MATHEMATICSNumber & Arithmetic
Place Value
● 11+ Verified Core Topic Master Poster Included
Place Value & Number Sense
Place value tells us the value of each digit in a number based on its position (place). Master whole numbers up to 10 million, decimals to 3 places, expanded form, comparing, and rounding!
BIG NUMBERS MADE EASY!★ 11+ Ready
Place Value Explorer
Understanding numbers helps you do BIG things! Type any number below to see how each digit works.
Enter Your Number
MILLIONS
THOUSANDS
ONES
DOT
DECIMAL
100,000,000
10,000,000
1,000,000
100,000
10,000
1,000
100
10
1
.
0.1
0.01
0.001
hundred millions
ten millions
millions
hundred thousands
ten thousands
thousands
hundreds
tens
ones
tenths
hundredths
thousandths
·
·
·
4
8
3
5
2
9
1
7
6
Hover over any digit or column in the chart above to see its place value explanation!
standardform
483,529.176
expandedform
483,529.176 =400,000+80,000+3,000+500+20+9+0.1+0.07+0.006
wordform
“Four hundred and eighty-three thousand, five hundred and twenty-nine and one hundred and seventy-six thousandths”
What We LearntPlace Value Essentials
Everything you need to master numbers, expanded form, and word form in one simple recap!
1. Position is Power×10 / ÷10
How Place Value Works
- A digit's value depends on where it sits.
- Moving left: each place is 10× bigger.
- Moving right: each place is 10× smaller (1/10).
- Zero is a hero placeholder: never leave an empty column inside a number!
💡 Example: In 540, the 5 is worth 500. In 54, it is only worth 50!
2. One Number, 3 WaysForms
Standard, Expanded & Word
Standard FormNormal digits
25,307.84
Expanded FormSkip zeros!
20,000 + 5,000 + 300 + 7 + 0.8 + 0.04
Word Form'and' = decimal
“Twenty-five thousand, three hundred and seven and eighty-four hundredths”
✨ Tip: Expanded form breaks each digit into its real math value!
⭐ GOLDEN RULEThe farther LEFT a digit is, the GREATER its value!• PRACTICE + FOCUS = SUCCESS! ★
5. Comparing Numbers
Comparing Numbers Using Place Value
Compare digits from left to right. The first place where the digits are different determines which number is greater.
45,672.3vs45,689.1
Ten Thousands:4 = 4
Thousands:5 = 5
Hundreds:6 = 6
Tens:7 < 8 (Determining Place!)
So, 45,672.3 < 45,689.1
6. Rounding Rules
Rounding Using Place Value
Look at the digit in the place to the right:
5 or more → Round UPLess than 5 → Keep SAME
Round 34,567 to nearest hundred
Tens digit is 6 (≥ 5) → Round UP
34,600
Round 8.742 to nearest tenth
Hundredths digit is 4 (< 5) → Keep SAME
8.7
Round 91.25 to nearest whole
Tenths digit is 2 (< 5) → Keep SAME
91
★ Master Topic Section11+ Exam Essential
Rounding to 10, 100, 1000
Look at the place value. Then decide whether to round down or up.
KEY IDEA
Rounding gives an approximate value that is easier to use but still close to the original number.
1. Rounding to 10
Look at the ones digit:
• 0, 1, 2, 3, 4→ round down
• 5, 6, 7, 8, 9→ round up
TENSONES
37
7 (≥ 5) → so round up.
37 → 40 = 40
Examples:
23 →20
67 →70
14 →10
89 →90
2. Rounding to 100
Look at the tens digit:
• 0, 1, 2, 3, 4→ round down
• 5, 6, 7, 8, 9→ round up
HUNDREDSTENSONES
467
6 (≥ 5) → so round up.
467 → 500 = 500
Examples:
243 →200
678 →700
154 →200
849 →800
3. Rounding to 1000
Look at the hundreds digit:
• 0, 1, 2, 3, 4→ round down
• 5, 6, 7, 8, 9→ round up
THOU.HUND.TENSONES
2378
3 (< 5) → so round down.
2,378 → 2,000 = 2,000
Examples:
2,345 →2,000
7,891 →8,000
1,499 →1,000
5,555 →6,000
TOP TIPS FOR ROUNDINGKey Rules
- Always look at the correct digit (the column right next to your target place).
- If it is 5 or more, round up.
- If it is less than 5, round down (keep target digit the same).
- Zeros at the end act as essential placeholders.
QUICK SUMMARY TABLECheat Sheet
| ROUND TO... | LOOK AT... | IF 0, 1, 2, 3, 4... | IF 5, 6, 7, 8, 9... |
|---|---|---|---|
| 10 | Ones digit | Round down | Round up |
| 100 | Tens digit | Round down | Round up |
| 1000 | Hundreds digit | Round down | Round up |
★ Master Topic Section11+ Exam Essential
Rounding Decimals
Look at the next digit (the digit to the right of the place you are rounding to). If it is 5 or more, round up. If it is less than 5, round down.
KEY IDEA
Rounding gives an approximate value that is easier to use but still close to the original number.
1. To 1 Decimal Place (tenths)
Look at the hundredths digit:
ONESTENTHSHUND.THOU.
2.378
7 (≥ 5) so round up.
2.378 → 2.4
Examples:
1.24 →1.2
3.67 →3.7
9.85 →9.9
2. To 2 Decimal Places (hundredths)
Look at the thousandths digit:
ONESTENTHSHUND.THOU.TEN-TH.
5.6248
4 (< 5) so round down.
5.6248 → 5.62
Examples:
2.345 →2.35
8.999 →9.00
1.234 →1.23
3. To 3 Decimal Places (thousandths)
Look at the ten-thousandths digit:
ONESTEN.HUN.THO.10K.
1.2346
6 (≥ 5) so round up.
1.2346 → 1.235
Examples:
0.12345 →0.123
6.78954 →6.790
4.9996 →5.000
4. To Whole Number (no decimals)
Look at the tenths digit:
ONESTENTHSHUND.
4.73
7 (≥ 5) so round up.
4.73 → 5
Examples:
2.49 →2
5.50 →6
9.01 →9
DECIMALS QUICK GUIDECheat Sheet
| ROUND TO... | LOOK AT... | IF 0, 1, 2, 3, 4... | IF 5, 6, 7, 8, 9... |
|---|---|---|---|
| 1 d.p. (tenths) | Hundredths (2nd digit) | Round down (keep) | Round up (+1) |
| 2 d.p. (hundredths) | Thousandths (3rd digit) | Round down (keep) | Round up (+1) |
| 3 d.p. (thousandths) | Ten-thousandths (4th) | Round down (keep) | Round up (+1) |
| Whole Number | Tenths (1st digit) | Round down (drop) | Round up (+1) |
REMEMBERKey Rules
Zeros at the end act as placeholders.
Example: 2.30 rounds to 2.3 (to 1 d.p.)
Trailing zeros after rounding can be shown or omitted.
Example: 9.00 can be written as 9
Rounding does not change the overall value very much.
TOP TIPS FOR DECIMALS
- ★ Underline the digit you are rounding to.
- ★ Circle the next digit to help you decide.
- ★ Use a number line to check your answer.
Example: Round 3.467 to 2 decimal places
3.467 → look at the thousandths digit 7
7 ≥ 5, so round up! Answer: 3.47
3.463.473.48
★ Master Topic Section11+ Exam Essential
🏛️ Roman Numerals
Roman numerals are a system of numbers used by the ancient Romans. They are still used today in clocks, chapters, years, and many other places!
ANCIENT SYSTEM
Roman numerals use 7 basic letter symbols combined with addition & subtraction rules to form all numbers!
1. BASIC SYMBOLS7 Core Values
There are 7 basic symbols in Roman numerals:
| Symbol | I | V | X | L | C | D | M |
|---|---|---|---|---|---|---|---|
| Value | 1 | 5 | 10 | 50 | 100 | 500 | 1000 |
I = 1
V = 5
X = 10
L = 50
C = 100
D = 500
M = 1000
2. RULES TO REMEMBER5 Core Rules
1
Symbols are written from largest to smallest left to right.
Example: LX = 50 + 10 = 60
2
A smaller value placed after a larger value is added.
Example: VI = 5 + 1 = 6
3
A smaller value placed before a larger value is subtracted.
Example: IV = 5 - 1 = 4
4
No symbol can be repeated more than three times in a row.
Example: III = 3, not IIII
5
Only one smaller value can be placed before a larger value.
IX = 9 (10 - 1) ✓ | IIX = 8 ✗
3. SUBTRACTIVE PAIRS6 Special Pairs
These are the special subtractive combinations:
| Pair | Meaning | Example | Value |
|---|---|---|---|
| IV | I before V | 5 – 1 | 4 |
| IX | I before X | 10 – 1 | 9 |
| XL | X before L | 50 – 10 | 40 |
| XC | X before C | 100 – 10 | 90 |
| CD | C before D | 500 – 100 | 400 |
| CM | C before M | 1000 – 100 | 900 |
4. EXAMPLES (NUMBERS → ROMAN NUMERALS)Key Benchmarks
| Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| Roman | I | II | III | IV | V | VI | VII | VIII | IX | X |
| Number | 11 | 20 | 30 | 40 | 50 | 60 | 90 | 100 | 500 | 1000 |
|---|---|---|---|---|---|---|---|---|---|---|
| Roman | XI | XX | XXX | XL | L | LX | XC | C | D | M |
5. MORE EXAMPLES11+ Frequently Tested
| Number | Roman |
|---|---|
| 12 | XII |
| 14 | XIV |
| 18 | XVIII |
| 19 | XIX |
| 21 | XXI |
| Number | Roman |
|---|---|
| 24 | XXIV |
| 29 | XXIX |
| 39 | XXXIX |
| 44 | XLIV |
| 49 | XLIX |
| Number | Roman |
|---|---|
| 58 | LVIII |
| 73 | LXXIII |
| 88 | LXXXVIII |
| 99 | XCIX |
| 145 | CXLV |
| Number | Roman |
|---|---|
| 202 | CCII |
| 399 | CCCXCIX |
| 512 | DXII |
| 944 | CMXLIV |
| 2024 | MMXXIV |
6. REAL-WORLD USESEveryday
🕒
Clock faces
I to XII
📖
Book chapters
Chapter IV
🏆
Super Bowl events
Super Bowl LVIII
🏛️
Monuments & buildings
Completed in MCMXCVI
👑
Movie sequels & dates
Rocky IV
7. TIPS TO REMEMBERTop Strategy
Always start with the largest value symbol.
Look out for subtractive pairs (IV, IX, XL, XC, CD, CM).
Keep symbols in descending order left to right.
💡 Rule of Thumb:
• Big before small = ADD
• Small before big = SUBTRACT
• Big before small = ADD
• Small before big = SUBTRACT
8. PRACTICE TIME!Quick Quiz
Write the Roman numeral for each number:
1. 7 =
2. 16 =
3. 28 =
4. 56 =
5. 91 =
6. 365 =
TOP TIPSGuide
- Always start from the left when comparing numbers.
- Use a place value chart to help layout big digits.
- Zeros are crucial place-holders – never ignore them!
- Practice reading, writing and rounding numbers daily.
- The more you practise, the easier 11+ questions get!
REMEMBERRules
Left MovementBigger (10×)
Right MovementSmaller (1/10)
Each place: 10× the place to its right, and 1/10 of the place to its left.
11+ Maths Foundation
Master Place Value!
"Understanding place value helps you build a strong foundation for all maths topics!"
🎓
Pro Mode Academy
11+ Verified Learning Guide
Interactive Practice Playgrounds
Test your place value, Roman numerals, and rounding skills live!
Digit Detective
Click the digit in the requested place:
Target: Ten Thousands
Roman Numeral Converter
Romans didn't have a zero!
MMXXIV
The Rounding Machine
Rounding to the nearest 100. Is the tens digit 50 or higher?
342
300
400
Midpoint: 350
42
🚀 Ready to Test Your Knowledge?
Take our graded 11+ Place Value assessment now!