Comparing, Ordering, and Rounding

Number and Operations · 5 min read

Comparing, Ordering, and Rounding

Comparing Numbers with >, <, and =

To compare two numbers, decide which one is greater, which one is less, or if they are equal. Use a symbol to show your answer.

is greater than: 9,000 > 8,999

is less than: 52,318 < 52,381

is equal to: 4,000 + 50 = 4,050

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

Line up

Write the numbers so the places line up: ones under ones, tens under tens.

Start at the left

Look at the greatest place first.

Find the first difference

Move right until two digits are different.

Decide

The number with the greater digit in that place is the greater number.

The first different digit is in the tens place: 1 ten < 8 tens
Number	Ten Thousands	Thousands	Hundreds	Tens	Ones
52,318	5	2	3	1	8
52,381	5	2	3	8	1

Worked Example

Oak School collected 8,705 cans. Elm School collected 8,750 cans. Which comparison is true?

Step 1: Line up the places. Both numbers have 8 thousands and 7 hundreds.
Step 2: Look at the tens: 8,705 has 0 tens and 8,750 has 5 tens.
Step 3: 0 tens is less than 5 tens, so 8,705 is less.
Answer: 8,705 < 8,750. Elm School collected more cans.

Watch Out

When two whole numbers have a different number of digits, the one with more digits is greater. 10,002 > 9,999 because 10,002 has a digit in the ten thousands place.

Ordering Numbers

To order numbers, put them from least to greatest or from greatest to least. Compare two numbers at a time, using place value.

Town populations
Town	Population
Ashton	34,912
Bayville	39,214
Cedar Hill	34,219
Dale	43,129

Worked Example

Use the table. List the towns from the greatest population to the least population.

Step 1: Compare the ten thousands. Dale has 4 ten thousands. The others have 3. Dale is the greatest.
Step 2: Compare the thousands for the other three towns. Bayville has 9 thousands. Ashton and Cedar Hill have 4 thousands. Bayville is next.
Step 3: Ashton and Cedar Hill tie in the thousands. Compare the hundreds: Ashton has 9 and Cedar Hill has 2. 900 > 200.
Answer: Dale (43,129), Bayville (39,214), Ashton (34,912), Cedar Hill (34,219)

Locating Numbers on an Open Number Line

A number line shows numbers in order. An open number line shows only the marks you need. A benchmark number is a friendly number, like a multiple of 10, 100, or 1,000, or the number halfway between two of them.

To read a point, first find what each space is worth. Divide the distance between the end numbers by the number of equal spaces.

Point A on a Number Line from 400 to 500

There are 10 equal spaces between 400 and 500.

Worked Example

The number line goes from 400 to 500 and has 10 equal spaces. What number does point A represent?

Step 1: Find the size of each space: 500 − 400 = 100, and 100 ÷ 10 = 10. Each space is 10.
Step 2: Count the spaces from 400 to point A. There are 7 spaces.
Step 3: Count by 10s from 400: 410, 420, 430, 440, 450, 460, 470.
Answer: Point A represents 470.

Rounding to the Nearest 10 and 100

To round a number means to find the closest ten or the closest hundred. A number line helps you see which one is closer.

How to round with a number line

Find the two tens (or hundreds) the number is between

▼

Mark the halfway number

▼

See which side the number is on

▼

Halfway or more rounds up

Rounding 347 to the Nearest Ten

347 is past the halfway mark of 345.

Rounding practice
Number	Nearest 10	Nearest 100
347	350	300
683	680	700
455	460	500
925	930	900
951	950	1,000

Worked Example

A farm stand sold 683 apples in one week. What is 683 rounded to the nearest hundred?

Step 1: 683 is between 600 and 700.
Step 2: The halfway number is 650.
Step 3: 683 is greater than 650, so it is closer to 700.
Answer: 683 rounds to 700.

Watch Out

A number exactly halfway rounds up. 455 rounds to 460 (nearest ten), and 450 rounds to 500 (nearest hundred).

Estimating with Rounding and Compatible Numbers

An estimate is an answer that is close to the exact answer. Estimate to check if an answer makes sense. You can round, or you can use compatible numbers. Compatible numbers are close to the real numbers and easy to add or subtract in your head.

Worked Example

A library has 512 fiction books and 289 nonfiction books. Round each number to the nearest hundred. About how many more fiction books are there?

Step 1: 512 rounds to 500. 289 rounds to 300.
Step 2: Subtract the rounded numbers: 500 − 300 = 200.
Answer: There are about 200 more fiction books. (The exact answer is 223, so 200 is a good estimate.)

Worked Example

Ben read 126 pages in May and 371 pages in June. Use compatible numbers to estimate how many pages he read in all.

Step 1: 126 is close to 125. 371 is close to 375.
Step 2: 125 + 375 is easy to add in your head: 125 + 375 = 500.
Answer: Ben read about 500 pages. (The exact total is 497.)

Common mistake: Reading > and < backward. 4,315 < 4,351 is read "4,315 is less than 4,351."

Common mistake: Looking at the wrong digit when rounding. To round to the nearest ten, look at the ones digit.

Common mistake: Forgetting that a number exactly halfway, like 450, rounds up to 500.

STAAR Tip: On a number line question, find the value of one space before you count. Many wrong answers come from counting by 1s when each space is 10 or 100.

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← Place Value to 100,000

Comparing, Ordering, and Rounding

Comparing Numbers with >, <, and =

To compare two numbers, decide which one is greater, which one is less, or if they are equal. Use a symbol to show your answer.

is greater than: 9,000 > 8,999

is less than: 52,318 < 52,381

is equal to: 4,000 + 50 = 4,050

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

Line up

Write the numbers so the places line up: ones under ones, tens under tens.

Start at the left

Look at the greatest place first.

Find the first difference

Move right until two digits are different.

Decide

The number with the greater digit in that place is the greater number.

The first different digit is in the tens place: 1 ten < 8 tens
Number	Ten Thousands	Thousands	Hundreds	Tens	Ones
52,318	5	2	3	1	8
52,381	5	2	3	8	1

Worked Example

Oak School collected 8,705 cans. Elm School collected 8,750 cans. Which comparison is true?

Step 1: Line up the places. Both numbers have 8 thousands and 7 hundreds.
Step 2: Look at the tens: 8,705 has 0 tens and 8,750 has 5 tens.
Step 3: 0 tens is less than 5 tens, so 8,705 is less.
Answer: 8,705 < 8,750. Elm School collected more cans.

Watch Out

When two whole numbers have a different number of digits, the one with more digits is greater. 10,002 > 9,999 because 10,002 has a digit in the ten thousands place.

Ordering Numbers

To order numbers, put them from least to greatest or from greatest to least. Compare two numbers at a time, using place value.

Town populations
Town	Population
Ashton	34,912
Bayville	39,214
Cedar Hill	34,219
Dale	43,129

Worked Example

Use the table. List the towns from the greatest population to the least population.

Step 1: Compare the ten thousands. Dale has 4 ten thousands. The others have 3. Dale is the greatest.
Step 2: Compare the thousands for the other three towns. Bayville has 9 thousands. Ashton and Cedar Hill have 4 thousands. Bayville is next.
Step 3: Ashton and Cedar Hill tie in the thousands. Compare the hundreds: Ashton has 9 and Cedar Hill has 2. 900 > 200.
Answer: Dale (43,129), Bayville (39,214), Ashton (34,912), Cedar Hill (34,219)

Locating Numbers on an Open Number Line

To read a point, first find what each space is worth. Divide the distance between the end numbers by the number of equal spaces.

Point A on a Number Line from 400 to 500

There are 10 equal spaces between 400 and 500.

Worked Example

The number line goes from 400 to 500 and has 10 equal spaces. What number does point A represent?

Step 1: Find the size of each space: 500 − 400 = 100, and 100 ÷ 10 = 10. Each space is 10.
Step 2: Count the spaces from 400 to point A. There are 7 spaces.
Step 3: Count by 10s from 400: 410, 420, 430, 440, 450, 460, 470.
Answer: Point A represents 470.

Rounding to the Nearest 10 and 100

To round a number means to find the closest ten or the closest hundred. A number line helps you see which one is closer.

How to round with a number line

Find the two tens (or hundreds) the number is between

▼

Mark the halfway number

▼

See which side the number is on

▼

Halfway or more rounds up

Rounding 347 to the Nearest Ten

347 is past the halfway mark of 345.

Rounding practice
Number	Nearest 10	Nearest 100
347	350	300
683	680	700
455	460	500
925	930	900
951	950	1,000

Worked Example

A farm stand sold 683 apples in one week. What is 683 rounded to the nearest hundred?

Step 1: 683 is between 600 and 700.
Step 2: The halfway number is 650.
Step 3: 683 is greater than 650, so it is closer to 700.
Answer: 683 rounds to 700.

Watch Out

A number exactly halfway rounds up. 455 rounds to 460 (nearest ten), and 450 rounds to 500 (nearest hundred).

Estimating with Rounding and Compatible Numbers

Worked Example

A library has 512 fiction books and 289 nonfiction books. Round each number to the nearest hundred. About how many more fiction books are there?

Step 1: 512 rounds to 500. 289 rounds to 300.
Step 2: Subtract the rounded numbers: 500 − 300 = 200.
Answer: There are about 200 more fiction books. (The exact answer is 223, so 200 is a good estimate.)

Worked Example

Ben read 126 pages in May and 371 pages in June. Use compatible numbers to estimate how many pages he read in all.

Step 1: 126 is close to 125. 371 is close to 375.
Step 2: 125 + 375 is easy to add in your head: 125 + 375 = 500.
Answer: Ben read about 500 pages. (The exact total is 497.)

Common mistake: Reading > and < backward. 4,315 < 4,351 is read "4,315 is less than 4,351."

Common mistake: Looking at the wrong digit when rounding. To round to the nearest ten, look at the ones digit.

Common mistake: Forgetting that a number exactly halfway, like 450, rounds up to 500.

STAAR Tip: On a number line question, find the value of one space before you count. Many wrong answers come from counting by 1s when each space is 10 or 100.

Finished reading?

Lock it in with a quick Number and Operations quiz.

Quiz me Next chapter →

STAAR Grade 3 Math