Estimating and rounding
🎯 In this topic you will
- Estimate quantities by giving a reasonable range of values.
- Round numbers to the nearest 10.
- Round numbers to the nearest 100.
🧠 Key Words
- estimate
- range
- round
- rounding
Show Definitions
- estimate: A sensible value (or set of values) that is close to the true answer, found using quick reasoning instead of exact calculation.
- range: A span of values between a lower and an upper limit, used to show where an answer is likely to lie.
- round: To replace a number with a nearby, simpler number (such as to the nearest 10 or 100) while keeping it close in value.
- rounding: The process of rounding numbers, based on which digit is next after the place value you are rounding to.
📏 When an Estimate Is Enough
You don’t always need to know how many there are. Often, an estimate is enough. You can estimate by giving a range of numbers or by rounding a number to the nearest 10 or 100.
❓ EXERCISES
$1$. Estimate how many spots there are in the box.
👀 Show answer
One way: count roughly how many spots are in one row and how many rows there are, then multiply, and adjust a little because the spots do not fill the border perfectly.
$2$. Class $3$ used this table to check their estimates of the number of beans in different plastic bags.
| Number of beans | Mass of beans |
|---|---|
| $100$ | $10$ grams |
| $200$ | $20$ grams |
| $300$ | $30$ grams |
| $400$ | $40$ grams |
| $500$ | $50$ grams |
| $600$ | $60$ grams |
| $700$ | $70$ grams |
| $800$ | $80$ grams |
| $900$ | $90$ grams |
| $1000$ | $100$ grams |
a. Marcus estimated that his bowl had $400$ to $500$ beans. They weighed $56$ grams. Is this a good estimate?
b. Zara estimated that her plastic bag had $200$ to $300$ beans. They weighed $24$ grams. Is this a good estimate?
c. Arun’s beans weighed $78$ grams. What range would be a good estimate for his beans?
👀 Show answer
b. Yes, it is a good estimate. $24$ grams is about $240$ beans, which is within $200$ to $300$.
c. A good estimate range is $700$ to $800$ beans (because $78$ grams lies between $70$ grams and $80$ grams).
$3$. Round each number to the nearest $10$.
👀 Show answer
$678 \to 680$
$385 \to 390$
$907 \to 910$
$740 \to 740$
$598 \to 600$
$4$. Round each number to the nearest $100$.
👀 Show answer
$678 \to 700$
$385 \to 400$
$907 \to 900$
$740 \to 700$
$598 \to 600$
$5$. Which number in questions $3$ and $4$ rounds to the same number when rounded to the nearest $10$ and to the nearest $100$?
👀 Show answer
🧠 Think like a Mathematician
A number rounded to the nearest $10$ and to the nearest $100$ is a multiple of $100$. What could the number be?
Sofia includes $100, 200, 300, 400, 500, 600, 700, 800, 900$ and $1000$ in her list of numbers. Do you agree with her? Why?
👀 show answer
For a number to round to a multiple of $100$ when rounded to the nearest $10$, it must round to something ending in $00$. That happens only if the number is within $5$ of a multiple of $100$.
So if the rounded result is $100k$, the number could be any integer from: $100k - 5$ to $100k + 4$.
Examples (within $1$ to $1000$):
$96$ to $104$ all round to $100$ (nearest $10$ and nearest $100$).
$195$ to $204$ all round to $200$.
$995$ to $1004$ all round to $1000$.
About Sofia’s list: you can agree that $100, 200, \dots, 1000$ are all valid answers (they work). However, her list is not complete, because many other numbers also work (for example $98$, $203$, $999$, etc.).