3A · Chapter 1 · Lesson 09
Rounding to the Nearest Ten
Locate a number between adjacent multiples of 10., Round whole numbers to the nearest ten including halfway cases., Choose whether a ten, hundred, or thousand estimate suits a problem.
Your starting challenge
Which number is nearer to 4,375: 4,370 or 4,380? What convention resolves the tie?
By the end, you can…
- Locate a number between adjacent multiples of 10.
- Round whole numbers to the nearest ten including halfway cases.
- Choose whether a ten, hundred, or thousand estimate suits a problem.
Before starting, you should know…
- Round to nearest hundred and thousand.
Entry · 2 questions
Quick prerequisite check
Try these two before the lesson. If either is confusing, review the listed prerequisites first.
- E1 Round 6,749 to the nearest hundred.
Show answer and reasoning
Answer: 6,700
It lies between 6,700 and 6,800; the midpoint is 6,750. With halfway values rounded up, choose 6,700.
- E2 A number line runs from 700 to 720 in 2 equal intervals. What is the step per interval?
Show answer and reasoning
Answer: 10
The total distance is 20. Divide by 2 equal intervals: 10.
Vocabulary to know
| nearest ten | The closest multiple of 10. |
|---|---|
| ones digit | The digit indicating single units. |
| reasonableness | Whether an answer fits the size and context of the quantities. |
Learn the concept
Ten-unit neighborhoods
3,476 lies between 3,470 and 3,480. The midpoint is 3,475. Since 3,476 is above midpoint, it rounds to 3,480.
The ones-digit shortcut
If the ones digit is 0–4, keep the lower multiple of ten. If it is 5–9, move to the upper multiple. Explain the shortcut with distance at least once.
Choose useful precision
Estimating a crowd might call for a hundred or thousand; estimating seats in a small room may call for the nearest ten. Rounding should serve the question rather than become a reflex.
Work through examples
Study the explanation; then try each check before opening its answer.
Worked example 1
Use distance, not a slogan
Round 3,476 to nearest ten.
- 3,470 and 3,480 are the two multiples of ten.
- Distance to 3,470 is 6; distance to 3,480 is 4.
Result: 3,480
Now you try · Understanding check 1
Round 5,724 to the nearest ten.Reveal answer and explanation
5,720 — It lies between 5,720 and 5,730; the midpoint is 5,725. With halfway values rounded up, choose 5,720.
Worked example 2
A halfway value
Round 4,375 to nearest ten.
- Midpoint between 4,370 and 4,380 is 4,375.
- The agreed classroom rule sends a positive halfway value upward.
Result: 4,380
Now you try · Understanding check 2
Round 2,065 to the nearest ten.Reveal answer and explanation
2,070 — It lies between 2,060 and 2,070; the midpoint is 2,065. With halfway values rounded up, choose 2,070.
Worked example 3
Changing a hundred
Round 2,997 to nearest ten.
- The nearest bounding tens are 2,990 and 3,000.
- 2,997 is only 3 from 3,000.
Result: 3,000
Now you try · Understanding check 3
Round 9,995 to the nearest ten.Reveal answer and explanation
10,000 — It lies between 9,990 and 10,000; the midpoint is 9,995. With halfway values rounded up, choose 10,000.
Guided · 4 questions
Guided practice
Try each problem; return to a visual model if you need one.
- G1 Round 1,624 to the nearest ten.
Show answer and reasoning
Answer: 1,620
It lies between 1,620 and 1,630; the midpoint is 1,625. With halfway values rounded up, choose 1,620.
- G2 Round 1,625 to the nearest ten.
Show answer and reasoning
Answer: 1,630
It lies between 1,620 and 1,630; the midpoint is 1,625. With halfway values rounded up, choose 1,630.
- G3 Round 3,499 to the nearest ten.
Show answer and reasoning
Answer: 3,500
It lies between 3,490 and 3,500; the midpoint is 3,495. With halfway values rounded up, choose 3,500.
- G4 Round 7,004 to the nearest ten.
Show answer and reasoning
Answer: 7,000
It lies between 7,000 and 7,010; the midpoint is 7,005. With halfway values rounded up, choose 7,000.
Independent · 8 questions
Independent practice
Work without looking at examples first. Show your thinking on paper.
- I1 Round 2,371 to the nearest ten.
Show answer and reasoning
Answer: 2,370
It lies between 2,370 and 2,380; the midpoint is 2,375. With halfway values rounded up, choose 2,370.
- I2 Round 4,875 to the nearest ten.
Show answer and reasoning
Answer: 4,880
It lies between 4,870 and 4,880; the midpoint is 4,875. With halfway values rounded up, choose 4,880.
- I3 Round 6,584 to the nearest ten.
Show answer and reasoning
Answer: 6,580
It lies between 6,580 and 6,590; the midpoint is 6,585. With halfway values rounded up, choose 6,580.
- I4 Round 9,509 to the nearest ten.
Show answer and reasoning
Answer: 9,510
It lies between 9,500 and 9,510; the midpoint is 9,505. With halfway values rounded up, choose 9,510.
- I5 Round 1,045 to the nearest ten.
Show answer and reasoning
Answer: 1,050
It lies between 1,040 and 1,050; the midpoint is 1,045. With halfway values rounded up, choose 1,050.
- I6 Round 9,999 to the nearest ten.
Show answer and reasoning
Answer: 10,000
It lies between 9,990 and 10,000; the midpoint is 9,995. With halfway values rounded up, choose 10,000.
- I7 Round 5,001 to the nearest ten.
Show answer and reasoning
Answer: 5,000
It lies between 5,000 and 5,010; the midpoint is 5,005. With halfway values rounded up, choose 5,000.
- I8 Round 7,346 to the nearest ten.
Show answer and reasoning
Answer: 7,350
It lies between 7,340 and 7,350; the midpoint is 7,345. With halfway values rounded up, choose 7,350.
Challenge · 2 questions
Challenge and transfer
These nonroutine problems require you to explain or adapt what you learned.
- C1 A whole number rounds to 3,860 to the nearest ten. What is the smallest whole number it could have been?
Show answer and reasoning
Answer: 3,855
The interval of whole numbers rounding to 3,860 starts halfway below, at 3,855, and ends at 3,864 (with halfway values rounded up).
- C2 Give the nearest-ten, nearest-hundred, and nearest-thousand roundings of 7,485.
Show answer and reasoning
Answer: 7,490; 7,500; 7,000
Nearest ten: halfway 7,485 rounds up. Nearest hundred: ≥7,450 rounds to 7,500. Nearest thousand: <7,500 rounds to 7,000.
Exit · 3 questions
Exit check
Use these fresh problems to decide whether to proceed. Answers should be independent.
- E1 Round 2,585 to the nearest ten.
Show answer and reasoning
Answer: 2,590
It lies between 2,580 and 2,590; the midpoint is 2,585. With halfway values rounded up, choose 2,590.
- E2 Round 9,544 to the nearest ten.
Show answer and reasoning
Answer: 9,540
It lies between 9,540 and 9,550; the midpoint is 9,545. With halfway values rounded up, choose 9,540.
- E3 What is the nearest ten to 8,999?
Show answer and reasoning
Answer: 9,000
8,999 is one away from 9,000, and nine away from 8,990.