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Video: Arranging a Set of Decimal Numbers in Word Problems

Tim Burnham

To keep track of the inventory at his store’s warehouse, Nicholas must arrange items on shelves according to their stock numbers. Arrange the numbers in the table below in ascending order.

04:32

Video Transcript

To keep track of the inventory at his store’s warehouse, Nicholas must arrange items on shelves according to their stock numbers. Arrange the numbers in the table below in ascending order. And then we got a table with nine hundred and thirteen point nine, nine hundred and thirteen point nine three one, and nine hundred and thirteen point nine three. Now the first thing to think about is the word “ascending.” Ascending means going up in order, so starting with the smallest and ending with the largest. A bit like ascending a staircase, you start with the lowest and you end at the highest.

Now let’s have a look at these numbers; they all begin with nine hundred and thirteen point nine and then followed by something. So what we’re gonna do is think about the place value of each of those digits and we’re gonna write out the numbers in full-pattern amount with zeros when we need to. So let’s start with the number nine hundred and thirteen point nine. The nine is in the hundreds column, one is in the tens column; that means one ten, three is in the one or the units column; so three in there. Then we’ve got point. The nine is in the tenth column; so that’s nine-tenths. We don’t have any hundredths and we don’t have any thousandths.

Now nine hundred and thirteen point nine three one, that again has got a nine in the hundreds column, a one in the tens column, a three in the ones column, and then we got a nine in the tenth column; so that’s nine-tenths. We gotta three in the hundredth column; so that’s three hundredths and one in the thousandth column; so that’s one thousandth. And with nine hundred and thirteen point nine three, that’s a nine in the hundreds column, one in the tens column, three in the ones column. And then it’s point. Nine in the tenth column and three in the hundredth column and it’s got nothing in the thousandth column.

So now let’s go through and compare those numbers. So starting from the left, they all begin with a nine and all of those nines are in the hundreds column; so these digits all have the same value. Now it’s important that we have started on the left there because any digits at this end of the number have a higher value, a hundred in this case, than any digits at the other end of the number, where you’re looking at tenths or hundredths or even thousandths — tiny little fractions.

Now we’ll look at the tens column. Though they’ve all got a digit of one in that column, so, so far they’re all equal. And now in the ones column, they’ve all got a digit of three. And now even in the tenth column, they’ve all got a digit of nine. So, so far we haven’t been able to detect any difference in the value of the overall size of any of these three numbers. Now we get to the hundredth column and we can see that our first number has got zero in this column, but the others have both got a three in that column. So the zero is worth less than the three; so we’ve identified the value of the lowest number. Now we can move on to the thousandth column.

And we’ve already eliminated the first number from our enquiries; that’s the smallest number. So at this point we’re just comparing the value of these two- these last two numbers here. So in the thousandth column, this number here has got a zero; so it’s got no thousands. And this number has got one, so one thousandth. So up to this point, all of the digits in all of the columns were equal. Now at this point, the second number nine one three point nine three zero doesn’t have any thousandths, but nine one three point nine three one does. So nine one three point nine three is smaller than nine one three point nine three one.

So we’ve identified the order of those numbers. All we need to do now is write them out in order. But it’s important to write them out in the format that they were given in the question. So nine one three point nine zero zero is this number, nine one three point nine three one is this number, and nine one three point nine three zero is this number. So let’s write them out now. So in ascending order, we have nine one three point nine, nine one three point nine three, and nine one three point nine three one.