Comparing and Ordering Numbers | Functional Skills Maths

Learning Objectives

Use \(<\), \(>\), \(=\) symbols to compare whole numbers
Compare and order decimal numbers by aligning decimal points
Apply comparison skills to real-life problems

Real-World Applications

Shopping: Comparing prices £3.45 vs £3.09 requires decimal comparison to find the better deal.
Weather: Ordering rainfall totals like 12.4 mm, 8.05 mm, 12.04 mm helps identify the wettest day.
Sport: Ranking sprint times like 9.83 s vs 9.08 s — the smaller time wins the race.

How Do You Compare Two Whole Numbers?

To compare two whole numbers, first count how many digits each one has — the number with more digits is larger. If they have the same number of digits, compare them digit by digit from left to right until you find a difference.

Example 1 — Compare 7,354 and 7,345 using \(<\) or \(>\)

Step 1

Same number of digits (4) — compare digit by digit from left to right.

Step 2

Thousands: \(7 = 7\). Hundreds: \(3 = 3\). Tens: \(5\) vs \(4\).

Step 3

\(5 > 4\), so \(7{,}354 > 7{,}345\).

Step 4

Answer: \(7{,}354 > 7{,}345\)

Example 2 — Order 34,521; 3,452; 345,210 from smallest to largest

Step 1

Count digits: 3,452 has 4 digits; 34,521 has 5 digits; 345,210 has 6 digits.

Step 2

Fewer digits = smaller number (for positive whole numbers).

Step 3

Order: \(3{,}452 < 34{,}521 < 345{,}210\)

✓ Quick Check 1 — Comparing Whole Numbers

Question 1 of 10

Comparing and Ordering Decimals

When comparing decimals, align the decimal points and compare digit by digit. Pad with trailing zeros so all numbers have the same number of decimal places. (You'll get a deeper follow-up on this technique in Lesson 6.2 — Ordering Decimals.)

Example 3 — Which is larger: 0.8 or 0.08?

Step 1

Write with equal decimal places: \(0.80\) vs \(0.08\).

Step 2

Tenths column: \(8\) vs \(0\) — \(8 > 0\).

Step 3

\(0.80 > 0.08\), i.e. \(0.8 > 0.08\).
Note: 0.8 is ten times larger than 0.08.

Example 4 — Order 5.07, 5.7, 5.007, 5.70 from smallest to largest

Step 1

Pad to 3 decimal places: \(5.070\), \(5.700\), \(5.007\), \(5.700\).

Step 2

Note: \(5.7 = 5.70\) (same value).

Step 3

Tenths: \(5.007\) has \(0\); \(5.070\) has \(0\); \(5.700\) has \(7\) — the 5.700 values are largest.

Step 4

Compare \(5.007\) vs \(5.070\): hundredths \(0\) vs \(7\) — \(5.007 < 5.070\).

Step 5

Order: \(5.007 < 5.07 < 5.7\) (= 5.70)

Trailing zeros do not change value: \(5.7 = 5.70 = 5.700\). But leading zeros after the decimal point DO matter: \(0.7 \neq 0.07\).

✓ Quick Check 2 — Comparing and Ordering Decimals

Question 1 of 10

Comparing and Ordering Using Place Value

You've now compared whole numbers and decimals separately — this section brings both together, and tackles the trickier case of ordering a mix of whole numbers and decimals in the same list (see Example 5 below).

Example 5 — Order 1,056, 15.6, 156, 1,560 from smallest to largest (mixing whole numbers and decimals)

Step 1

15.6 is the only number less than 100 — a decimal with just one whole unit digit, so it's the smallest.

Step 2

Of the remaining whole numbers, count the digits: 156 has 3 digits; 1,056 and 1,560 both have 4 digits. Fewer digits means smaller, so 156 comes next.

Step 3

Compare the two 4-digit numbers column by column: 1,056 vs 1,560 — thousands 1=1, hundreds 0 vs 5. Since 0 < 5, 1,056 < 1,560.

Step 4

Order: 15.6, 156, 1,056, 1,560

Example 6 — Which is larger, 0.3 or 0.03?

Step 1

Align by decimal point: 0.30 vs 0.03

Step 2

Tenths column: 3 vs 0 → 3 > 0

Step 3

Answer: 0.3 > 0.03 (0.3 is ten times larger)

Example 7 — Real-Life Application: A recipe lists three ingredient weights — 2.15 kg, 2.5 kg and 2.05 kg. Put them in order from lightest to heaviest for the shopping list.

Step 1

Write all three with the same number of decimal places: 2.150 kg, 2.500 kg, 2.050 kg.

Step 2

Compare the tenths digit: 2.050 has 0, 2.150 has 1, 2.500 has 5.

Step 3

Ordering the tenths digits smallest to largest: 0 < 1 < 5, so 2.05 < 2.15 < 2.5.

Step 4

Answer: 2.05 kg, 2.15 kg, 2.5 kg (lightest to heaviest)

⚠ Common mistake: Students think 0.03 > 0.3 because 3 seems further right. Always align at the decimal point and compare column by column.

✓ Quick Check 3 — Comparing and ordering

Question 1 of 10

Practice: Comparing and Ordering

Answer each question, then click Check All.

#	Question	Answer	Result
1	Which is larger: 4,523 or 4,532?
2	Order from smallest: 0.3, 0.03, 0.33 (commas)
3	Which is smaller: 3.4 or 3.04?
4	True or false: 0.30 = 0.3
5	Order smallest first: 2.15, 2.5, 2.05 (commas)
6	Write "four thousand, two hundred and six" as a number, then write the next even number.
7	Order smallest first: twelve thousand, one thousand two hundred, twenty-one thousand (write in digits, commas)
8	Which is larger: 7.09 or 7.9?
9	Order smallest first: 500, 5,000, 50 (commas)
10	Write "three thousand and forty" as a number, then write the next odd number.

⚠ Things to Watch Out For

Comparing decimals without aligning: Write numbers with the same number of decimal places before comparing: 0.5 = 0.50, so 0.50 vs 0.47 — now easy to compare.
Confusing > and <: The arrow always points to the SMALLER number. 5 > 3 means 5 is greater; 3 < 5 means 3 is less.
Forgetting to check all digits: When comparing 4,523 and 4,532, check digit by digit left to right — the thousands are equal (4), hundreds are equal (5), then tens differ: 2 < 3, so 4,523 < 4,532.

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