Math Core

Which stadium holds more fans, one with 61,500 seats or one with 61,050 seats? The numbers look almost the same. Place value lets you compare them quickly, one digit at a time.

Symbols for comparing

You use three symbols to compare numbers:

Symbol	Meaning	Example
$>$	is greater than	$900 > 90$
$<$	is less than	$45 < 54$
$=$	is equal to	$1{,}000 = 1{,}000$

The open side of $>$ or $<$ always faces the bigger number. The point faces the smaller one.

Step 1: Count the digits

If two whole numbers have a different number of digits, the one with more digits is greater. A six-digit number is always bigger than a five-digit number, because it has hundred thousands.

So $100{,}000 > 99{,}999$ , even though 99,999 is full of 9s.

Step 2: Compare from the left

If the numbers have the same number of digits, line them up by place and compare from the left. The first place where the digits are different decides the answer.

	Ten thousands	Thousands	Hundreds	Tens	Ones
61,500	6	1	5	0	0
61,050	6	1	0	5	0

The ten thousands match and the thousands match. In the hundreds place, 5 is greater than 0. So $61{,}500 > 61{,}050$ . The first stadium holds more fans.

Comparing multi-digit numbers

The number with more digits is greater.
If they have the same number of digits, compare place by place from the left.
The first place with different digits decides which number is greater.

Worked example: Same number of digits

Compare 347,912 and 347,219.

Both have six digits. Compare from the left: 3 and 3 match, 4 and 4 match, 7 and 7 match. In the hundreds place, 9 is greater than 2.

So $347{,}912 > 347{,}219$ .

Seeing it on a number line

On a number line, numbers get bigger as you move to the right. Here are 23,000 and 27,000:

27,000 is to the right of 23,000, so it is greater.

Ordering numbers

To put several numbers in order, compare them the same way. Find the smallest (or largest) first, then the next, and so on.

Worked example: Order from least to greatest

Put these numbers in order from least to greatest:

52,806 ⋅ 9,995 ⋅ 52,068 ⋅ 58,000

9,995 has only four digits, so it is the least.
The other three all start with 5 in the ten thousands place.
Thousands place: 2, 2 and 8. So 58,000 is the greatest.
For 52,806 and 52,068, look at the hundreds place: 8 is greater than 0, so 52,068 comes first.

Order: 9,995 ⋅ 52,068 ⋅ 52,806 ⋅ 58,000

Worked example: Build the biggest number

Use the digits 4, 0, 8, 2, 6 and 1 once each. What is the greatest six-digit number you can make? What is the least?

For the greatest, put the biggest digits in the biggest places: 864,210.

For the least, put the smallest digits first. But a number can't start with 0, so start with 1, then 0: 102,468.

Common mistake

Don't compare numbers by their last digits or by how many big digits they have. Always start at the left, in the biggest place. For example, 40,001 is greater than 39,999, because 4 ten thousands beats 3 ten thousands.

Practice

Practice 1

Which symbol makes this true? $45{,}209 \;\square\; 45{,}290$

Practice 2

Which number is greater: 99,999 or 100,001?

Type a number.

Practice 3

Two towns have 128,450 people and 128,405 people. Which number is greater?

Type a number.

Practice 4

Which number is the least?

Practice 5

Which list is in order from least to greatest?

Practice 6

What is the smallest digit that can go in the box to make this true? $6\square 4{,}210 > 684{,}000$

Type a number.

Practice 7

Use the digits 3, 0, 7, 5, 1 and 9 once each. What is the greatest six-digit number you can make?

Type a number.

Practice 8

Use the same digits, 3, 0, 7, 5, 1 and 9, once each. What is the least six-digit number you can make?

Type a number.