Rounding Whole Numbers

🔢 Rounding Whole Numbers

Part 1 of 5 — Place Value, the Map Behind Rounding

Topics in This Part

🔑 Key Concept: Rounding means trading an exact number for a close, easier number. Before we can round, we have to know our place values cold — they are the map that tells us where to round. That is what Part 1 builds.

Why We Round

You don't always need an exact number. When a number is close enough to be useful, we round it.

• A stadium holds $48{,}273$ people. The newspaper says "about $48{,}000$ fans."
• A school raised $1,962. The principal announces "nearly $2,000!"
• A road trip is $311$ miles. Mom says "around $300$ miles."

Each rounded number is easier to say, remember, and picture — and it's still honest, because it stays close to the real value.

💡 Round = "make it friendlier." We keep the size of the number but smooth off the messy end so it's quick to use.

Place Value up to the Millions

Every digit in a number sits in a place, and each place is worth 10 times the place to its right.

Let's read $527{,}364$ properly:

So $527{,}364$ = five hundred twenty-seven thousand, three hundred sixty-four.

🔑 The comma helps you read. It splits the number into groups of three: millions | thousands | ones.

Concept Check 🎯

Name That Place 🧮

Look at the number $734{,}892$ and answer with a single digit.

1) Which digit is in the hundreds place? 2) Which digit is in the ten-thousands place? 3) Which digit is in the ones place?

Match the Place 🔽

Use the number $615{,}049$ to fill in each blank.

You're Ready to Round

You can now spot the digit in any place. That's the whole foundation, because rounding always starts the same way: "To which place am I rounding?"

In Part 2 we'll meet the number line, the picture that makes rounding feel obvious — you'll see which way a number leans.

🔢 Rounding Whole Numbers

Part 2 of 5 — The Number Line Picture

🔑 The Idea: Rounding asks, "Which landmark number is my number closest to?" A number line lets you see the two nearest landmarks and decide which one wins.

Nearest Ten

To round to the nearest ten, find the two tens your number sits between, then pick the closer one.

Round $47$ to the nearest ten:

40 ----------------------- 47 -- 50
          (lower)               (upper)

• $47$ is between $40$ and $50$.
• It's only $3$ away from $50$ but $7$ away from $40$.
• So $47$ rounds up to $\mathbf{50}$.

The Halfway Mark

The exact middle between $40$ and $50$ is $45$. This is the tie-breaker line:

• Below $45$ → round down to $40$.
• At $45$ or above → round up to $50$.

🔑 The rule of $5$: if a number lands on the halfway mark ($45$, $450$, etc.) we agree to round up. Math teachers everywhere use this "round half up" rule.

Concept Check 🎯

Nearest Hundred

The same picture works for hundreds — just use hundred landmarks.

Round $273$ to the nearest hundred:

200 -------------- 250 ------ 273 -- 300
              (halfway)            (upper)

• $273$ is between $200$ and $300$.
• The halfway mark is $250$.
• $273$ is past $250$, so it rounds up to $\mathbf{300}$.

And round $612$ to the nearest hundred:

• Between $600$ and $700$, halfway is $650$.
• $612$ is before $650$, so it rounds down to $\mathbf{600}$.

💡 You never have to draw the whole line. Just ask: "Did my number pass the halfway mark?" Past it → up. Before it → down.

Up or Down? 🔽

Decide which way each number leans, then give the rounded result.

Round with the Picture 🧮

1) Round $61$ to the nearest ten. $=\,?$ 2) Round $85$ to the nearest ten. $=\,?$ 3) Round $349$ to the nearest hundred. $=\,?$

🔢 Rounding Whole Numbers

Part 3 of 5 — The Digit Rule (No Number Line Needed)

🔑 Why it works: Drawing a line is slow. The digit rule does the same thing instantly: just peek at the digit one place to the right of where you're rounding.

The 4-Step Digit Rule

To round any whole number:

1. Find the digit in the place you are rounding to. Call it the rounding digit. Underline it.
2. Look right — at the very next digit. This is the decider.
3. Decide:
   • Decider is $0,1,2,3,4$ → round down (rounding digit stays the same).
   • Decider is $5,6,7,8,9$ → round up (rounding digit goes up by $1$).
4. Replace every digit to the right of the rounding digit with $0$.

🔑 "$5$ or more, raise the score. $4$ or less, let it rest." That rhyme is the whole rule.

Worked Example: round $3{,}471$ to the nearest hundred

1. Rounding digit (hundreds) = $4$ → $3{,}\underline{4}71$
2. Decider (next digit right) = $7$
3. $7$ is "$5$ or more" → round up: $4 \to 5$
4. Zero out the rest → $3{,}500$

$3{,}471 \;\longrightarrow\; 3{,}500$

Worked Example: round $3{,}471$ to the nearest thousand

1. Rounding digit (thousands) = $3$ → $\underline{3}{,}471$
2. Decider = $4$ (the hundreds digit)
3. $4$ is "$4$ or less" → round down: $3$ stays $3$
4. Zero out the rest → $3{,}000$

$3{,}471 \;\longrightarrow\; 3{,}000$

Worked Example: round $58{,}640$ to the nearest ten-thousand

1. Rounding digit (ten-thousands) = $5$ → $\underline{5}8{,}640$
2. Decider = $8$ (the thousands digit)
3. $8$ is "$5$ or more" → round up: $5 \to 6$
4. Zero out the rest → $60{,}000$

$58{,}640 \;\longrightarrow\; 60{,}000$

⚠️ Only the decider matters! When rounding $58{,}640$ to the nearest ten-thousand, the $640$ at the end does not vote. Just the one digit to the right of your rounding place.

Concept Check 🎯

Walk the Rule 🔽

Round $\mathbf{6{,}248}$ to the nearest hundred, one step at a time.

Use the Digit Rule 🧮

1) Round $4{,}826$ to the nearest hundred. $=\,?$ 2) Round $4{,}826$ to the nearest thousand. $=\,?$ 3) Round $73{,}500$ to the nearest thousand. $=\,?$

🔢 Rounding Whole Numbers

Part 4 of 5 — Tricky Cases & Real-World Estimation

🔑 Big Payoff: Two things trip students up — carrying a 9 up to a new place and choosing what to round in a word problem. Master both here and you've mastered rounding.

When the Rounding Digit Is a 9

What happens if you round up a $9$? A $9$ can't become a "$10$" in one box — it rolls over, just like $9 + 1 = 10$ does.

Worked Example: round $397$ to the nearest ten

1. Rounding digit (tens) = $9$ → $3\underline{9}7$
2. Decider = $7$ → "$5$ or more," round up.
3. The $9$ would become $10$, so it carries: the tens become $0$ and the hundreds go from $3$ to $4$.

$397 \;\longrightarrow\; 400$

Worked Example: round $1{,}960$ to the nearest hundred

1. Rounding digit (hundreds) = $9$ → $1{,}\underline{9}60$
2. Decider = $6$ → round up.
3. The $9$ carries: hundreds → $0$, thousands $1 \to 2$.

$1{,}960 \;\longrightarrow\; 2{,}000$

⚠️ Don't write "$3{,}\!(10)0$". When a $9$ rounds up, let it roll into the next place — exactly like regrouping in addition.

Concept Check 🎯

Rounding to Estimate in Word Problems

Rounding makes estimating quick. The trick is choosing a sensible place to round to.

Example: A book fair sold $312$ books on Friday and $589$ on Saturday. About how many in all?

Round each to the nearest hundred, then add:

$312 \approx 300, \qquad 589 \approx 600$ $300 + 600 = 900 \text{ books (about)}$

The exact total is $312 + 589 = 901$, so our estimate of $900$ is excellent.

Example: A theater has $48$ rows of $52$ seats. About how many seats?

Round to the nearest ten, then multiply:

$48 \approx 50, \qquad 52 \approx 50$ $50 \times 50 = 2{,}500 \text{ seats (about)}$

💡 Estimate first, then check. If your exact answer is wildly far from your estimate, you probably made a mistake somewhere.

Estimate the Trip 🔽

A family drives $278$ miles on Day 1 and $431$ miles on Day 2. Estimate the total by rounding to the nearest hundred.

Carries & Estimates 🧮

1) Round $798$ to the nearest ten. $=\,?$ 2) Round $2{,}951$ to the nearest hundred. $=\,?$ 3) A store sold $194$ shirts and $207$ hats. Round each to the nearest hundred and add: $=\,?$

🔢 Rounding Whole Numbers

Part 5 of 5 — Mixed Practice & Mastery Check

You can now (1) name any place value, (2) use the number-line picture, (3) apply the digit rule, and (4) handle $9$-carries and word-problem estimates. Time to put it all together.

Quick Reference

⚠️ The two classic mistakes: (1) looking at all the digits instead of just the decider, and (2) forgetting to zero out the digits to the right. Avoid those and you're golden.

Mixed Practice 🎯

One More Round 🧮

1) Round $84{,}500$ to the nearest thousand. $=\,?$ 2) Round $6{,}098$ to the nearest hundred. $=\,?$ 3) Estimate $403 + 298$ by rounding each to the nearest hundred. $=\,?$

Exit Quiz ✅

Answer all three to finish the lesson.