Unit 2 • 5.NBT.4 Rounding Decimals
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Rounding Decimals

How do we round decimals to different place values?

📚
Unit
2
📅
Standard
NBT.4
⏱️
Duration
60m

📋 Standards & Objectives

📐Standard
5.NBT.4Use place value understanding to round decimals to any place.
🎯SWBAT
  • Round decimals to the nearest whole number
  • Round decimals to the nearest tenth
  • Round decimals to the nearest hundredth
  • Use number lines and place value rules to round

💭 When Do We Round?

⛽Gas Prices

Gas costs $3.459 per gallon. We say "about $3.46" — that's rounding to the nearest hundredth!

⚾Sports Stats

A batting average of .3246 gets reported as .325 — rounded to the nearest thousandth!

🧁Cooking

A recipe calls for 2.347 cups. We measure "about 2.3 cups" — rounding to the nearest tenth!

📚 Key Vocabulary

🔢Place Value

The value of a digit based on its position in a number. In 4.538: 5 is in the tenths, 3 is in the hundredths, 8 is in the thousandths.

⬆️Round Up

Increase the target digit by 1 when the digit to its right is 5, 6, 7, 8, or 9.

⬇️Round Down

Keep the target digit the same when the digit to its right is 0, 1, 2, 3, or 4.

📏Benchmark Numbers

The two numbers a decimal falls between. For 7.83, the benchmarks are 7 and 8.

💡 Nearest Whole: Number Line

To round to the nearest whole number, find which two whole numbers the decimal falls between.

Example: Where does 7.83 fall?

7
7.5
8
7.83

7.83 is past the midpoint (7.5), so it rounds UP to 8!

📏 The Rounding Rule

Look at the digit to the right of the place you're rounding to:

0, 1, 2, 3, 4
"0 to 4... Do No More!"
Round DOWN — keep the digit the same
5, 6, 7, 8, 9
"5 to 9... Climb the Vine!"
Round UP — increase the digit by 1

3.72 → tenths digit is 7 → Round UP → 4

12.28 → tenths digit is 2 → Round DOWN → 12

📌 Writing Your Rounded Answer

Follow these 4 steps every time you round:

1 Find the Star ⭐

Underline the digit in the rounding place. This is your Star.

2 Check the Helper 🔎

Look at the digit one place to the right. It tells you: round up or stay?

3 Round the Star ✅

Helper is 5–9? Star goes up by 1. Helper is 0–4? Star stays.

4 Write Your Answer ✍️

Digits left of Star stay. Everything right (including helper) → becomes 0 or drops off.

Example: Round 5.67893 to the nearest tenth

① Find the Star

5.67893

② Check the Helper

5.67893

③ Round UP

5.7

Helper is 7 (≥ 5) → Star goes from 6 to 7 → trailing zeros drop off → 5.7

📌 The Zero Cleanup Rule

When the Replacements become zeros, ask: are those zeros doing a job?

✅Placeholder Zeros STAY

Zeros between the rounding place and the decimal point are holding a place. They do important work!

Round 73,999 to the nearest hundred:

73,999 → 74,000 = 74,000

The zeros hold the tens and ones places — they STAY! ✅

🚫Trailing Zeros DROP OFF

Zeros after the decimal with nothing after them aren't holding any place. They're not doing any work!

Round 5.67893 to the nearest tenth:

5.70000 → 5.7

The zeros aren't holding any places — they DROP OFF! 🚫

💡 Quick Test: Are the zeros between the rounding place and the decimal point?

YES → Keep them!    NO → Drop them!

✏️ Writing Practice A

👨‍🏫 I Do • Writing Your Answer
Round 8.4932
to the nearest tenth
1 2 3 4 Four-Step Strategy
1 Find the Star: The tenths place is the rounding place → 8.4932
2 Check the Helper: The digit to the right is 9 — Since 9 ≥ 5 → we round UP
3 Round the Star: The 4 goes up by 1 → 8.5
4 Write it: Digits left of Star stay (8.) ✅ — Everything right becomes 0 → 8.5000 → Trailing zeros drop off → 8.5
✓ Answer
8.4932 ≈ 8.5

✏️ Writing Practice B

👨‍🏫 I Do • Writing Your Answer
Round 47,562
to the nearest thousand
1 2 3 4 Four-Step Strategy
1 Find the Star: The thousands place is the rounding place → 47,562
2 Check the Helper: The digit to the right is 5 — Since 5 ≥ 5 → we round UP
3 Round the Star: The 7 goes up by 1 → 48,___
4 Write it: Digits left of Star stay (4) ✅ — Everything right becomes 0 → 48,000 — Placeholder zeros hold the hundreds, tens, ones → 48,000
✓ Answer
47,562 ≈ 48,000

✏️ Writing Practice C

👥 We Do • Writing Your Answer
Round 3.08716
to the nearest hundredth
1 2 3 4 Four-Step Strategy
1 Find the Star: The hundredths place is the rounding place → 3.08716
2 Check the Helper: The digit to the right is 7 — Since 7 ≥ 5 → we round UP
3 Round the Star: The 8 goes up by 1 → 3.09
4 Write it: Digits left of Star stay (3.0) ✅ — Everything right becomes 0 → 3.09000 → Trailing zeros drop off → 3.09
✓ Answer
3.08716 ≈ 3.09

✏️ Writing Practice D

👥 We Do • Writing Your Answer
Round 6,347
to the nearest hundred
1 2 3 4 Four-Step Strategy
1 Find the Star: The hundreds place is the rounding place → 6,347
2 Check the Helper: The digit to the right is 4 — Since 4 < 5 → we round DOWN (Star stays)
3 Round the Star: The 3 stays the same → 6,3__
4 Write it: Digits left of Star stay (6,) ✅ — Everything right becomes 0 → 6,300 — Placeholder zeros hold the tens and ones → 6,300
✓ Answer
6,347 ≈ 6,300

✏️ Writing Practice E

✏️ You Do • Writing Your Answer
Round 12.8651
to the nearest tenth
1 2 3 4 Four-Step Strategy
1 Find the Star: The tenths place is the rounding place → 12.8651
2 Check the Helper: The digit to the right is 6 — Since 6 ≥ 5 → we round UP
3 Round the Star: The 8 goes up by 1 → 12.9
4 Write it: Digits left of Star stay (12.) ✅ — Everything right becomes 0 → 12.9000 → Trailing zeros drop off → 12.9
✓ Answer
12.8651 ≈ 12.9

✏️ Writing Practice F

✏️ You Do • Writing Your Answer
Round 85,472
to the nearest thousand
1 2 3 4 Four-Step Strategy
1 Find the Star: The thousands place is the rounding place → 85,472
2 Check the Helper: The digit to the right is 4 — Since 4 < 5 → we round DOWN (Star stays)
3 Round the Star: The 5 stays the same → 85,___
4 Write it: Digits left of Star stay (8) ✅ — Everything right becomes 0 → 85,000 — Placeholder zeros hold the hundreds, tens, ones → 85,000
✓ Answer
85,472 ≈ 85,000

✏️ Problem 1

👨‍🏫 I Do • Nearest Whole
Round 5.72
to the nearest whole number
💡 Number Line Strategy
1 Find the benchmarks. 5.72 is between 5 and 6. The midpoint is 5.5.
2 Look at the tenths digit: it's 7. Since 7 ≥ 5 → "5 to 9... Climb the Vine!" Round UP.
⬆️ The tenths digit (7) tells us to round UP because 7 ≥ 5
Number Line
5
5.5
6
5.72
0.28
0.72
✓ Answer
5.72 ≈ 6

✏️ Problem 2

👨‍🏫 I Do • Nearest Whole
Round 14.36
to the nearest whole number
💡 Number Line Strategy
1 Find the benchmarks. 14.36 is between 14 and 15. The midpoint is 14.5.
2 Look at the tenths digit: it's 3. Since 3 < 5 → "0 to 4... Do No More!" Round DOWN.
⬇️ The tenths digit (3) tells us to round DOWN because 3 < 5
Number Line
14
14.5
15
14.36
0.36
0.64
✓ Answer
14.36 ≈ 14

✏️ Problem 3

👥 We Do • Nearest Whole
Round 8.51
to the nearest whole number
💡 Number Line Strategy
1 Find the benchmarks. 8.51 is between 8 and 9. The midpoint is 8.5.
2 Look at the tenths digit: it's 5. Since 5 ≥ 5 → "5 to 9... Climb the Vine!" Round UP.
⬆️ Exactly 5? That still rounds UP! 5 to 9... Climb the Vine!
Number Line
8
8.5
9
8.51
0.49
0.51
✓ Answer
8.51 ≈ 9

✏️ Problem 4

👥 We Do • Nearest Whole
Round 21.47
to the nearest whole number
💡 Number Line Strategy
1 Find the benchmarks. 21.47 is between 21 and 22. The midpoint is 21.5.
2 Look at the tenths digit: it's 4. Since 4 < 5 → "0 to 4... Do No More!" Round DOWN.
⬇️ The tenths digit (4) tells us to round DOWN because 4 < 5
Number Line
21
21.5
22
21.47
0.47
0.53
✓ Answer
21.47 ≈ 21

✏️ Problem 5

💪 You Do • Nearest Whole
Round 6.83
to the nearest whole number
💡 Number Line Strategy
1 Find the benchmarks. 6.83 is between 6 and 7. The midpoint is 6.5.
2 Look at the tenths digit: it's 8. Since 8 ≥ 5 → "5 to 9... Climb the Vine!" Round UP.
⬆️ The tenths digit (8) tells us to round UP because 8 ≥ 5
Number Line
6
6.5
7
6.83
0.17
0.83
✓ Answer
6.83 ≈ 7

✏️ Problem 6

💪 You Do • Nearest Whole
Round 37.15
to the nearest whole number
💡 Number Line Strategy
1 Find the benchmarks. 37.15 is between 37 and 38. The midpoint is 37.5.
2 Look at the tenths digit: it's 1. Since 1 < 5 → "0 to 4... Do No More!" Round DOWN.
⬇️ The tenths digit (1) tells us to round DOWN because 1 < 5
Number Line
37
37.5
38
37.15
0.15
0.85
✓ Answer
37.15 ≈ 37

💡 Nearest Tenth: Number Line

To round to the nearest tenth, find which two tenths the decimal falls between.

Example: Where does 3.47 fall?

3.4
3.45
3.5
3.47

3.47 is past the midpoint (3.45), so it rounds UP to 3.5!

📏 Nearest Tenth: The Rule

When rounding to the nearest tenth, look at the hundredths digit:

Which digit do we look at?

3.47

Rounding place ↑   Look here ↑

0, 1, 2, 3, 4
"0 to 4... Do No More!"
Keep the tenths digit the same
5, 6, 7, 8, 9
"5 to 9... Climb the Vine!"
Increase the tenths digit by 1

6.538 → hundredths digit is 3 → Round DOWN → 6.5

9.281 → hundredths digit is 8 → Round UP → 9.3

✏️ Problem 7

👨‍🏫 I Do • Nearest Tenth
Round 2.74
to the nearest tenth
💡 Number Line Strategy
1 Find the benchmarks. 2.74 is between 2.7 and 2.8. The midpoint is 2.75.
2 Look at the hundredths digit: it's 4. Since 4 < 5 → "0 to 4... Do No More!" Round DOWN.
⬇️ The hundredths digit (4) tells us to round DOWN because 4 < 5
Number Line
2.7
2.75
2.8
2.74
0.04
0.06
✓ Answer
2.74 ≈ 2.7

✏️ Problem 8

👨‍🏫 I Do • Nearest Tenth
Round 15.628
to the nearest tenth
💡 Number Line Strategy
1 Find the benchmarks. 15.628 is between 15.6 and 15.7. The midpoint is 15.65.
2 Look at the hundredths digit: it's 2. Since 2 < 5 → "0 to 4... Do No More!" Round DOWN.
⬇️ The hundredths digit (2) tells us to round DOWN because 2 < 5
Number Line
15.6
15.65
15.7
15.628
0.028
0.072
✓ Answer
15.628 ≈ 15.6

✏️ Problem 9

👥 We Do • Nearest Tenth
Round 9.35
to the nearest tenth
💡 Number Line Strategy
1 Find the benchmarks. 9.35 is between 9.3 and 9.4. The midpoint is 9.35 — our number is RIGHT on it!
2 Look at the hundredths digit: it's 5. Since 5 ≥ 5 → "5 to 9... Climb the Vine!" Round UP.
⬆️ Exactly at the midpoint? That STILL rounds UP! 5 to 9... Climb the Vine!
Number Line
9.3
9.35
9.4
9.35
0.05
0.05
✓ Answer
9.35 ≈ 9.4

✏️ Problem 10

👥 We Do • Nearest Tenth
Round 4.817
to the nearest tenth
💡 Number Line Strategy
1 Find the benchmarks. 4.817 is between 4.8 and 4.9. The midpoint is 4.85.
2 Look at the hundredths digit: it's 1. Since 1 < 5 → "0 to 4... Do No More!" Round DOWN.
⬇️ The hundredths digit (1) tells us to round DOWN because 1 < 5
Number Line
4.8
4.85
4.9
4.817
0.017
0.083
✓ Answer
4.817 ≈ 4.8

✏️ Problem 11

✏️ You Do • Nearest Tenth
Round 7.42
to the nearest tenth
💡 Number Line Strategy
1 Find the benchmarks. 7.42 is between 7.4 and 7.5. The midpoint is 7.45.
2 Look at the hundredths digit: it's 2. Since 2 < 5 → "0 to 4... Do No More!" Round DOWN.
⬇️ The hundredths digit (2) tells us to round DOWN because 2 < 5
Number Line
7.4
7.45
7.5
7.42
0.02
0.08
✓ Answer
7.42 ≈ 7.4

✏️ Problem 12

✏️ You Do • Nearest Tenth
Round 22.965
to the nearest tenth
💡 Number Line Strategy
1 Find the benchmarks. 22.965 is between 22.9 and 23.0. The midpoint is 22.95.
2 Look at the hundredths digit: it's 6. Since 6 ≥ 5 → "5 to 9... Climb the Vine!" Round UP.
⬆️ The hundredths digit (6) tells us to round UP. Notice: 22.965 rounds to 23.0 — keep that trailing zero!
Number Line
22.9
22.95
23.0
22.965
0.035
0.065
✓ Answer
22.965 ≈ 23.0

💡 Nearest Hundredth: Number Line

To round to the nearest hundredth, find which two hundredths the decimal falls between.

Example: Where does 4.637 fall?

4.63
4.635
4.64
4.637

4.637 is past the midpoint (4.635), so it rounds UP to 4.64!

📏 Nearest Hundredth: The Rule

When rounding to the nearest hundredth, look at the thousandths digit:

Which digit do we look at?

4.637

Rounding place ↑   Look here ↑

0, 1, 2, 3, 4
"0 to 4... Do No More!"
Keep the hundredths digit the same
5, 6, 7, 8, 9
"5 to 9... Climb the Vine!"
Increase the hundredths digit by 1

8.123 → thousandths digit is 3 → Round DOWN → 8.12

5.749 → thousandths digit is 9 → Round UP → 5.75

✏️ Problem 13

👨‍🏫 I Do • Nearest Hundredth
Round 7.453
to the nearest hundredth
💡 Number Line Strategy
1 Find the benchmarks. 7.453 is between 7.45 and 7.46. The midpoint is 7.455.
2 Look at the thousandths digit: it's 3. Since 3 < 5 → "0 to 4... Do No More!" Round DOWN.
⬇️ The thousandths digit (3) tells us to round DOWN because 3 < 5
Number Line
7.45
7.455
7.46
7.453
0.003
0.007
✓ Answer
7.453 ≈ 7.45

✏️ Problem 14

👥 We Do • Nearest Hundredth
Round 11.8276
to the nearest hundredth
💡 Number Line Strategy
1 Find the benchmarks. 11.8276 is between 11.82 and 11.83. The midpoint is 11.825.
2 Look at the thousandths digit: it's 7. Since 7 ≥ 5 → "5 to 9... Climb the Vine!" Round UP.
⬆️ The thousandths digit (7) tells us to round UP because 7 ≥ 5
Number Line
11.82
11.825
11.83
11.8276
0.0024
0.0076
✓ Answer
11.8276 ≈ 11.83

✏️ Problem 15

👥 We Do • Nearest Hundredth
Round 6.395
to the nearest hundredth
💡 Number Line Strategy
1 Find the benchmarks. 6.395 is between 6.39 and 6.40. The midpoint is 6.395 — our number is RIGHT on it!
2 Look at the thousandths digit: it's 5. Since 5 ≥ 5 → "5 to 9... Climb the Vine!" Round UP.
⬆️ Exactly at the midpoint? That STILL rounds UP! Notice: we write 6.40, keeping the trailing zero to show hundredths!
Number Line
6.39
6.395
6.40
6.395
0.005
0.005
✓ Answer
6.395 ≈ 6.40

✏️ Problem 16

✏️ You Do • Nearest Hundredth
Round 8.5247
to the nearest hundredth
💡 Number Line Strategy
1 Find the benchmarks. 8.5247 is between 8.52 and 8.53. The midpoint is 8.525.
2 Look at the thousandths digit: it's 4. Since 4 < 5 → "0 to 4... Do No More!" Round DOWN.
⬇️ The thousandths digit (4) tells us to round DOWN because 4 < 5
Number Line
8.52
8.525
8.53
8.5247
0.0047
0.0053
✓ Answer
8.5247 ≈ 8.52

✏️ Problem 17

✏️ You Do • Nearest Hundredth
Round 14.0683
to the nearest hundredth
💡 Number Line Strategy
1 Find the benchmarks. 14.0683 is between 14.06 and 14.07. The midpoint is 14.065.
2 Look at the thousandths digit: it's 8. Since 8 ≥ 5 → "5 to 9... Climb the Vine!" Round UP.
⬆️ The thousandths digit (8) tells us to round UP because 8 ≥ 5
Number Line
14.06
14.065
14.07
14.0683
0.0017
0.0083
✓ Answer
14.0683 ≈ 14.07

🏆 Challenge: Round Three Ways!

🏆 Challenge • All Three
45.738
Round to nearest whole, tenth, AND hundredth
🏆 Three Rounds, One Number!
1 Nearest Whole: Look at tenths digit (7). 7 ≥ 5 → Round UP → 46
2 Nearest Tenth: Look at hundredths digit (3). 3 < 5 → Round DOWN → 45.7
3 Nearest Hundredth: Look at thousandths digit (8). 8 ≥ 5 → Round UP → 45.74
💡 Same number, three different answers! The place you round to determines which digit you look at.
✓ All Three Answers
Whole: 46  |  Tenth: 45.7  |  Hundredth: 45.74

🏃 Word Problem

🏆 Challenge • Word Problem
A runner finishes the race in 58.473 seconds.
Round to the nearest tenth of a second.
💡 Word Problem Strategy
1 Identify: Round 58.473 to the nearest tenth. The benchmarks are 58.4 and 58.5.
2 Apply the rule: Look at hundredths digit (7). Since 7 ≥ 5 → "5 to 9... Climb the Vine!" Round UP.
🏃 The runner's time rounds UP to 58.5 seconds!
Number Line
58.4
58.45
58.5
58.473
0.027
0.073
✓ Answer
58.473 seconds ≈ 58.5 seconds

🍎 Word Problem

🏆 Challenge • Word Problem
A bag of apples weighs 3.8264 pounds.
Round to the nearest hundredth of a pound.
💡 Word Problem Strategy
1 Identify: Round 3.8264 to the nearest hundredth. The benchmarks are 3.82 and 3.83.
2 Apply the rule: Look at thousandths digit (6). Since 6 ≥ 5 → "5 to 9... Climb the Vine!" Round UP.
🍎 The bag of apples rounds UP to 3.83 pounds!
Number Line
3.82
3.825
3.83
3.8264
0.0036
0.0064
✓ Answer
3.8264 pounds ≈ 3.83 pounds

💬 Turn & Talk

🤔Discuss with a Partner

Talk with your partner about these questions:

1. When you round 4.35 to the nearest tenth, you get 4.4. But when you round 4.34 to the nearest tenth, you get 4.3. Why does just one digit make such a big difference?

2. Can a number round UP for one place value and DOWN for another? Give an example!

3. A store sign says an item costs "about $5." What are some possible exact prices it could be? What's the LOWEST and HIGHEST price that rounds to $5?

📝 Key Takeaways

📏 The Golden Rule
Always look at the digit to the RIGHT of the place you're rounding to. That digit decides everything!
⬇️ 0 to 4... Do No More!
If the digit is 0, 1, 2, 3, or 4 — the rounding digit stays the same. Round DOWN.
⬆️ 5 to 9... Climb the Vine!
If the digit is 5, 6, 7, 8, or 9 — the rounding digit goes up by 1. Round UP.
📊 Use Number Lines
Placing a decimal on a number line between its benchmarks helps you SEE which way to round.

🎫 Exit Ticket

Solve each problem on your whiteboard, then check your answers!

1️⃣Nearest Whole

Round 17.842 to the nearest whole number.

Tenths digit = 8 (≥ 5) → Round UP
17.842 ≈ 18

2️⃣Nearest Tenth

Round 5.673 to the nearest tenth.

Hundredths digit = 7 (≥ 5) → Round UP
5.673 ≈ 5.7

3️⃣Nearest Hundredth

Round 9.3485 to the nearest hundredth.

Thousandths digit = 8 (≥ 5) → Round UP
9.3485 ≈ 9.35