D.2 Round to place values up to millions
What is rounding?
Rounding is a mathematical process that changes a number to a nearby number that is simpler but still close in value to the original. The rounded number is usually less exact, but it is much easier to use for estimation, mental math, and understanding large quantities. When we round, we decide which "round number" (often a number ending in zero) the original number is closest to.
- If 28,417 people attend a football game, we might say about 28,000 people attended.
- If a house costs $347,525, we might say it costs about $350,000.
- If a state has a population of 4,822,109, we might say it has about 4.8 million people.
Rounding does not give an exact answer. Instead, it gives an estimate, which is a close guess. The symbol ≈ means "approximately equal to." For example, 28,417 ≈ 28,000.
The rounding rule: four or less, let it rest; five or more, raise the score
All rounding follows one simple rule. To round a number, you must look at the digit directly to the right of the place value you are rounding to. This digit is the deciding digit.
If the deciding digit is 4 or less, the digit in the rounding place stays the same, and all digits to the right become zero. This is called "rounding down."
If the deciding digit is 5 or more, the digit in the rounding place increases by one, and all digits to the right become zero. This is called "rounding up."
- Four or less, let it rest. (The digit stays the same.)
- Five or more, raise the score. (The digit goes up by one.)
Always look only at the digit immediately to the right of the place you are rounding. The digits farther to the right do not matter when deciding to round up or down.
Rounding to the nearest ten
When rounding to the nearest ten, you are finding which multiple of ten the number is closest to. Look at the ones place digit to decide.
- Round 42 to the nearest ten. The ones digit is 2. Since 2 is less than 5, we round down. 42 ≈ 40.
- Round 87 to the nearest ten. The ones digit is 7. Since 7 is greater than or equal to 5, we round up. The tens digit (8) becomes 9. 87 ≈ 90.
- Round 125 to the nearest ten. The ones digit is 5. Since it is 5 or more, we round up. The tens digit (2) becomes 3. 125 ≈ 130.
- Round 9,994 to the nearest ten. The ones digit is 4, so we round down. 9,994 ≈ 9,990.
When you round up and the digit is a 9, be careful! For example, rounding 196 to the nearest ten: the ones digit is 6, so the tens digit 9 becomes 10. That means 196 ≈ 200.
Rounding to the nearest hundred
When rounding to the nearest hundred, you find which multiple of one hundred the number is closest to. Look at the tens digit to make your decision.
- Round 342 to the nearest hundred. The tens digit is 4. Since 4 is less than 5, we round down. The hundreds digit (3) stays the same. 342 ≈ 300.
- Round 1,850 to the nearest hundred. The tens digit is 5. Since it is 5 or more, we round up. The hundreds digit (8) becomes 9. 1,850 ≈ 1,900.
- Round 29,437 to the nearest hundred. The tens digit is 3. Since 3 is less than 5, we round down. 29,437 ≈ 29,400.
- Round 399,512 to the nearest hundred. The tens digit is 1, so we round down. 399,512 ≈ 399,500.
Always underline the place value you are rounding to first. Then, circle the digit to its right. This helps you avoid mistakes.
Rounding to the nearest thousand
When rounding to the nearest thousand, you find which multiple of one thousand is closest. Look at the hundreds digit to decide whether to round up or down.
- Round 6,342 to the nearest thousand. The hundreds digit is 3. Since 3 is less than 5, we round down. 6,342 ≈ 6,000.
- Round 7,892 to the nearest thousand. The hundreds digit is 8. Since 8 is 5 or more, we round up. The thousands digit (7) becomes 8. 7,892 ≈ 8,000.
- Round 14,501 to the nearest thousand. The hundreds digit is 5. Since it is 5 or more, we round up. The thousands digit (4) becomes 5. 14,501 ≈ 15,000.
- Round 345,678 to the nearest thousand. The hundreds digit is 6, so we round up. The thousands digit (5) becomes 6. 345,678 ≈ 346,000.
When rounding large numbers, all digits to the right of the thousands place become zeros. Only the digits to the left may change.
Rounding to the nearest ten thousand
When rounding to the nearest ten thousand, you find the closest multiple of ten thousand. The thousands digit is the deciding digit.
- Round 45,678 to the nearest ten thousand. The thousands digit is 5. Since 5 is 5 or more, we round up. The ten-thousands digit (4) becomes 5. 45,678 ≈ 50,000.
- Round 82,345 to the nearest ten thousand. The thousands digit is 2. Since 2 is less than 5, we round down. 82,345 ≈ 80,000.
- Round 129,432 to the nearest ten thousand. The thousands digit is 9. Since 9 is 5 or more, we round up. The ten-thousands digit (2) becomes 3. 129,432 ≈ 130,000.
- Round 545,000 to the nearest ten thousand. The thousands digit is 5, so we round up. The ten-thousands digit (4) becomes 5. 545,000 ≈ 550,000.
A common mistake is to look at the hundreds digit when rounding to the nearest ten thousand. Always look at the thousands place, which is directly to the right of the ten-thousands place.
Rounding to the nearest hundred thousand
When rounding to the nearest hundred thousand, you find the closest multiple of one hundred thousand. The ten-thousands digit tells you whether to round up or down.
- Round 234,567 to the nearest hundred thousand. The ten-thousands digit is 3. Since 3 is less than 5, we round down. 234,567 ≈ 200,000.
- Round 789,123 to the nearest hundred thousand. The ten-thousands digit is 8. Since 8 is 5 or more, we round up. The hundred-thousands digit (7) becomes 8. 789,123 ≈ 800,000.
- Round 450,000 to the nearest hundred thousand. The ten-thousands digit is 5. Since it is 5 or more, we round up. The hundred-thousands digit (4) becomes 5. 450,000 ≈ 500,000.
- Round 949,999 to the nearest hundred thousand. The ten-thousands digit is 4, so we round down. 949,999 ≈ 900,000.
Numbers exactly halfway between two rounding choices (like 250,000 rounded to the nearest hundred thousand) always round up to 300,000 because the rule says "five or more, raise the score."
Round to place values up to million
Rounding to a specific place value means finding the closest number with zeros in all lower places. The digit to the right of your target place value tells you whether to round up or down.
- Round 1,234,567 to the nearest million. The hundred-thousands digit is 2. Since 2 is less than 5, we round down. 1,234,567 ≈ 1,000,000.
- Round 3,765,432 to the nearest hundred thousand. The ten-thousands digit is 6. Since 6 is 5 or more, we round up. The hundred-thousands digit (7) becomes 8. 3,765,432 ≈ 3,800,000.
- Round 5,500,000 to the nearest million. The hundred-thousands digit is 5. Since it is 5 or more, we round up. The millions digit (5) becomes 6. 5,500,000 ≈ 6,000,000.
- Round 8,449,999 to the nearest million. The hundred-thousands digit is 4, so we round down. 8,449,999 ≈ 8,000,000.
- Round 6,987,654 to the nearest ten thousand. The thousands digit is 7. Since 7 is 5 or more, we round up. The ten-thousands digit (8) becomes 9. 6,987,654 ≈ 6,990,000.
When rounding, always look at the digit immediately to the right of the place you are rounding to. If that digit is 5 or greater, round up. If it is 4 or less, round down. This rule applies to all place values, from units to millions and beyond.
Using a number line to understand rounding
A number line can help you visualize rounding. When you round a number, you are finding which "benchmark" number it is closest to. If the number is exactly in the middle, we round to the higher benchmark.
- To round 63 to the nearest ten, picture a number line from 60 to 70. 63 is closer to 60 than to 70, so 63 ≈ 60.
- To round 86 to the nearest ten, picture 80 to 90. 86 is closer to 90, so 86 ≈ 90.
- To round 450 to the nearest hundred, picture 400 to 500. 450 is exactly halfway. By rule, we round up to 500.
- To round 3,250 to the nearest thousand, picture 3,000 to 4,000. 3,250 is closer to 3,000, so 3,250 ≈ 3,000.
Drawing a quick number line in the margin of your paper can help you check your work when you are first learning to round.
Rounding in real-world problem solving
Rounding is used every day to make sense of large numbers, to estimate costs, and to check if an answer is reasonable. When you see a problem that asks "about how many" or "estimate," you should round the numbers first.
- A school has 2,487 students. About how many students are there? Rounded to the nearest hundred, there are about 2,500 students.
- A store sold 34,792 bottles of water. About how many did they sell? Rounded to the nearest thousand, they sold about 35,000 bottles.
- A state park had 128,456 visitors last year. Rounded to the nearest ten thousand, there were about 130,000 visitors.
- A company made $987,250 in profit. Rounded to the nearest hundred thousand, the profit was about $1,000,000.
Estimating with rounded numbers helps you quickly check if a calculated answer is reasonable. If your exact answer is very different from your estimate, you may have made a mistake.
Avoiding common rounding mistakes
Even experienced mathematicians make rounding errors. Knowing the most common mistakes can help you avoid them. Always slow down and follow the steps carefully.
- Looking at the wrong digit: To round 4,837 to the nearest hundred, look at the tens digit (3), not the hundreds digit.
- Forgetting to change all digits to zero: When rounding 3,456 to the nearest ten, the answer is 3,460, not 3,46.
- Rounding to the wrong place value: Read the question carefully. Does it say "nearest ten" or "nearest thousand"?
- Making a mistake with nines: Rounding 1,996 to the nearest ten: the ones digit is 6, so round up. The tens digit 9 becomes 10, affecting the hundreds and thousands. 1,996 ≈ 2,000.
Practice with numbers that have many 9's. They are tricky, but mastering them will make you a rounding expert!
Common Core alignment: CCSS.MATH.CONTENT.4.NBT.A.3 – Use place value understanding to round multi-digit whole numbers to any place.
Notes for teachers
This lesson is aligned with CCSS.MATH.CONTENT.4.NBT.A.3. Use it for whole-class instruction, independent practice, or homework.
All content is 100% free, student-safe, and designed for classroom and home use.