Express eighty-three point seven percent as a decimal. So in this question, we’ve been given a number as a percent or percentage, and we’ve got to express it in a decimal format.
Now in this context, percentages and decimals are both ways of representing the concept of proportion. By proportion, we mean what share of the whole thing are we talking about. For example, let’s think about a cake. If we’re going to share out a cake between a number of people, what share is each person going to get? Well, in particular, what share am I going to get? Am I gonna get none of it? Am I gonna get all of it? Or am I gonna get something in between?
Now if we think of that scale from none of it to all of it as being represented by percentages, we go from the worst-case scenario where I get zero percent of the cake, I don’t get any cake, to the best-case scenario where I get all of the cake, a hundred percent of it. And in the middle, I could get something like fifty percent. And there is a sliding scale of values between all of those, so I can get one percent, one point seven percent, nine point six percent, ninety-eight point three percent. There’re lots of different percentage values that I could get.
Now, we can represent those same proportions or shares using decimals on a scale of zero to one, where zero represents me getting no cake and one represents me getting the entire cake, so halfway between those, a decimal of nought point five represents me getting half the cake.
So we’ve got two sets of numbers that we can place against our sliding scale from none of it to all of it, and they are percentages and decimals. And as we said, with percentages, our numbers go from zero to a hundred percent, and with decimals they go from zero to one.
Now in reality, I could have two or three or even four whole cakes, in which case I would have two hundred percent of a cake or three hundred percent of a cake or four hundred percent of a cake, or I could have two or three or four cakes, so it is possible to represent proportions which are greater than one and it’s also possible to represent proportions which are negative; that’s not really what we’re talking about right now though.
So on our scale, let’s just look at the numbers we’ve got; if I have a decimal of one, it represents a percentage of one hundred; if I have a decimal of nought point five, it represents a percentage of fifty; and if I have a decimal of zero, it represents a percentage of zero. What I’m doing to get from one to a hundred or nought point five to fifty or even zero to zero is multiplying those numbers by a hundred.
And going in the other direction to get from a hundred to one or fifty to nought point five or zero to zero, I’m dividing by a hundred. So to convert my percentages into decimals, I need to divide by one hundred.
So back to the question then, express eighty-three point seven percent as a decimal. I’ve got to take eighty-three point seven percent and I’ve got to divide it by one hundred. So what is eighty-three point seven divided by a hundred? Well let’s think about the place value of each of the digits: eight three point seven. The eight is in the tens column, the three is in the ones column, and the seven is in the tenths column.
Now if we were dividing by ten, each of our digits would move one place to the right and would be worth a tenth as much. We’re dividing by a hundred, so each of those digits needs to move two places to the right and it’ll be worth a hundredth as much.
So the seven is going to move from here to here, the three is gonna move from here to here, and the eight is gonna move from here to here. So we’ve got the number point eight three seven, but normally we’d put a zero in front of that to make it clear that there’s nothing in the units or the ones column.
So our answer is nought point eight three seven. And that means that eighty-three point seven percent is at the same point on our sliding scale, it represents the same proportion, as the decimal nought point eight three seven.