Compare, Order and Round Whole Numbers | Grade 5 Math | LevelKite

Which is greater, $52{,}840$ or $52{,}790$ ? To compare two numbers means to decide which one is greater, or whether they are equal. You record the result with one of three symbols:

$>$ means is greater than, as in $9 > 4$
$<$ means is less than, as in $4 < 9$
$=$ means is equal to, as in $9 = 9$

The open side of $>$ or $<$ always faces the greater number.

You already know that the value of a digit depends on its place. Here is why that matters when you compare. A $1$ in any place is worth more than all the places to its right put together. For example, $1$ thousand is more than $999$ , and $999$ is the most that the hundreds, tens and ones can make together. So the place that is worth the most decides first. It is called the greatest place, and that is where you start.

The table below lines up both numbers by place so that you can compare them one place at a time.

Both numbers with their digits lined up by place

Number	Ten thousands	Thousands	Hundreds	Tens	Ones
$52{,}840$	$5$	$2$	$8$	$4$	$0$
$52{,}790$	$5$	$2$	$7$	$9$	$0$

Worked example

Compare two five-digit numbers

Compare $52{,}840$ and $52{,}790$ . Write $<$ , $>$ or $=$ between them.

Start at the greatest place, the ten-thousands place, because it is worth the most. The table shows a 5 there for both numbers, so both have 5 ten thousands. This place cannot tell the numbers apart. Move one place to the right.
$50{,}000 = 50{,}000$
Look at the thousands place. Both numbers have a 2 there, so both have 2 thousands. The digits match again, so move one more place to the right.
$2{,}000 = 2{,}000$
Look at the hundreds place. Here the digits differ. The number 52,840 has 8 hundreds and the number 52,790 has 7 hundreds, and 8 hundreds is more than 7 hundreds.
$800 > 700$
Stop at the first place where the digits differ. The number 52,790 does have more tens, 9 tens against 4 tens, but that cannot change the result. Tens and ones together make 99 at most, which is less than 1 hundred. So the number with more hundreds is the greater number.
$52{,}840 > 52{,}790$

Answer

The number $52{,}840$ is greater than $52{,}790$ , so you write $52{,}840 > 52{,}790$ .

To order numbers means to line them up by size. Least to greatest starts with the smallest number and ends with the largest. Greatest to least goes the other way. You do not need a new method for this. You compare place by place, just as you did above, and pick out one number at a time.

Worked example

Order four numbers

Put these numbers in order from least to greatest: $47{,}310$ , $8{,}965$ , $47{,}130$ and $45{,}900$ . Then write them from greatest to least.

Start at the greatest place that any of the numbers has, the ten-thousands place. Three of the numbers have 4 ten thousands. The number 8,965 has only four digits, so it has no ten thousands at all. That makes 8,965 the least.
The three numbers that are left all have 4 ten thousands, so move right to the thousands place. Their thousands digits are 7, 7 and 5. Since 5 thousands is less than 7 thousands, 45,900 is the least of these three.
$5{,}000 < 7{,}000$
Now compare 47,310 and 47,130. Their ten thousands match and their thousands match, so move right to the hundreds place. Since 1 hundred is less than 3 hundreds, 47,130 is less than 47,310.
$47{,}130 < 47{,}310$
Write the four numbers in the order you picked them. Each time you picked the least number that was left, so the list runs from least to greatest.
$8{,}965 < 45{,}900 < 47{,}130 < 47{,}310$
For greatest to least, read the same list from right to left. The less-than signs turn into greater-than signs, because now each number is greater than the one after it.
$47{,}310 > 47{,}130 > 45{,}900 > 8{,}965$

Answer

From least to greatest, the order is $8{,}965$ , $45{,}900$ , $47{,}130$ , $47{,}310$ . From greatest to least, the order is $47{,}310$ , $47{,}130$ , $45{,}900$ , $8{,}965$ .

Sometimes you do not need an exact number. To round a number means to swap it for a nearby number that is easier to work with. A rounding question always names a place, such as the nearest thousand. You then choose the nearest multiple of that place. A multiple of a place is a number you say when you count by that place. For thousands, the multiples are $1{,}000$ , $2{,}000$ , $3{,}000$ and so on.

Try rounding $36{,}700$ to the nearest thousand. First find the two multiples of $1{,}000$ on either side of it. Every multiple of $1{,}000$ has zeros in the hundreds, tens and ones places. So keep the digit in the thousands place and every digit to its left, and change the digits to its right to zeros. That gives $36{,}000$ , the multiple just before your number. One more thousand gives $37{,}000$ , the multiple just after it. Which one is closer? The number line below runs from $36{,}000$ to $37{,}000$ , and each step is $100$ .

The marker at

36{,}500

is in the exact middle of the line. The marker at

36{,}700

is

3

steps of

100

from

37{,}000

and

7

steps of

100

from

36{,}000

.

The number line has two markers. One is at $36{,}500$ , the halfway number. That is the number in the exact middle of the two multiples. The two multiples are $1{,}000$ apart and half of $1{,}000$ is $500$ , so the halfway number is $36{,}000 + 500 = 36{,}500$ .

The other marker is your number, $36{,}700$ . It is to the right of the halfway number, because $36{,}700 > 36{,}500$ . So it is closer to $37{,}000$ . You can check with subtraction: $37{,}000 - 36{,}700 = 300$ , but $36{,}700 - 36{,}000 = 700$ . Rounded to the nearest thousand, $36{,}700$ is $37{,}000$ .

If your number is to the left of the halfway number, it is closer to the multiple just before it. If your number is the halfway number, it is just as close to one multiple as to the other. For that case, everyone follows the same rule: the halfway number rounds up, to the greater multiple.

Key concept

Greatest place first, closer multiple wins

Place value is the tool for both jobs in this lesson.

To compare or order, line up the places and start at the greatest place. Move right until the digits differ. The number with the greater digit in that place is the greater number. If every place matches, the numbers are equal.

To round, find the two multiples of the named place on either side of your number. Choose the closer one. The halfway number rounds up.

Worked example

Round one number to two different places

Round $284{,}350$ to the nearest ten thousand. Then round $284{,}350$ to the nearest hundred.

Begin with the nearest ten thousand. Keep the digit in the ten-thousands place and every digit to its left, and change the digits to its right to zeros. That gives 280,000, the multiple of 10,000 just before 284,350. One more ten thousand gives 290,000, the multiple just after it.
$280{,}000 < 284{,}350 < 290{,}000$
Find the halfway number. The two multiples are 10,000 apart and half of 10,000 is 5,000, so the halfway number is 280,000 + 5,000 = 285,000. Now compare. The hundred thousands match and the ten thousands match, but in the thousands place 4 is less than 5. So 284,350 is less than the halfway number, and it is closer to 280,000.
$284{,}350 < 285{,}000$
Now round to the nearest hundred. Keep the digit in the hundreds place and every digit to its left, and change the digits to its right to zeros. That gives 284,300, the multiple of 100 just before 284,350. One more hundred gives 284,400, the multiple just after it.
$284{,}300 < 284{,}350 < 284{,}400$
Find the halfway number. The two multiples are 100 apart and half of 100 is 50, so the halfway number is 284,300 + 50 = 284,350. That is the very number you are rounding, so it is just as close to 284,300 as to 284,400. The halfway number rounds up, so choose the greater multiple, 284,400. The number line after this example shows the marker in the exact middle.
$284{,}300 + 50 = 284{,}350$

Answer

Rounded to the nearest ten thousand, $284{,}350$ is $280{,}000$ . Rounded to the nearest hundred, $284{,}350$ is $284{,}400$ .

Each step is

10

. The marker at

284{,}350

is

5

steps from

284{,}300

and

5

steps from

284{,}400

, so it is the halfway number and rounds up to

284{,}400

.

Here is the idea to keep. When you compare or order whole numbers, the greatest place where the digits differ decides. When you round, your number goes to the closer of the two multiples on either side of it, and the halfway number goes up. Either way, you start by asking what each digit is worth in its place.