciding digit is five or above, we round our number up. And so, the seven rounds to an eight. We don’t, however, right 138 because that would be changing the size of our number. We add a zero where our eight was originally as a placeholder. And we say that 1,378 correct to the nearest 10 is 1,380.
Let’s repeat this process with our second number, 232. The tens column is here. It contains the number three. This time, the deciding digit, the digit immediately to its right, is two. In this case, when the deciding digit is less than five, we round the number down. Now that doesn’t mean we round the three down to a two; what we’re saying is the nearest ten is the 10 that’s below 232. So, it’s 230. So, we’ve rounded each of our numbers to the nearest ten.
We’re now going to perform the calculation 1,380 divided by 230. There are a number of ways we can do this. One method we have is to write our calculation as a fraction. We know the fraction line means divide. So, 1,380 over 230 is the same as 1,380 divided by 230. This can be quite a nice method because what we can do is begin by simplifying our fraction as fully as possible. We see that both of our fractions can be divisible by 10. And so, we divide both the numerator and denominator by 10. In this case, that looks like just crossing out the zeros.
And so, next, we’re going to perform the calculation 138 divided by 23. This will give us the same answer to our original sum, and this is because we’ve created an equivalent fraction. And probably, the easiest way to do this is just to simply list the 23 times tables. By starting at one times 23 and then repeatedly adding 23, we find that six times 23 is equal to 138. This means that 138 divided by 23 and hence 1380 divided by 230 is six.
And so, by rounding each number in the calculation 1,378 divided by 232 to the nearest ten, we’ve approximated the result as being equal to six.
