3A · Chapter 1 · Lesson 08
Rounding to the Nearest Hundred
Find adjacent hundreds around a given number., Use the midpoint to choose the nearer hundred., Compare nearest-hundred and nearest-thousand estimates.
Your starting challenge
Would a number of 3,449 become 3,400 or 3,500 when rounded to the nearest hundred? What one-digit change flips the answer?
By the end, you can…
- Find adjacent hundreds around a given number.
- Use the midpoint to choose the nearer hundred.
- Compare nearest-hundred and nearest-thousand estimates.
Before starting, you should know…
- Round to the nearest thousand.
- Read number-line intervals.
Entry · 2 questions
Quick prerequisite check
Try these two before the lesson. If either is confusing, review the listed prerequisites first.
- E1 Round 7,399 to the nearest thousand.
Show answer and reasoning
Answer: 7,000
It lies between 7,000 and 8,000; the midpoint is 7,500. With halfway values rounded up, choose 7,000.
- E2 A number line runs from 3,400 to 3,500 in 2 equal intervals. What is the step per interval?
Show answer and reasoning
Answer: 50
The total distance is 100. Divide by 2 equal intervals: 50.
Vocabulary to know
| nearest hundred | The closest multiple of 100. |
|---|---|
| bounding hundreds | The multiples of 100 immediately below and above a number. |
| precision | The degree of detail kept in a measurement or estimate. |
Learn the concept
Find the hundreds first
3,449 lies between 3,400 and 3,500. The halfway point is 3,450, so 3,449 rounds to 3,400.
The tens digit is a shortcut
For whole numbers, looking at the tens digit tells which side of the hundred midpoint the number lies on. A tens digit of 5–9 rounds up, while 0–4 rounds down.
Different precision, different answers
3,449 rounds to 3,400 (nearest hundred) and 3,000 (nearest thousand). Neither is the exact number. Always state the required precision.
Work through examples
Study the explanation; then try each check before opening its answer.
Worked example 1
Just below halfway
Round 3,449 to the nearest hundred.
- Bounds: 3,400 and 3,500.
- Midpoint: 3,450.
- 3,449 lies just below midpoint.
Result: 3,400
Now you try · Understanding check 1
Round 3,450 to the nearest hundred.Reveal answer and explanation
3,500 — It lies between 3,400 and 3,500; the midpoint is 3,450. With halfway values rounded up, choose 3,500.
Worked example 2
A carrying boundary
Round 4,970 to the nearest hundred.
- Bounding hundreds are 4,900 and 5,000.
- Midpoint is 4,950.
- 4,970 lies above the midpoint.
Result: 5,000
Now you try · Understanding check 2
Round 9,949 to the nearest hundred.Reveal answer and explanation
9,900 — It lies between 9,900 and 10,000; the midpoint is 9,950. With halfway values rounded up, choose 9,900.
Worked example 3
Compare precisions
Round 6,749 to nearest hundred, then nearest thousand.
- Nearest hundred: midpoint 6,750; 6,749 rounds to 6,700.
- Nearest thousand: midpoint 6,500; 6,749 rounds to 7,000.
Result: 6,700 and 7,000
Now you try · Understanding check 3
Round 4,480 to nearest hundred and thousand.Reveal answer and explanation
4,500 and 4,000 — 4,480 is ≥4,450 and <4,500, so 4,500 to hundred; it is <4,500, so 4,000 to thousand.
Guided · 4 questions
Guided practice
Try each problem; return to a visual model if you need one.
- G1 Round 3,749 to the nearest hundred.
Show answer and reasoning
Answer: 3,700
It lies between 3,700 and 3,800; the midpoint is 3,750. With halfway values rounded up, choose 3,700.
- G2 Round 3,750 to the nearest hundred.
Show answer and reasoning
Answer: 3,800
It lies between 3,700 and 3,800; the midpoint is 3,750. With halfway values rounded up, choose 3,800.
- G3 Round 5,051 to the nearest hundred.
Show answer and reasoning
Answer: 5,100
It lies between 5,000 and 5,100; the midpoint is 5,050. With halfway values rounded up, choose 5,100.
- G4 Round 9,961 to the nearest hundred.
Show answer and reasoning
Answer: 10,000
It lies between 9,900 and 10,000; the midpoint is 9,950. With halfway values rounded up, choose 10,000.
Independent · 8 questions
Independent practice
Work without looking at examples first. Show your thinking on paper.
- I1 Round 1,218 to the nearest hundred.
Show answer and reasoning
Answer: 1,200
It lies between 1,200 and 1,300; the midpoint is 1,250. With halfway values rounded up, choose 1,200.
- I2 Round 1,550 to the nearest hundred.
Show answer and reasoning
Answer: 1,600
It lies between 1,500 and 1,600; the midpoint is 1,550. With halfway values rounded up, choose 1,600.
- I3 Round 4,601 to the nearest hundred.
Show answer and reasoning
Answer: 4,600
It lies between 4,600 and 4,700; the midpoint is 4,650. With halfway values rounded up, choose 4,600.
- I4 Round 4,799 to the nearest hundred.
Show answer and reasoning
Answer: 4,800
It lies between 4,700 and 4,800; the midpoint is 4,750. With halfway values rounded up, choose 4,800.
- I5 Round 7,299 to the nearest hundred.
Show answer and reasoning
Answer: 7,300
It lies between 7,200 and 7,300; the midpoint is 7,250. With halfway values rounded up, choose 7,300.
- I6 Round 8,750 to the nearest hundred.
Show answer and reasoning
Answer: 8,800
It lies between 8,700 and 8,800; the midpoint is 8,750. With halfway values rounded up, choose 8,800.
- I7 Round 9,950 to the nearest hundred.
Show answer and reasoning
Answer: 10,000
It lies between 9,900 and 10,000; the midpoint is 9,950. With halfway values rounded up, choose 10,000.
- I8 Round 6,048 to the nearest hundred.
Show answer and reasoning
Answer: 6,000
It lies between 6,000 and 6,100; the midpoint is 6,050. With halfway values rounded up, choose 6,000.
Challenge · 2 questions
Challenge and transfer
These nonroutine problems require you to explain or adapt what you learned.
- C1 A whole number rounds to 7,200 to the nearest hundred. What is the smallest whole number it could have been?
Show answer and reasoning
Answer: 7,150
The interval of whole numbers rounding to 7,200 starts halfway below, at 7,150, and ends at 7,249 (with halfway values rounded up).
- C2 Round 4,450 first to the nearest hundred and then round that result to the nearest thousand. Compare with rounding the original number directly to the nearest thousand.
Show answer and reasoning
Answer: Two-stage: 5,000; direct: 4,000
First 4,450 rounds to 4,500 at the hundred, then 4,500 rounds to 5,000 at the thousand. Direct rounding of the original 4,450 to the nearest thousand gives 4,000 because it is below the midpoint 4,500. Repeated rounding can mislead.
Exit · 3 questions
Exit check
Use these fresh problems to decide whether to proceed. Answers should be independent.
- E1 Round 5,649 to the nearest hundred.
Show answer and reasoning
Answer: 5,600
It lies between 5,600 and 5,700; the midpoint is 5,650. With halfway values rounded up, choose 5,600.
- E2 Round 5,650 to the nearest hundred.
Show answer and reasoning
Answer: 5,700
It lies between 5,600 and 5,700; the midpoint is 5,650. With halfway values rounded up, choose 5,700.
- E3 What midpoint separates numbers rounding to 8,300 versus 8,400?
Show answer and reasoning
Answer: 8,350
The two hundreds are 100 apart; halfway is 50 beyond 8,300.