Lesson 1.1.5

Comparing & Ordering Numbers

Three symbols

We often compare two numbers with three short symbols. “Less than” is written < — the small end points to the smaller number. “Greater than” is written > — the wide opening faces the larger number. When two numbers match, we use an equals sign: =.

Say it in words as well: “ $24$ is less than $31$ ,” “ $80$ is greater than $65$ ,” “ $17$ equals $17$ .” The symbols are just a compact way to write the same idea.

Number line picture

If two numbers sit on the same number line, the one farther to the right is greater. The gap between them is how far apart they are — like steps you would count going from one to the other.

Try sliding A and B. When they land on the same spot, the numbers are equal and the gap is zero.

Move both sliders. The highlighted segment shows the gap between the two values. On a number line, the greater number always sits to the right.

A: 38B: 72

38 < 72

38 is less than 72. The number farther right is greater.

Gap: 34 units

A (blue marker): 38

B (amber marker): 72

Bigger numbers: compare by place value

The number line idea still works for large numbers, but we rarely draw a line all the way to thousands. Instead, compare digits from the left. First compare the thousands; if those tie, compare the hundreds; then tens; then ones.

Example: $4,250$ and $4,307$ both start with $4$ thousands — tie. Next column: $2$ hundreds vs $3$ hundreds. The second number wins, so $4,307 > 4,250$ . You do not need to look at the tens once the hundreds have decided it.

Ordering more than two

To order a list from smallest to largest, you can pick the smallest number first, then the next smallest, and so on — like standing people in a line by height. Another way is to group those with the same thousands, then sort inside each group.

Always check whether the question asks for smallest-to-largest or largest-to-smallest; reverse the list if needed.

Try it

Answer in your head or on paper, then open “Show answer” to check.

Fill in the symbol: $47$ ___ $52$
Show answer
$47$ < $52$ . Forty-seven is less than fifty-two (fewer steps along the number line from zero).
Fill in the symbol: $190$ ___ $91$
Show answer
$190$ > $91$ . One hundred ninety is greater: it has a digit in the hundreds place while $91$ does not.
Fill in the symbol: $605$ ___ $605$
Show answer
$605$ = $605$ . The two numbers are the same, so use the equals sign.
Order from smallest to largest: $420$ , $42$ , $402$ , $240$ .
Show answer
$42$ , $240$ , $402$ , $420$ . Only $42$ is below $100$ . Among the rest, $240$ has the smallest hundreds digit ( $2$ ), then $402$ , then $420$ .
Which is greater, $6$ , $088$ or $6$ , $808$ ? Which place value column decides it?
Show answer
$6$ , $808$ is greater. The thousands tie ( $6$ ). The hundreds digit decides it: $8$ hundreds beats $0$ hundreds in the hundreds column.
List from largest to smallest: $1$ , $010$ , $1$ , $100$ , $1$ , $001$ .
Show answer
$1$ , $100$ , $1$ , $010$ , $1$ , $001$ . All have $1$ thousand; compare hundreds next — $1$ , $100$ has $1$ hundred while the others have $0$ . Between $1$ , $010$ and $1$ , $001$ , the tens digit breaks the tie ( $1$ ten vs $0$ tens).

Repeatable practice

Pools are shuffled, variants and multiple-choice order change each visit. Press Check, fix mistakes, then try “New question (same type)” after a correct answer.

1. $Which number is greater?$
Choose one answer6,810They are equal6,086
2. $Which symbol belongs between 38 and 45? (38 _ 45)$
Choose one answer><=
3. $Put 289, 25, 43, and 233 in order from smallest to largest. Which line is correct?$
Choose one answer43, 25, 233, 289289, 233, 43, 2525, 43, 233, 289
4. $What whole number is between 73 and 75? (Type one number.)$
Your answer

End of this module

You can read symbols, use a number line, compare large numbers by place value, and order lists in either direction. That finishes the Numbers & Counting lessons for now — use the Path page any time to revisit a lesson. From the Path, open Module quiz under this module when you want to check the whole topic. Next on the Path: module 1.2, Addition & Subtraction.