Calculate 38.72 divided by 8.73, rounding your answer to the nearest tenth.
First, we want to set up our division problem 38.72 is the dividend, 8.73 is the divisor. We don’t want our division problem to start with decimal values. So I take 8.73, move the decimal one, two places to the right. If I move the decimal place from 8.73 two places to the right, then I’ll need to move the decimal place from 38.72 two places to the right. Our new division problem will look like this: 873 divided by 3872.
First, we asked, can 873 be divided into 387? No, it’s not possible. So we’ll have to divide 873 into 3872. Instead of just guessing random numbers, I want to use rounding here: 873 is almost 900. I want to think of something I can multiply 900 by that will equal about 3800. If I multiply 900 times four, it becomes 3600. I’m going to use this information to try to divide 873 into 3872 four times.
In our dividing procedure, we multiply four by 873. Starting in the units place, four times three equals 12. Write down your two, carry your one. Moving on to the tens place, four times seven equals 28 plus one that we carried over equals 29. We write down our nine and carry our two. Next, we multiply four times eight which equals 32 and we add the two we carried over, 34.
Now, we need to subtract. Two minus two equals zero. Moving to the left, we can’t take nine away from seven. So we need to borrow from the hundreds place. We’ll have a seven hundreds and now 17 tens. Then, we say 17 minus nine equals eight, seven minus four equals three, and three minus three equals zero. From here, we need to bring up our decimal place and add a zero in the tenths place, bring down the next digit, and then find out how many times 873 can be divided into 3800.
Remember the first part of this problem we divided 873 into 3872. 3800 is very close to 3872. We can use four again. We know that four times 873 equals 3492, which means we can copy that value again.
From there, we need to subtract. We can’t subtract two from zero. So we need to borrow. But we can’t borrow from the 10. We’ll have to borrow from our eight. That leaves seven hundreds and 10 tens. We take one of those tens away, leaving us with nine tens and 10 ones. From there, 10 minus two equals eight, nine minus nine equals zero, seven minus four equals three, three minus three equals zero.
At this point, you might be tempted to think we have the nearest tenth. But we have to remember that when we’re rounding to the nearest tenth, we have to look to the right of the tenths place — to the hundredths place. And that means we’ll need to do another round of division. So we add a zero to the hundredths place, bring down that zero. And then, we see we’re dealing with 3080 and we’ll need to go back to our estimating.
We no longer need something about 3800. We now need to multiply 900 by something that’s close to 3000. We know 900 times three would be equal to 2700 and that’s pretty close. So we estimate that 873 will be divided into 3080 three times. And that means we need to multiply 873 by three. Three times three equals nine, seven times three equals 21. Write down our one, carry the two. Eight times three equals 24 plus two equals 26.
We’ll go ahead and subtract one last time. We can’t subtract nine from zero. So we borrow from the eight, leaving us with seven. We bring the one over. 10 minus nine equals one, seven minus one equals six. We can’t take six away from zero. We’ll borrow for our three, leaving us with two, carrying a one over. 10 minus six equals four. And finally, two minus two equals zero. We could add another zero, bring it down, and divide again, over and over again. But we don’t have to because we’re trying to round this answer to the nearest tenth.
We take the quotient we found 4.43, we look at the tenths place, and then we look to the right in the hundredths place, where there is a three. Three is less than five. Therefore, we round down. When we round down, the digit we’re rounding, in this place the four, stays the same. Everything to the left of the four, in this case just the units place, also stays the same. And everything to the right of what we’re rounding becomes a zero. 4.40 in its simplest form is 4.4.
When we divide 38.72 by 8.73 and round our answer to the nearest tenth, we get 4.4.