5 P5: Rounding
Rounding Whole Numbers and Decimals
Introduction
Rounding helps simplify numbers while keeping their value close to the original.
It’s an essential skill for estimation, measurement, and real-world problem solving.
Pre-service teachers should model the rounding process carefully, using place value reasoning and explaining why numbers are rounded up or down.
Rounding Whole Numbers
When rounding a whole number:
- Identify the place value you are rounding to.
- Look at the digit to the right of that place:
- If it’s 5 or greater, round up.
- If it’s 4 or less, round down.
- Replace digits to the right with zeros.
Example 1
Round 544,364 to the nearest ten thousand.
- The ten-thousand digit is 4.
- The next digit (thousand place) is 4 → round down.
- [latex]544{,}364 approx 540{,}000[/latex]
Example 2
Round 85,453,393 to the nearest million.
- The million digit is 5.
- The next digit is 4 → round down.
- [latex]85{,}453{,}393 approx 85{,}000{,}000[/latex]
Example 3
Round 617,589,149 to the nearest hundred thousand.
- The hundred-thousand digit is 5.
- The next digit is 8 → round up.
- [latex]617{,}589{,}149 approx 617{,}600{,}000[/latex]
Rounding to Tens, Hundreds, and Thousands
| Number | Nearest Ten | Nearest Hundred | Nearest Thousand |
|---|---|---|---|
| 564 | 560 | 600 | 1,000 |
| 141 | 140 | 100 | 0 |
| 424 | 420 | 400 | 0 |
| 386 | 390 | 400 | 0 |
Example: Round 83,992 to the nearest thousand → [latex]84{,}000[/latex]
Rounding Very Large Numbers
Example 4
Round 7,145,283,910 to the nearest billion.
- The billion digit is 7.
- The next digit (hundred-million place) is 1 → round down.
- [latex]7{,}145{,}283{,}910 approx 7{,}000{,}000{,}000[/latex]
Example 5
Round 4,750,183 to the nearest hundred thousand.
- The hundred-thousand digit is 7.
- The next digit (ten-thousand place) is 5 → round up.
- [latex]4{,}750{,}183 approx 4{,}800{,}000[/latex]
Rounding Decimals
When rounding decimals, follow the same pattern:
- Locate the rounding place.
- Look at the digit immediately to the right.
- Round up if that digit is 5 or more; otherwise, round down.
Example 6
Round 1.1499391566:
| Place | Rounded Value |
|---|---|
| Whole number | [latex]1[/latex] |
| Tenths | [latex]1.1[/latex] |
| Hundredths | [latex]1.15[/latex] |
| Thousandths | [latex]1.15[/latex] |
| Ten-thousandths | [latex]1.1499[/latex] |
| Hundred-thousandths | [latex]1.14994[/latex] |
Example 7
Round 1.1883331128:
| Place | Rounded Value |
|---|---|
| Whole number | [latex]1[/latex] |
| Tenths | [latex]1.2[/latex] |
| Hundredths | [latex]1.19[/latex] |
| Thousandths | [latex]1.188[/latex] |
| Ten-thousandths | [latex]1.1883[/latex] |
| Hundred-thousandths | [latex]1.18833[/latex] |
Practical Tip: Visualizing Rounding
Imagine rounding as deciding which number line “step” a value is closer to.
For example, when rounding 1.47 to the nearest tenth:
- 1.47 is between 1.4 and 1.5.
- It’s closer to 1.5 → [latex]1.47 approx 1.5[/latex].
Common Student Errors and Corrections
| Error | Example | Correction Strategy |
|---|---|---|
| Looking at the wrong place value | Rounding 153,994 to 150,000 instead of 160,000 | Highlight or underline the rounding digit first. |
| Rounding down when the digit is 5 | 27,465 → 27,460 | Remember “5 or more, raise the score.” |
| Adding instead of replacing with zeros | 540,000 → 540,364 | Emphasize that rounding simplifies, not adds. |
| Truncating decimals | 1.1499 → 1.14 | Always check the next digit before rounding. |
H5P Practice Activities
H5P 1: Rounding Whole Numbers
Prompt: Round each number to the indicated place value.
H5P Placeholder:
Examples
- 544,364 → nearest ten thousand →
540,000 - 85,453,393 → nearest million →
85,000,000 - 617,589,149 → nearest hundred thousand →
617,600,000
H5P 2: Rounding to Tens and Hundreds
Prompt: Round each number as indicated.
H5P Placeholder:
Examples
- 564 → nearest ten →
560 - 141 → nearest hundred →
100 - 424 → nearest ten →
420 - 386 → nearest hundred →
400
H5P 3: Rounding Decimals
Prompt: Round each decimal to the place value indicated.
H5P Placeholder:
Examples
- 1.149939 → nearest hundredth →
1.15 - 1.0478587 → nearest thousandth →
1.048 - 1.2046473 → nearest ten-thousandth →
1.2046
H5P 4: Rounding Mixed Numbers and Large Values
Prompt: Round the given numbers to the indicated place value.
H5P Placeholder:
Examples
- 26,999,642 → nearest ten thousand →
27,000,000 - 716,151,355 → nearest hundred thousand →
716,200,000 - 82,499,479 → nearest million →
82,000,000
H5P 5: Applied Rounding
Prompt: Round to the place value needed to make a reasonable estimate.
H5P Placeholder:
Examples
- The population of a city is 617,589,149. Approximate to the nearest million. →
618,000,000 - A car costs $26,999. Round to the nearest thousand to estimate price. →
$27,000 - A measurement reads 1.2046472994 m. Round to the nearest hundredth. →
1.20 m
Reflection for Pre-Service Teachers
- Why is rounding important in real-world problem solving?
- How can number lines, base-ten blocks, or place-value charts support understanding of rounding?
- What misconceptions arise when students round decimals incorrectly?
- How can estimation strategies support checking reasonableness of answers?
Summary
Rounding simplifies numbers for estimation and communication.
Pre-service teachers should help students:
- Identify the rounding place.
- Use the digit to the right to decide up or down.
- Replace digits after with zeros or truncate decimals appropriately.
By practicing rounding with both whole numbers and decimals, students build number sense and accuracy in everyday math contexts.