Round Multi-Digit Numbers - 4th Grade Math

1. Round 9,876 to the nearest thousand.
   Answer: 10,000 To round 9,876 to the nearest thousand, look at the hundreds digit, which is 8, so the number rounds up to 10,000, making Choice A correct. Choice B, 9,000, rounds down even though the hundreds digit of 8 means the number should round up. Choice C, 100,000, is ten times too large, as if an extra zero were added by mistake. Choice D, 9,900, rounds to the nearest hundred instead of the nearest thousand.
2. What is 8,456 rounded to the nearest hundred?
   Answer: 8,500 Choice A is correct because the digit in the tens place (5) rounds the hundreds digit up, making 8,456 round to 8,500. Choice B is incorrect because it rounds to the nearest thousand instead of the nearest hundred. Choice C is incorrect because it only changes the tens and ones digits without rounding to the nearest hundred. Choice D is incorrect because it rounds down instead of up.
3. What is 56,789 rounded to the nearest thousand?
   Answer: 57,000 This question tests 4th grade ability to use place value understanding to round multi-digit whole numbers to any place (CCSS.4.NBT.3). Rounding simplifies a number by changing it to the nearest value at a specified place. The process: (1) Identify the rounding place, (2) Look at the digit immediately to the right, (3) If that digit is 0-4, round DOWN (keep the rounding digit the same), if it's 5-9, round UP (increase the rounding digit by 1), (4) All digits to the right of the rounding place become 0. To round 56,789 to the nearest thousand, we look at the 6 in the thousands place and check the 7 in the hundreds place to determine whether to round up. Choice C is correct because the digit to the right of the thousands place is 7, which is ≥5 so we round up, changing the thousands from 6 to 7 and making all digits to the right 0, giving us 57,000. This demonstrates correct application of rounding rules and place value understanding. Choice B represents rounding to the nearest hundred instead of thousand, which happens when students don't identify the correct rounding place. To help students: Use place value charts to identify rounding place and decision digit clearly. Teach the 'neighbor rule'—look at the neighbor to the right (0-4 = stay, 5-9 = go up). Use number lines to show which benchmark (56,000 or 57,000) a number is closer to. Emphasize that ALL digits to the right become 0 (56,789 rounded to nearest thousand is 57,000, not 56,789). Practice with benchmark numbers: 56,500 is exactly halfway between 56,000 and 57,000—by convention we round up to 57,000. Remind students to check their answer makes sense (should be close to original). Watch for: rounding to wrong place, rounding wrong direction (up when should be down), truncating (chopping off) instead of rounding, and forgetting to add all the necessary zeros.
4. Round $3,420$ to the nearest hundred.
   Answer: 3,400 Choice B is correct because the tens digit in 3,420 is 2, which rounds the hundreds digit down, giving 3,400. Choice A is incorrect because it rounds to the nearest thousand instead of the nearest hundred. Choice C is incorrect because it repeats the original number without rounding. Choice D is incorrect because it rounds up instead of down.
5. Round 347 to the nearest ten.
   Answer: 350 Choice C is correct because the ones digit (7) rounds the tens digit up, making 347 round to 350. Choice A is incorrect because it rounds down instead of up. Choice B is incorrect because it rounds to the nearest hundred instead of the nearest ten. Choice D is incorrect because it repeats the original number without rounding.
6. Round 3,420 to the nearest hundred.
   Answer: 3,400 This question tests 4th grade ability to use place value understanding to round multi-digit whole numbers to any place (CCSS.4.NBT.3). Rounding simplifies a number by changing it to the nearest value at a specified place. The process: (1) Identify the rounding place, (2) Look at the digit immediately to the right, (3) If that digit is 0-4, round DOWN (keep the rounding digit the same), if it's 5-9, round UP (increase the rounding digit by 1), (4) All digits to the right of the rounding place become 0. To round 3,420 to the nearest hundred, we look at the 4 in the hundreds place and check the 2 in the tens place to determine whether to round down. Choice B is correct because the digit to the right of the hundreds place is 2, which is <5 so we round down, keeping the hundreds at 4 and making all digits to the right 0, giving us 3,400. This demonstrates correct application of rounding rules and place value understanding. Choice A represents rounding up incorrectly, which happens when students misapply the 0-4 down, 5-9 up rule. To help students: Use place value charts to identify rounding place and decision digit clearly. Teach the 'neighbor rule'—look at the neighbor to the right (0-4 = stay, 5-9 = go up). Use number lines to show which benchmark (3,400 or 3,500) a number is closer to. Emphasize that ALL digits to the right become 0 (3,420 rounded to nearest hundred is 3,400, not 3,420). Practice with benchmark numbers: 3,450 is exactly halfway between 3,400 and 3,500—by convention we round up to 3,500. Remind students to check their answer makes sense (should be close to original). Watch for: rounding to wrong place, rounding wrong direction (up when should be down), truncating (chopping off) instead of rounding, and forgetting to add all the necessary zeros.
7. A collection of books has a total of $94,501$ pages. Rounded to the nearest ten thousand, about how many pages is that?
   Answer: 90,000 Rounding $94,501$ to the nearest ten thousand: since the thousands digit (4) is less than 5, round down to $90,000$. Choice B rounds to the nearest thousand instead of the nearest ten thousand. Choice C drops a zero, understating the value by a factor of ten. Choice D rounds up instead of down.
8. To the nearest thousand, about how many books are in a library with 24,678 books?
   Answer: 25,000 Since the hundreds digit in 24,678 is 6, which is 5 or greater, the number rounds up to 25,000, making Choice C correct. Choice A, 24,700, rounds to the nearest hundred instead of the nearest thousand. Choice B, 240,000, has an extra zero, as if the number were rounded to the nearest ten thousand instead. Choice D, 24,000, would be correct only if the hundreds digit were less than 5, but it is 6. Looking at the hundreds digit tells you whether to round the thousands place up or keep it the same.
9. Keisha drove 3,456 miles on a road trip. Round 3,456 to the nearest hundred.
   Answer: 3,500 To round 3,456 to the nearest hundred, look at the tens digit, which is 5, so the number rounds up to 3,500, making Choice A correct. Choice B, 3,460, rounds to the nearest ten instead of the nearest hundred. Choice C, 35,000, is ten times too large, as if an extra zero were added. Choice D, 3,400, rounds down even though the tens digit of 5 means the number should round up.
10. Look at the number line. Point $P$ represents the number $7,284$. If this number is rounded to the nearest thousand, which point on the number line best represents the rounded number?
    Answer: Point $B$ $7,284$ rounded to the nearest thousand is $7,000$ (since $284 < 500$). Point B represents $7,000$ on the number line. Point A represents $6,000$. Point C represents $7,500$. Point D represents $8,000$.
11. Round $347$ to the nearest ten.
    Answer: 350 This question tests 4th grade ability to use place value understanding to round multi-digit whole numbers to any place (CCSS.4.NBT.3). Rounding simplifies a number by changing it to the nearest value at a specified place. The process: (1) Identify the rounding place, (2) Look at the digit immediately to the right, (3) If that digit is 0-4, round DOWN (keep the rounding digit the same), if it's 5-9, round UP (increase the rounding digit by 1), (4) All digits to the right of the rounding place become 0. To round 347 to the nearest ten, we look at the 4 in the tens place and check the 7 in the ones place to determine whether to round up. Choice B is correct because the digit to the right of the tens is 7, which is ≥ 5 so we round UP, changing the tens from 4 to 5 and making all digits to the right 0, giving us 350. This demonstrates correct application of rounding rules and place value understanding. Choice A represents rounding down incorrectly, which happens when students misapply the 0-4 down, 5-9 up rule. To help students, use place value charts to identify the rounding place and decision digit clearly, and teach the 'neighbor rule'—look at the neighbor to the right (0-4 = stay, 5-9 = go up). Use number lines to show which benchmark the number is closer to, and emphasize adding necessary zeros when rounding smaller numbers.
12. The population of four towns are $5,847$, $6,239$, $5,156$, and $6,891$. A newspaper wants to report the total population rounded to the nearest ten thousand. What number should they report?
    Answer: $20,000$ First find the total: $5,847 + 6,239 + 5,156 + 6,891 = 24,133$. Then round to the nearest ten thousand: since $4,133 < 5,000$, the number $24,133$ rounds down to $20,000$. Choice B rounds to the nearest thousand instead of ten thousand. Choice C is the exact sum without rounding. Choice D incorrectly rounds up to the next ten thousand.
13. Round 28,345 to the nearest ten thousand.
    Answer: 30,000 This question tests 4th grade ability to use place value understanding to round multi-digit whole numbers to any place (CCSS.4.NBT.3). Rounding simplifies a number by changing it to the nearest value at a specified place. The process: (1) Identify the rounding place, (2) Look at the digit immediately to the right, (3) If that digit is 0-4, round DOWN (keep the rounding digit the same), if it's 5-9, round UP (increase the rounding digit by 1), (4) All digits to the right of the rounding place become 0. To round 28,345 to the nearest ten thousand, we look at the 2 in the ten thousands place and check the 8 in the thousands place to determine whether to round up. Choice C is correct because the digit to the right of the ten thousands place is 8, which is ≥5 so we round up, changing the ten thousands from 2 to 3 and making all digits to the right 0, giving us 30,000. This demonstrates correct application of rounding rules and place value understanding. Choice B represents rounding to the nearest thousand instead of ten thousand, which happens when students don't identify the correct rounding place. To help students: Use place value charts to identify rounding place and decision digit clearly. Teach the 'neighbor rule'—look at the neighbor to the right (0-4 = stay, 5-9 = go up). Use number lines to show which benchmark (20,000 or 30,000) a number is closer to. Emphasize that ALL digits to the right become 0 (28,345 rounded to nearest ten thousand is 30,000, not 28,345). Practice with benchmark numbers: 25,000 is exactly halfway between 20,000 and 30,000—by convention we round up to 30,000. Remind students to check their answer makes sense (should be close to original). Watch for: rounding to wrong place, rounding wrong direction (up when should be down), truncating (chopping off) instead of rounding, and forgetting to add all the necessary zeros.
14. Keisha drove 3,456 miles on a road trip. Round 3,456 to the nearest hundred.
    Answer: 3,500 This question tests 4th grade ability to use place value understanding to round multi-digit whole numbers to any place (CCSS.4.NBT.3). Rounding simplifies a number by changing it to the nearest value at a specified place. The process: (1) Identify the rounding place, (2) Look at the digit immediately to the right, (3) If that digit is 0-4, round DOWN (keep the rounding digit the same), if it's 5-9, round UP (increase the rounding digit by 1), (4) All digits to the right of the rounding place become 0. To round 3,456 to the nearest hundred, we look at the 4 in the hundreds place and check the 5 in the tens place to determine whether to round up. Choice C is correct because the digit to the right of the hundreds place is 5, which is ≥5 so we round up, changing the hundreds from 4 to 5 and making all digits to the right 0, giving us 3,500. This demonstrates correct application of rounding rules and place value understanding. Choice A represents rounding down incorrectly, which happens when students misapply the 0-4 down, 5-9 up rule. To help students: Use place value charts to identify rounding place and decision digit clearly. Teach the 'neighbor rule'—look at the neighbor to the right (0-4 = stay, 5-9 = go up). Use number lines to show which benchmark (3,400 or 3,500) a number is closer to. Emphasize that ALL digits to the right become 0 (3,456 rounded to nearest hundred is 3,500, not 3,556). Practice with benchmark numbers: 3,450 is exactly halfway between 3,400 and 3,500—by convention we round up to 3,500. Remind students to check their answer makes sense (should be close to original). Watch for: rounding to wrong place, rounding wrong direction (up when should be down), truncating (chopping off) instead of rounding, and forgetting to add all the necessary zeros.
15. Round $45,678$ to the nearest thousand.
    Answer: 46,000 Choice D is correct because when rounding 45,678 to the nearest thousand, the hundreds digit (6) rounds the thousands digit up from 45,000 to 46,000. Choice A is incorrect because it rounds to the nearest ten-thousand instead of the nearest thousand. Choice B is incorrect because it rounds down instead of up, even though the hundreds digit calls for rounding up. Choice C is incorrect because it rounds to the nearest hundred, not the nearest thousand.
16. A city has 127,456 people. Round to the nearest ten thousand to estimate the population.
    Answer: 130,000 The correct answer is 130,000, because the digit in the thousands place is 7, which rounds the ten-thousands place up from 120,000 to 130,000. Choice A, 120,000, rounds down instead of up, ignoring that the thousands digit is 5 or greater. Choice C, 1,270,000, mistakenly adds an extra place value, making the number ten times too large. Choice D, 127,000, rounds to the nearest thousand instead of the nearest ten thousand.
17. Round 45,678 to the nearest thousand.
    Answer: 46,000 Since the hundreds digit in 45,678 is 6, which is 5 or greater, the number rounds up to 46,000, making Choice A correct. Choice B, 45,000, would be correct only if the hundreds digit were less than 5, but it is not. Choice C, 45,700, rounds to the nearest hundred instead of the nearest thousand. Choice D, 460,000, has an extra zero, as if the number were rounded to the nearest ten thousand instead. Looking at the hundreds digit tells you whether to round the thousands place up or keep it the same.
18. Emma rounds a mystery number to the nearest ten and gets $3,490$. She rounds the same number to the nearest hundred and gets $3,500$. Which of these could be Emma's mystery number?
    Answer: $3,493$ When you encounter rounding problems with two different place values, you need to find a number that satisfies both rounding conditions simultaneously. Think about the range of numbers that would round to each given value. For a number to round to $3,490$ when rounded to the nearest ten, it must be between $3,485$ and $3,494$ (since $3,485$ rounds up to $3,490$, while $3,495$ would round up to $3,500$). For the same number to round to $3,500$ when rounded to the nearest hundred, it must be between $3,450$ and $3,549$. The mystery number must fall in both ranges, so it's between $3,485$ and $3,494$. Only choice D) $3,493$ fits this range. Let's verify: $3,493$ rounds to $3,490$ (nearest ten) and $3,500$ (nearest hundred) ✓ Choice A) $3,485$ rounds to $3,490$ for the nearest ten, but rounds to $3,500$ for the nearest hundred, which seems right at first glance. However, $3,485$ is exactly at the boundary and would round to $3,490$ for tens, but the hundreds rounding works. Choice B) $3,504$ rounds to $3,500$ for both tens and hundreds, not $3,490$ for tens. Choice C) $3,496$ rounds to $3,500$ for tens (not $3,490$) and $3,500$ for hundreds. Study tip: When solving two-condition rounding problems, find the overlap between the two ranges. Draw number lines if it helps visualize which numbers satisfy both conditions.
19. A store manager rounds a four-digit number of the form 9,_67, where the blank is an unknown hundreds digit, to the nearest hundred and gets 9,600. Later, she rounds the same number to the nearest thousand and gets 10,000. What digit must be in the hundreds place?
    Answer: $5$ With a hundreds digit of 5, the number is 9,567; rounding to the nearest hundred looks at the tens digit (6), which rounds up to 9,600, and rounding to the nearest thousand looks at the hundreds digit (5), which rounds up to 10,000. Choice B would round to 9,700 for the nearest hundred, which doesn't match the given result. Choice C would round to 9,800 for the nearest hundred, which doesn't match either. Choice D would round to 9,900 for the nearest hundred, which also doesn't match. Choice A is the only digit that produces both given rounded values.
20. Keisha rounded $9,876$ to the nearest thousand. What is the result?
    Answer: 10,000 Since 9,876 is closer to 10,000 than to 9,000, it rounds up to 10,000, making Choice D correct. Choice A, 90,000, has an extra zero, as if the number were rounded to the nearest ten thousand instead of the nearest thousand. Choice B, 9,900, comes from rounding to the nearest hundred instead of the nearest thousand. Choice C, 9,000, would be correct only if the hundreds digit were less than 5, but since it is 8, the number rounds up instead. Looking at the hundreds digit tells you which thousand the number is closer to.

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