Alfred is trying to drink one point eight liters of water every day. Given that he drank nine hundred and eighty-seven milliliters of water one morning, how many milliliters of water should he drink during the rest of the day?
Okay. The first thing we need to think about are, what are liters and milliliters. Well liters and milliliters are measurements of volume, and they’re a part of the metric system. And one liter is made up of a thousand milliliters. And that means that one milliliter is a thousandth of a liter.
If we look back at the question, we can see that Alfred’s trying to drink one point eight liters of water, and he’s already drunk nine hundred and eighty-seven milliliters of water. So he’s not aiming for one liter, he is aiming for one point eight times as much, which is one point eight liters. And if we consider the same thing in milliliters, he’s not aiming for a thousand milliliters, the same as one liter, he’s aiming for one point eight times as much, so one point eight times a thousand.
Let’s look at the number one point eight and consider the place value of each of its digit. The one is in the units, so the ones column. And the eight is eight-tenths, it’s in the tenths column. When we multiply by a thousand, the place value of each of our digits is gonna go up by a thousand. So it’s gonna move three places to the left in our diagram. That means a thousand times this digit is going to move it into this column here. So we’ll have one in the thousands column. And a thousand times this digit is gonna move it to this column here, it’s gonna move it to the hundreds column. But we can’t leave our number as just one eight space space and then a decimal point, because it’s not entirely clear what that number is. We have to put zeros in the tens and ones column. And now we’ve got a choice. With- we can either put a zero after the decimal point to say it’s one thousand eight hundred point zero, or since there are only zeros in those columns, we can miss them out altogether, so one thousand eight hundred.
So Alfred then is trying to drink one thousand eight hundred milliliters of water every day. Now we can get on to do the actual calculation we want to do. Alfred is trying to drink one thousand eight hundred milliliters, and he’s already drunk nine hundred and eighty-seven milliliters. So the difference between those two is the amount that he should try to drink in the rest of the day.
Now we can do this subtraction using the column method, zero take away seven. That’s no good, so we’re gonna need to borrow one from the next column. But that’s a zero as well, so we’re gonna have to borrow one from the next column. So that eight’s gonna become a seven. And one gets carried to the next column. So now the next column, from the first column, has got a ten in it. So we can borrow one of those ten, which makes it nine, and then one over here. Now we’ve got ten take away seven, which is three. Nine take away eight, which is one. Seven take away nine, that doesn’t quite work. So we’re gonna have to borrow one from the next column, which means we’ve now got seventeen take away nine, which is eight. And then zero take away nothing is zero. So the difference is eight hundred and thirteen milliliters.
Now all of that borrowing was rather messy. Let’s look at another way of doing the same calculation. Picture a number line, what’s the difference between nine hundred and eighty-seven and one thousand eight hundred? Well if I add thirteen to nine hundred and eighty-seven, it takes me up to a thousand. And then if I add eight hundred to a thousand, it takes me up to one thousand eight hundred. So the step from nine hundred and eighty-seven up to one thousand eight hundred was thirteen plus eight hundred, which is just eight hundred and thirteen.
It’s the same answer, but it was a bit easier to get to. So our answer is: He would need to drink eight hundred and thirteen milliliters of water during the rest of the day.