Rounding Multi-Digit Whole Numbers

Grade 4 Number and Operations in Base Ten: 4.NBT.A.3

In this lesson:

• Round any number to any place, with a reason why
• Use rounding to make quick, useful estimates

Learning Objectives for This Lesson

You will learn to:

1. Round a number to any place, tens through hundred-thousands
2. Use a number line to explain a rounding result
3. Apply the round-up rule for exact halfway numbers
4. Explain which digits change and which stay the same
5. Use rounding to make real-world estimates

$4,738 — "About $5,000" or "About $4,700"?

• The principal says the fundraiser earned about $5,000.
• The treasurer says it earned about $4,700.
• Both are talking about the same $4,738. Can they both be right?

Warm-Up Review: Round 73 to the Nearest Ten

• The nearest tens are 70 and 80.
• 73 is closer to 70.
• So 73 rounds to 70.

Two Words That Carry This Lesson

• A multiple of 1,000 is a number you land on counting by thousands: 4,000, 5,000, 6,000.
• The midpoint is the number exactly halfway between two neighboring multiples.

4,271 on the Number Line

4,271 falls to the left of the midpoint, 4,500 — closer to 4,000.

4,738 on the Same Line

4,738 falls to the right of the midpoint — closer to 5,000.

Predict First: Where Does Exactly-Halfway Go?

If a number lands exactly on the midpoint, 4,500, is it closer to 4,000, closer to 5,000, or neither? Predict before advancing.

The Convention: Halfway Rounds Up

4,500 is exactly halfway. By agreement, exactly-halfway numbers round up — to 5,000.

Extending the Pattern to Ten-Thousands

• Neighboring multiples of 10,000: 30,000 and 40,000.
• Midpoint: 35,000.
• 36,200 is to the right of 35,000 — it rounds to 40,000.

Plot It, Then Round It

For each number, name the two neighboring multiples, plot the number, and state the rounded value:

1. 850 (nearest hundred)
2. 6,150 (nearest thousand)
3. 62,500 (nearest ten-thousand) — watch for the midpoint

The Number Line Works, But It's Slow

Drawing a number line for every rounding question works, but it's slow once numbers get large.

Let's find a shortcut that gives the same answer, faster.

Predict First: Same as Rounding?

A student rounds 4,738 to the nearest thousand by simply dropping the last three digits, getting 4,000. Is that correct? Predict before advancing.

Look Right Before You Decide

• 4,738: dropping digits gives 4,000 — but 4,738 is actually closer to 5,000.
• Dropping digits always gives the lower multiple. That's not the same as rounding.
• The digit to the right (7) tells you: 7 ≥ 5, so round up.

Rounding 8,463 to the Nearest Hundred

Step 1: Underline the hundreds digit: 8,463.
Step 2: Look right — the tens digit is 6.
Step 3: 6 ≥ 5, so round up: 8,500.

Predict First: Does This 5 Round Up?

You're rounding 456,123 to the nearest ten-thousand. There's a 5 right there in the number. Does that mean you round up? Predict before advancing.

Only ONE Digit to the Right Decides

• The ten-thousands digit, 5, is the digit being rounded — not the decider.
• The digit to its right, the thousands digit 6, is the one that decides.
• 6 ≥ 5, so round up: 456,123 → 460,000.

Rounding 3,962: What Happens When 9 Rounds Up?

• Underline the hundreds digit: 3,962. Look right: 6 ≥ 5, round up.
• 9 + 1 = 10 — too big for one place!

Round at Every Place, Tens Through Hundred-Thousands

1. 52,347 (nearest ten-thousand)
2. 749,500 (nearest hundred-thousand)
3. 6,950 (nearest hundred) — watch for a carry
4. 620 (nearest ten)

One Digit Changes — What About the Rest?

You've been changing one underlined digit and zeroing the digits after it.

But what happens to the digits before the one you rounded?

Find the Error: 463,821 Rounded to 500,000

A student rounds 463,821 to the nearest ten-thousand and writes 500,000. What went wrong?

Left Stays, Right Becomes Zero

The student changed the hundred-thousands digit — but rounding to ten-thousands should never touch it. Correct answer: 460,000.

The One Exception: When 9 Carries Left

• Rule: digits left of the rounding place never change... except one case.
• Round 997 to the nearest ten: the tens digit 9 rounds up, carries all the way through.
• Result: 1,000 — the hundreds and thousands digits changed too.

One Number, Two Rounding Places

• 463,821 to the nearest thousand: the 3 rounds up (8 ≥ 5) → 464,000.
• 463,821 to the nearest hundred: the 8 stays (2 < 5) → 463,800.
• Same number, two different boundaries, two different answers.

Round One Number Five Ways

Round 597,346 to the nearest ten, hundred, thousand, ten-thousand, and hundred-thousand. Stack your five answers.

Back to the Fundraiser Question

Remember the $4,738 fundraiser from the start of class?

You now have everything you need to settle it.

Both Were Right — Different Places

• The principal rounded $4,738 to the nearest thousand: about $5,000.
• The treasurer rounded to the nearest hundred: about $4,700.
• Neither is wrong — they simply chose different rounding units.

Estimating a Total: $47 + $23 + $86

• Round each to the nearest ten: $50 + $20 + $90 = $160.
• Exact total: $47 + $23 + $86 = $156.
• Close enough for a quick estimate, and much faster to add.

Two Towns, Two Rounding Units

Rounding too coarsely can completely hide a real difference.

A Stadium of 67,428 — You Choose

A stadium holds 67,428 people. About how many is that?

Choose your own rounding unit, and be ready to explain why it fits.

Is "About the Same Size" a Fair Claim?

A classmate says: "Town A and Town B both round to about 30,000 people, so they're basically the same size." Is that a fair way to describe them?

Four Common Mistakes to Double-Check

Only digits right of the rounding place change.

Dropping digits isn't rounding — check if it's 5 or more.

A 5 elsewhere doesn't count — only the one digit right of the place decides.

9 rounding up carries into the next place, like addition.

Key Takeaways From This Lesson

✓ Rounding asks which multiple a number is closer to.
✓ The digit right of the rounding place answers that.
✓ Left-side digits never change — except through a 9-carry.
✓ Choose a rounding unit based on the precision you need.

Coming Up Next: Estimating Sums

Before you add or subtract large numbers, you'll round first to predict roughly what the answer should be.

That prediction is how you catch a computation mistake before it slips by.