Rounding Decimals

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Concept Review

Rounding Decimals: The Art of Mathematical Approximation

Imagine you're measuring the height of your bedroom door with a ruler. You get 6.73 feet. But when someone asks how tall your door is, do you really need to say "six point seven three feet"? Sometimes 6.73 is close enough to 7 that we can just say "about 7 feet tall."

This is the power of rounding decimals—taking a precise decimal number and finding the closest, simpler number that's easier to work with. It's like mathematical shorthand that helps us communicate and calculate more efficiently.

The Rounding Decision Point

When rounding decimals to the nearest whole number, we need to look at the tenths place (the first digit after the decimal point) to make our decision.

Here's how it works: If the tenths digit is 5 or greater, we round UP to the next whole number. If it's 4 or less, we round DOWN to the current whole number.

Round UP Examples

3.5 → 4

7.8 → 8

12.6 → 13

9.5 → 10

Round DOWN Examples

4.3 → 4

8.1 → 8

15.4 → 15

6.2 → 6

Let's Practice with Pizza Prices

The local pizza shop has these prices: a small pizza costs $8.73, a medium costs letter: 'C', title: 'Rounding Decimals', concept: 2.49, and a large costs letter: 'C', title: 'Rounding Decimals', concept: 5.67. Let's round each price to the nearest dollar:

Small pizza: $8.73 → Look at 7 in tenths place → 7 ≥ 5, so round UP → $9
Medium pizza: letter: 'C', title: 'Rounding Decimals', concept: 2.49 → Look at 4 in tenths place → 4 < 5, so round DOWN → letter: 'C', title: 'Rounding Decimals', concept: 2
Large pizza: letter: 'C', title: 'Rounding Decimals', concept: 5.67 → Look at 6 in tenths place → 6 ≥ 5, so round UP → letter: 'C', title: 'Rounding Decimals', concept: 6

💡 The "5" Surprise

Here's something that surprises many students: 5.5 rounds to 6, not 5.

When the tenths digit is exactly 5, we always round UP. Think of 5 as being right in the middle—it's exactly halfway between rounding up or down. Mathematicians decided long ago that when we're perfectly in the middle, we take the "up" path to the next whole number.

🔑 Key Takeaway

Just like estimating your door height, rounding decimals helps us communicate more simply while staying close to the truth. Whether you're working with money, measurements, or any decimal, the tenths place is your guide: 5 or more climbs to the next floor, 4 or less stays put.

Sample questions

1. Round 14.5 to the nearest whole number.

○ 14

○ 14.5

✓ 15

○ 20

Answer: 15 — When the digit to the right of the target place value is 5 or more, round up. The .5 pushes the 14 up to 15.

2. A board is 8.42 feet long. What is its length rounded to the nearest foot?

✓ 8 feet

○ 9 feet

○ 8.4 feet

○ 8.5 feet

Answer: 8 feet — Look at the tenths digit (4). Since it is less than 5, the whole number stays the same.

3. Which number rounds to 10 when rounded to the nearest whole number?

○ 9.49

✓ 9.5

○ 10.51

○ 9.05

Answer: 9.5 — 9.5 has a 5 in the tenths place, which triggers it to round up to 10. 9.49 rounds to 9.

Skills in this topic

Round decimals to the nearest whole number
Round decimals to the nearest tenth
Round decimals to the nearest hundredth
Estimate sums and differences of decimals by rounding
Determine if an estimated decimal calculation is reasonable

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