Comparing and ordering
🎯 In this topic you will
- Compare numbers by evaluating the place value of each digit.
- Use the inequality symbols $<$ (less than) and $>$ (greater than) to compare two numbers.
- Order numbers from smallest to greatest and from greatest to smallest.
🧠 Key Words
- inequalities
- is greater than >
- is less than <
- symbol
Show Definitions
- inequalities: Mathematical statements that show one value is greater than or less than another value.
- is greater than: Describes when the first number has a larger value than the second number.
- >: The inequality symbol that means “greater than”.
- is less than: Describes when the first number has a smaller value than the second number.
- <: The inequality symbol that means “less than”.
- symbol: A sign or mark used to represent an idea in mathematics.
🔎 Comparing and Ordering 3-Digit Numbers
When you know the value of each digit in a 3-digit number, you can compare numbers and use what you find out to put them in order. You can also estimate where a number belongs on the number line.
❓ EXERCISES
1. Complete these pieces from a $1000$ square.
👀 Show answer
Centre $320$: above $310$, below $330$, left $319$, right $321$.
Centre $890$: above $880$, below $900$, left $889$, right $891$.
Centre $653$: above $643$, below $663$, left $652$, right $654$.
2. Compare these numbers and complete the sentences.
a.
| 100s | 10s | 1s |
|---|---|---|
| $4$ | $5$ | $8$ |
| $6$ | $4$ | $3$ |
________ is greater than ________ and ________ is less than ________.
b.
| 100s | 10s | 1s |
|---|---|---|
| $4$ | $7$ | $5$ |
| $4$ | $7$ | $2$ |
________ is greater than ________ and ________ is less than ________.
c.
| 100s | 10s | 1s |
|---|---|---|
| $8$ | $3$ | $8$ |
| $8$ | $8$ | $3$ |
________ is greater than ________ and ________ is less than ________.
👀 Show answer
a) $643$ is greater than $458$ and $458$ is less than $643$.
b) $475$ is greater than $472$ and $472$ is less than $475$.
c) $883$ is greater than $838$ and $838$ is less than $883$.
3. Order these numbers from smallest to greatest.
👀 Show answer
$38,\; 475,\; 563,\; 621,\; 679$
4. Order these numbers from greatest to smallest.
👀 Show answer
$834,\; 483,\; 438,\; 384,\; 48$
5. Mark the numbers in question $4$ on the number line.
👀 Show answer
Mark points at: $48,\; 384,\; 438,\; 483,\; 834$.
(Approximate positions: $48$ just below $50$; $384$ just below $400$; $438$ between $400$ and $500$ closer to $400$; $483$ close to $500$; $834$ between $800$ and $900$ closer to $800$.)
🧠 Reasoning Tip
Remember that ‘estimate’ is a sensible guess.
6. Estimate the value of each number marked on the number line.
👀 Show answer
Estimated values (left to right):
About $170$, about $360$, about $850$.
7. Complete these inequalities
👀 Show answer
One possible set of answers is:
$262 < 263,\;\; 671 < 672,\;\; 458 > 457,\;\; 346 > 345$.
🧠 Think like a Mathematician
Use these numbers and symbols to make three correct mathematical statements:
$234,\;243,\;243,\;278,\;278,\;287$
Symbols: $<,\;=,\;>$
Find a different way to do it.
Compare your answers with another solution. Think carefully:
- How are the statements the same?
- How are they different?
- Can you find all possible correct solutions?
It is often easier to start by using the equals sign with two numbers that are the same.
Do you agree with Sophia? Why?
Show Answers
- Example 1:$243 = 243$
- Example 2:$234 < 278$
- Example 3:$287 > 278$
Other correct answers are possible as long as each comparison is mathematically true and only the given numbers and symbols are used.