Rounding Large Numbers
Place Value of Large Numbers: Rounding Large Numbers
Rounding Large Numbers
Rounding Large Numbers
What you'll learn
- To round numbers to the nearest 10, 100, 1,000, and 10,000.
- To use the "look at the next digit to the right" rule to decide whether to round up or down.
- To use rounding to estimate answers and check if a calculated answer is reasonable.
Key concepts
Level 1 — The rounding rule
Verbal: Look at the digit just to the right of the place you are rounding to. If it is 5 or more, round up; if it is 4 or less, round down.
Symbolic: Round 4,782 to the nearest hundred → look at the tens digit (8) → 8 ≥ 5 → round up → 4,800.
Level 2 — Rounding to different places
| Round to | What changes |
|---|---|
| Nearest 10 | ones digit becomes 0 |
| Nearest 100 | tens and ones digits become 0 |
| Nearest 1,000 | hundreds, tens, ones digits become 0 |
| Nearest 10,000 | thousands, hundreds, tens, ones digits become 0 |
Level 3 — Why rounding is useful
Real-life: Round the cost of shopping items to the nearest ₹10 to quickly estimate the total bill before checking the exact receipt.
Worked example
Round 36,482 to the nearest thousand
Step 1 — Look at the hundreds digit: 4
Step 2 — 4 < 5, so round down
Step 3 — Keep the thousands digit (6), make the rest 0
Answer: 36,000
Round 674,910 to the nearest ten-thousand
Step 1 — Look at the thousands digit: 4
Step 2 — 4 < 5, so round down
Answer: 670,000
Common mistakes
| Mistake | Why it happens | Fix |
|---|---|---|
| Rounding using the wrong digit | Looking one place too far left or right | Always check the digit immediately to the right of the target place |
| Forgetting to change all digits after the rounding place to 0 | Only changing one digit | Every digit to the right of the rounding place becomes 0 |
| Rounding down when the digit is exactly 5 | Confusing the "5 rounds up" rule | By convention, 5 always rounds up |
Quick check
- Round 8,349 to the nearest hundred.
- Round 52,650 to the nearest thousand.
- Round 194,500 to the nearest ten-thousand.
- Stretch: A number rounds to 5,000 when rounded to the nearest thousand. What is the smallest and largest number it could be?
Revision tip: Underline the digit you must check before deciding to round up or down — this stops careless mistakes.
Open the Practice tab for graded questions on Rounding Large Numbers.
Key Takeaways (TL;DR)
- What you'll learn
- Key concepts
- Worked example
- Common mistakes
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