Rounding, ordering and comparing whole numbers booklet
Rounding, ordering and comparing whole numbers booklet
- Unit 1: Numbers
- Unit 2: Geometry and measure
- Unit 3 : Statistics and probability
🎯 In this topic you will
- Round whole numbers to the nearest $10$, $100$, $1000$, $10{,}000$, or $100{,}000$.
- Write lists of whole numbers in order, starting with either the smallest or the largest value.
- Compare whole numbers using the symbols $=$, $<$, and $>$.
🧠 Key Words
- compare
- order
- round
- round to the nearest
Show Definitions
- compare: To check two numbers to decide whether one is greater than, less than, or equal to the other (using $>$, $<$, and $=$).
- order: To arrange numbers in a sequence, either from smallest to largest (ascending) or from largest to smallest (descending).
- round: To replace a number with a nearby “simple” number at a chosen place value, so it is easier to use or estimate.
- round to the nearest: To round a number to the closest multiple of a given unit (like $10$ or $100$) by looking at the digit to the right; $5$–$9$ rounds up, and $0$–$4$ rounds down.
📌 Why We Round Numbers
Rounding makes it easier to describe and understand numbers. It is easier to understand ‘the distance from Jakarta to New York is roughly 16 000 kilometres’ than ‘the distance is 16 167 kilometres’.
💡 Quick Math Tip
Fix the largest place value first: When you are asked to make numbers bigger than a given value (such as $7000$), decide the thousands digit first. This immediately reduces the number of possibilities and makes it easier to list all valid numbers systematically.
❓ EXERCISES
1. Round these numbers to the nearest $10\,000$.
a. $45\,678$
b. $24\,055$
c. $50\,505$
👀 Show answer
a. $50\,000$
b. $20\,000$
c. $50\,000$
2. Round these numbers to the nearest $100\,000$.
a. $147\,950$
b. $865\,507$
c. $157\,846$
👀 Show answer
a. $100\,000$
b. $900\,000$
c. $200\,000$
3. At a fundraising event, $5206$ people dressed up as children’s book characters to raise money for a children’s hospital.
a. Round $5206$ to the nearest $1000$.
b. Round $5206$ to the nearest $100$.
c. Round $5206$ to the nearest $10$.
👀 Show answer
a. $5000$
b. $5200$
c. $5210$
4. A number rounded to the nearest $10$ is $340$. Find all the possible numbers it could be.
👀 Show answer
All whole numbers from $335$ to $344$ inclusive.
5.
a. Round $5495$ to the nearest $10$.
b. Round $5495$ to the nearest $100$.
c. Round $5495$ to the nearest $1000$.
d. Round your answer to (a) to the nearest $100$, then round that answer to the nearest $1000$.
e. Compare your answers to (c) and (d). Discuss what you notice with your partner.
👀 Show answer
a. $5500$
b. $5500$
c. $5000$
d. $6000$
e. The results are different because rounding in stages can change the final value.
6. Copy and complete this number sentence using $<$, $>$ or $=$.
$645\,123 \ \square \ 645\,213$
👀 Show answer
$645\,123 < 645\,213$
7. The table shows the heights of mountains on five different continents.
| Mountain | Continent | Height (in metres) |
|---|---|---|
| Kilimanjaro | Africa | $5895$ |
| Everest | Asia | $8848$ |
| Kosciuszko | Australia | $2228$ |
| McKinley | North America | $6194$ |
| Aconcagua | South America | $6962$ |
a. Write the heights in order starting with the smallest.
b. Round each height to the nearest hundred metres.
👀 Show answer
a. $2228,\ 5895,\ 6194,\ 6962,\ 8848$
b. $5900,\ 8800,\ 2200,\ 6200,\ 7000$
🧠 Think like a Mathematician
Here are five numbers:
$5505 \qquad 5455 \qquad 5045 \qquad 5500 \qquad 5050$
a. Match each of these numbers to the correct letter A, B, C, D or E using the table.
| Nearest $10$ | Nearest $100$ | Nearest $1000$ | |
|---|---|---|---|
| A | $5500$ | $5500$ | $6000$ |
| B | $5050$ | $5100$ | $5000$ |
| C | $5050$ | $5000$ | $5000$ |
| D | $5460$ | $5500$ | $5000$ |
| E | $5510$ | $5500$ | $6000$ |
When numbers B and C are rounded to the nearest $10$, they are the same number ($5050$). When they are rounded to the nearest $1000$, numbers B and C are $5000$. But when rounded to the nearest $100$ they are different ($5000$ and $5100$).
b. Find other numbers that round to $5050$ to the nearest $10$ and $5000$ to the nearest $1000$.
c. Round each of your numbers to the nearest $100$.
👀 Show Answers
a.
- $5505 \rightarrow A$
- $5455 \rightarrow D$
- $5045 \rightarrow C$
- $5500 \rightarrow E$
- $5050 \rightarrow B$
b. Examples include $5046$, $5047$, $5048$, $5049$, $5051$, $5052$, $5053$, and $5054$.
c. All these numbers round to either $5000$ or $5100$ to the nearest $100$, depending on whether they are below or above $5050$.