How to round and estimate without going blank
TEAS 7 outline: Apply estimation and rounding to real-world problems
- To round, look only at the digit just right of the target place.
- 5 or more rounds up; 4 or less leaves the digit alone.
- Round once, straight from the original number, not in a chain.
- Round only the final answer, not numbers before you multiply.
- Calculator answer about 10 times off your estimate? Look for a misplaced decimal.
Key facts
- To round, look only at the digit immediately to the right of the target place: 5 or more adds 1 to the target digit, 4 or less leaves it unchanged.
- After rounding a whole number, the digits to the right of the target place become zeros; after rounding a decimal, they are dropped.
- When a 9 rounds up it becomes 0 and 1 carries to the left, so 6,972 rounded to the nearest hundred is 7,000.
Show all 7 key factsShow fewer
- Front-end rounding rounds each number to its leading (first) place, so 47.85 becomes 50 and 312 becomes 300.
- Money is usually rounded to the nearest cent (hundredths place) or the nearest dollar (ones place).
- Round only the final answer; rounding a number before you multiply can push the result far off.
- If a calculator answer is about 10 times bigger or smaller than your estimate, look for a misplaced decimal point.
Quick check1 question · 2 more at the end
Marcus orders 38 boxes of exam-table paper for a clinic at $21.40 per box. His calculator shows a total of $8,132.00. If he checks it with front-end rounding (rounding each number to its leading place), about what should the total be?
Correct answer: C.
Front-end rounding rounds each number to its leading place: 38 rounds to 40 and $21.40 rounds to $20, so the total should be about 40 × 20 = $800. The calculator's $8,132.00 is about 10 times too large, which points to a decimal slip; the exact total is 38 × 21.40 = $813.20. Always compare a calculator result with a quick estimate before choosing an answer.
A This matches the incorrect calculator result instead of checking it; it is 10 times the estimate.
B This chops 38 down to 30 instead of rounding it; the digit to the right of the 3 is 8, so 38 rounds up to 40.
C Correct: 40 × $20 = $800, close to the exact total of $813.20.
D This drops a zero; 40 × 20 is 800, not 80.
Full lesson
Each part starts with its main idea. Open a part when you want the details.
The short answer: To round, find the place you are rounding to and look only at the digit just to its right: 5 or more rounds up, 4 or less leaves it alone. To estimate, round each number to its leading digit and do the easy math. Then compare your estimate with the calculator result to see if it is reasonable.
1 How do you round a number?Rounding swaps an exact number for a simpler one that is close enough for the job. 1 min
Rounding swaps an exact number for a simpler one that is close enough for the job. You only ever need four steps:
- Find the target place (tenths, ones, hundreds...) and underline that digit.
- Look at the one digit just to its right. Ignore everything after it.
- If that digit is 5 or more, add 1 to the target digit. If it is 4 or less, leave the target digit as it is.
- Whole number: turn every digit to the right into a zero. Decimal: drop every digit to the right.
| Number | Round to | Digit you check | Result |
|---|---|---|---|
| 2,463 | nearest hundred | 6 | 2,500 |
| 6,972 | nearest hundred | 7 | 7,000 (the 9 rolls over to 0 and carries 1) |
| 0.846 | nearest tenth | 4 | 0.8 |
| $12.996 | nearest cent | 6 | $13.00 |
Front-end rounding is the fastest way to estimate: round every number to its first (leading) place, like 47.85 → 50 or 312 → 300. Use the normal rounding rule (47.85 becomes 50, not 40); the result is a ballpark, not an exact answer.
2 Worked example 1: How do you round a measurement?Always round once, straight from the original number, looking at only one digit. 1 min
Always round once, straight from the original number, looking at only one digit.
A patient's weight is recorded as 68.47 kg. Round it to the nearest tenth, then to the nearest whole kilogram.
- Nearest tenth: the target digit is 4. The digit to its right is 7, so round up: 68.5 kg.
- Nearest whole: the target digit is 8. The digit to its right is 4, so leave it: 68 kg.
Wrong turn: rounding in a chain, 68.47 → 68.5 → 69. Go back to 68.47 every time. No calculator needed here.
3 Worked example 2: Is the calculator answer reasonable?A quick estimate made with front-end rounding catches calculator slips such as a misplaced decimal point. 1 min
A quick estimate made with front-end rounding catches calculator slips such as a misplaced decimal point.
A clinic orders 48 boxes of gloves at $11.75 per box. The calculator shows $5,640.00.
- Front-end round: 48 → 50 and $11.75 → $10.
- Estimate in your head: 50 × 10 = about $500.
- Compare: $5,640 is about 10 times the estimate, so something went wrong (likely 117.5 was typed).
- Re-enter on the calculator: 48 × 11.75 = $564.00, which is close to $500.
Wrong turn: trusting the screen without a check. Use mental math for the estimate and the on-screen calculator for the exact product.
4 Worked example 3: Why round only at the end?Rounding a number before you multiply can throw the answer far off, because the rounding error gets multiplied too. 1 min
Rounding a number before you multiply can throw the answer far off, because the rounding error gets multiplied too.
A cafeteria buys 40 pounds of chicken at $3.45 per pound. Find the cost to the nearest dollar.
| Method | Work | Result | Off by |
|---|---|---|---|
| Exact, round at the end | 40 × 3.45 = 138.00 | $138 | $0 |
| Round price to $3 first | 40 × 3 | $120 | $18 low |
| Round price to $3.50 first | 40 × 3.5 | $140 | $2 high |
Wrong turn: rounding $3.45 down to $3 and giving $120 as the answer. If you only need an estimate, round to a value close to the real one; if you need the exact answer, round only the final result.
Common mistakes
The traps students fall into most. Read these before you practice.
Watch out: Check only the one digit next to the target place, not the whole tail: 2.449 to the nearest tenth is 2.4, not 2.5.
Watch out: Round once from the original number, not in a chain: 68.47 to the nearest whole number is 68, not 68.5 and then 69.
Watch out: Round at the end, not before you multiply; a small early rounding gets multiplied along with everything else.
Watch out: Nearest tenth means one digit after the decimal point, not the tens place.
Watch out: An estimate checks your work; when the question asks for an exact value, an estimate is not the answer.
How to remember it
One short rhyme and three quick drills are enough to lock in rounding.
Memory hook: "Five or more, raise the score. Four or less, let it rest." Only the next-door digit gets a vote.
Self-check:
- Round 7.65 to the nearest tenth, then go back to 7.65 and round it to the nearest whole number.
- Use front-end rounding to estimate 19 × $52.10 and say what calculator answer would be suspicious.
- Explain why 30 × $1.49 estimated as 30 × $1 is a poor estimate.
Show answers
- 7.7, then 8.
- Nearest tenth: the target digit is 6. The digit to its right is 5, so round up: 7.7.
- Nearest whole: go back to 7.65. The target digit is 7. The digit to its right is 6, so round up: 8.
- About $1,000.
- Front-end round: 19 → 20 and $52.10 → $50.
- Estimate: 20 × 50 = $1,000.
- The exact answer is 19 × 52.10 = $989.90, close to $1,000.
- A screen showing about $99 or about $9,899 is suspicious. Each is about 10 times off.
- $1 is too far from $1.49.
- 30 × $1 = $30, but the exact cost is 30 × $1.49 = $44.70.
- Rounding down cut $0.49 from each price, and that error was multiplied by 30.
- A closer estimate is 30 × $1.50 = $45.