Number systemUnderstandabout 45 min
How place value works, and how to use it
Precise rules for names, commas, comparing, forming, rounding and estimating
Exact rules for place and face value, expanded form, number names and both comma systems, with many worked examples. Then reliable methods for converting, comparing, ordering, forming numbers, rounding, estimating and Roman numerals, plus the mix-ups to avoid.
In this part you’ll
- Find the place value and face value of any digit in a number up to ten crore, and write numbers in expanded form.
- Write and read number names correctly in the Indian and International systems and convert between them.
- Compare and order large numbers, and form the greatest and smallest numbers from given digits with and without repetition.
- Round to the nearest 10, 100, 1,000, 10,000 or lakh and estimate sums, differences and products sensibly.
- Read and write Roman numerals using the addition, subtraction and repetition rules.
In Discover you met big numbers by bundling, reading and comparing them. This layer makes everything exact. You will learn the precise rules behind the words (place value, face value, expanded form, period), a reliable method for every common task, and the mistakes that trip people up most often.
The whole topic rests on one sentence: in our number system, every place is worth exactly ten times the place to its right. Almost every method in this lesson is that sentence used cleverly.
Chapter 01
Place value, precisely
A number is a row of digits. Counting from the right, the places are worth 1, 10, 100, 1,000, 10,000 and so on, each ten times the one before. Two definitions follow:
- Face value of a digit: the digit itself. It never changes.
- Place value of a digit: face value × value of its place.
So in 3,76,215 the digit 3 is in the lakhs place: face value 3, place value 3 × 1,00,000 = 3,00,000.
| Digit | Indian place | International place | Place value |
|---|---|---|---|
| 5 | ten crores | hundred millions | 50,00,00,000 |
| 8 | crores | ten millions | 8,00,00,000 |
| 4 | ten lakhs | millions | 40,00,000 |
| 0 | lakhs | hundred thousands | 0 |
| 2 | ten thousands | ten thousands | 20,000 |
| 7 | thousands | thousands | 7,000 |
| 1 | hundreds | hundreds | 100 |
| 9 | tens | tens | 90 |
| 3 | ones | ones | 3 |
Worked example
0 / 4 steps shownDifference between two place values
In 9,48,707, find the difference between the place values of the two 7s.
Worked example
0 / 3 steps shownPlace value times face value
In 3,82,564, what is the product of the place value and the face value of 8?
Try it
Chapter 02
Expanded form, three ways
Expanded form writes a number as the sum of the place values of its non-zero digits. There are three common styles, and you should be able to move between them.
| Style | Expanded form of 70,40,396 |
|---|---|
| Sum of place values | 70,00,000 + 40,000 + 300 + 90 + 6 |
| Digit × place | 7 × 10,00,000 + 4 × 10,000 + 3 × 100 + 9 × 10 + 6 × 1 |
| Standard form (back again) | 70,40,396 |
Worked example
0 / 4 steps shownFrom expanded form back to a number
Write as a number: 3 × 1,00,00,000 + 6 × 1,00,000 + 2 × 100 + 9 × 1.
Try it
Chapter 03
Number names: the exact rules
Writing any number in words
- Step 01Put in the commasIndian: 3,2,2 · Intl: 3,3,3
Use the system you are asked for. The commas split the number into periods.
- Step 02Read the leftmost period
Say its number (one or two digits in Indian, up to three in International) followed by the period name: crore, lakh, thousand, or billion, million, thousand.
- Step 03Move right, period by period
Repeat for each period. Skip any period that is all zeros; do not say "zero thousand".
- Step 04Finish with the ones period
Read the last three digits as an ordinary number up to 999, with no period name.
- Step 05Tidy the spelling
Hyphenate 21 to 99 (forty-five). Period names stay singular: five lakh, two crore, three million.
| Number | Indian name | International name |
|---|---|---|
| 505050 | 5,05,050: five lakh five thousand fifty | 505,050: five hundred five thousand fifty |
| 80080808 | 8,00,80,808: eight crore eighty thousand eight hundred eight | 80,080,808: eighty million eighty thousand eight hundred eight |
| 1000001 | 10,00,001: ten lakh one | 1,000,001: one million one |
| 99999999 | 9,99,99,999: nine crore ninety-nine lakh ninety-nine thousand nine hundred ninety-nine | 99,999,999: ninety-nine million nine hundred ninety-nine thousand nine hundred ninety-nine |
| 123456789 | 12,34,56,789: twelve crore thirty-four lakh fifty-six thousand seven hundred eighty-nine | 123,456,789: one hundred twenty-three million four hundred fifty-six thousand seven hundred eighty-nine |
Worked example
0 / 4 steps shownWords to digits, international
Write in digits: four hundred six million, seventy thousand, twelve.
Try it
Chapter 04
Indian ↔ International
The two systems write exactly the same numbers with exactly the same digits. Only the commas and the names change. Up to the thousands period, they agree completely. They part ways at the sixth digit: the Indian system calls it lakhs and starts a new two-place period, while the International system calls it hundred thousands and keeps going in threes.
| Place from right | Value | Indian name | International name |
|---|---|---|---|
| 1 | 1 = 1 | ones | ones |
| 2 | 10 = 10 | tens | tens |
| 3 | 100 = 100 | hundreds | hundreds |
| 4 | 1,000 = 1,000 | thousands | thousands |
| 5 | 10,000 = 10,000 | ten thousands | ten thousands |
| 6 | 1,00,000 = 100,000 | lakhs | hundred thousands |
| 7 | 10,00,000 = 1,000,000 | ten lakhs | millions |
| 8 | 1,00,00,000 = 10,000,000 | crores | ten millions |
| 9 | 10,00,00,000 = 100,000,000 | ten crores | hundred millions |
| 10 | 1,00,00,00,000 = 1,000,000,000 | arabs | billions |
Converting a number between systems
- Step 01Remove all commas
Start from the plain digits so old commas cannot confuse you.
- Step 02Re-insert commas
Indian: first after 3 digits from the right, then every 2. International: every 3.
- Step 03Read in the new system
Use the new period names. Check with the key facts below.
- Step 04Check with key facts
10 lakh = 1 million; 1 crore = 10 million; 10 crore = 100 million; 100 crore = 1 billion.
Worked example
0 / 3 steps shownCrores to millions
A state's budget is ₹2,45,00,00,000 (245 crore). Say it in millions and billions.
Worked example
0 / 3 steps shownMillions to lakhs
A film has 3.6 million views online. How many lakh views is that?
Predict first
Lab
Build numbers up to 999,999,999 in the International chart and read each one in both systems at once.
Millions
Thousands
Ones
Tip: tap a digit, then use ↑ ↓ or type 0–9. Ten in one column swaps for one in the next.
International name: three million six hundred thousand
Indian name: thirty-six lakh
Expanded form
3,000,000 + 600,000
Tap any digit to compare its face value and place value.
Build-the-number challenge
5 numbers to build. Each one is written a different way!
Text version of this activity
The lab has nine columns grouped in threes: Millions (hundred millions, ten millions, millions), Thousands (hundred thousands, ten thousands, thousands) and Ones (hundreds, tens, ones). It starts at 3,600,000, shown as three million six hundred thousand; because both systems are switched on, it also shows 36,00,000, thirty-six lakh.
Challenges: 1,000,000 (one million = ten lakh); 25,000,000 (twenty-five million = two crore fifty lakh); 100,000,000 (one hundred million = ten crore); 407,050,600 (four hundred seven million fifty thousand six hundred = forty crore seventy lakh fifty thousand six hundred); and 999,999,999, the largest nine-digit number (ninety-nine crore ninety-nine lakh ninety-nine thousand nine hundred ninety-nine).
As you add counters, notice that the digits never change between systems; only the commas and names do.
Worked example
0 / 4 steps shownInternational to Indian, digit by digit
Write 7,250,000 (7.25 million) with Indian commas and in words.
Try it
Lab
Play a memory game matching Indian and International names for the same amount.
Match each Indian amount with the same amount in the International system.
16 face-down cards hide 8 pairs. Flip two at a time and remember where things are!
Text version of this activity
Sixteen face-down cards hide eight pairs; turn two at a time and keep them if they match. The pairs are: 1 lakh and 100 thousand; 10 lakh and 1 million; 1 crore and 10 million; 25 lakh and 2.5 million; 10 crore and 100 million; 100 crore and 1 billion; 5 crore and 50 million; 140 crore and 1.4 billion (roughly India's population).
The key facts that unlock them all: 10 lakh = 1 million, so lakhs ÷ 10 = millions; and 100 crore = 1 billion, so crores ÷ 100 = billions.
Chapter 05
Neighbours, smallest and largest
The successor of a whole number n is n + 1 and its predecessor is n − 1. Every whole number has a successor, so there is no largest number. Every whole number except 0 has a predecessor.
Two facts link neighbours to the number of digits:
- The largest n-digit number is n nines. Its successor is the smallest (n + 1)-digit number: a 1 followed by n zeros.
- The smallest n-digit number is 1 followed by (n − 1) zeros. Its predecessor is the largest (n − 1)-digit number.
| Digits | Smallest | Largest | How many such numbers |
|---|---|---|---|
| 2 | 10 | 99 | 90 |
| 3 | 100 | 999 | 900 |
| 4 | 1,000 | 9,999 | 9,000 |
| 5 | 10,000 | 99,999 | 90,000 |
| 6 | 1,00,000 | 9,99,999 | 9,00,000 |
| 7 | 10,00,000 | 99,99,999 | 90,00,000 |
| 8 | 1,00,00,000 | 9,99,99,999 | 9,00,00,000 |
| 9 | 10,00,00,000 | 99,99,99,999 | 90,00,00,000 |
Worked example
0 / 3 steps shownHow many 5-digit numbers are there?
Count all the numbers from 10,000 to 99,999.
Try it
Chapter 06
Comparing and ordering
To compare two whole numbers (written without extra zeros in front):
- More digits means bigger. Any 6-digit number is bigger than any 5-digit number, because the smallest 6-digit number, 1,00,000, is bigger than the largest 5-digit number, 99,999.
- Same number of digits: scan from the left until two digits differ. The number with the bigger digit there is bigger; the digits after that do not matter.
Ascending order lists numbers from smallest to largest; descending order from largest to smallest. The symbols are > (greater than) and < (less than); the open, wide side always faces the bigger number.
Worked example
0 / 5 steps shownOrdering river lengths
Approximate lengths of five Indian rivers: Ganga 2,525 km, Godavari 1,465 km, Yamuna 1,376 km, Narmada 1,312 km, Krishna 1,400 km. Arrange them in ascending order.
Try it
Try it
Chapter 07
Forming the greatest and smallest numbers
Given some digits, which is the greatest number you can make using each digit once? Put the biggest digit in the biggest place: arrange the digits in descending order. For the smallest, arrange them in ascending order, with one catch: a number cannot start with 0 (then it would have fewer digits). So if 0 is among the digits, put the smallest non-zero digit first, then the 0, then the rest in ascending order.
Worked example
0 / 4 steps shownGreatest and smallest from 7, 0, 4, 9, 2
Using each of the digits 7, 0, 4, 9, 2 exactly once, form the greatest and smallest 5-digit numbers, and find their difference.
Worked example
0 / 4 steps shownWhen digits may repeat
Using only the digits 3, 0 and 8, with repetition allowed, form the greatest and smallest 6-digit numbers that use all three digits at least once.
Worked example
0 / 3 steps shownZeros, repetition and “at least once”
Using the digits 0, 1 and 2 (repetition allowed, each at least once), form the greatest and the smallest 6-digit numbers.
Try it
Chapter 08
Rounding, precisely
Rounding to any place
- Step 01Choose the rounding place
For example, the thousands place when rounding to the nearest 1,000.
- Step 02Look one place to the rightthe deciding digit
Only this digit decides. The digits after it are ignored.
- Step 030 to 4: round down
Keep the rounding digit as it is.
- Step 045 to 9: round up
Add 1 to the rounding digit. If it was 9, carry, just like addition.
- Step 05Zeros after
Every digit to the right of the rounding place becomes 0.
| Round to the nearest | Deciding digit | Result |
|---|---|---|
| 10 | 5 | 38,69,480 |
| 100 | 7 | 38,69,500 |
| 1,000 | 4 | 38,69,000 |
| 10,000 | 9 | 38,70,000 |
| 1,00,000 | 6 | 39,00,000 |
| 10,00,000 | 8 | 40,00,000 |
Worked example
0 / 3 steps shownRounding with a carry
Round 4,99,720 to the nearest thousand.
Lab
Round numbers up to ninety-nine lakh to the nearest thousand, ten thousand or lakh on a number line.
A number appears on a number line. Race to pick what it rounds to! Rounding to the nearest 1,000, 10,000, 1,00,000, 10 rounds.
Halfway? It rounds up.
Text version of this activity
Each of 10 rounds shows a number between 1,000 and 99,99,999 on a number line with the two nearest multiples marked, for example the nearest thousands, ten thousands or lakhs. You pick the mark it rounds to.
Example: 36,74,512 to the nearest lakh lies between 36,00,000 and 37,00,000; the deciding digit (ten thousands) is 7, so it rounds up to 37,00,000. The same number to the nearest thousand lies between 36,74,000 and 36,75,000; the deciding digit (hundreds) is 5, so it rounds up to 36,75,000. To the nearest ten thousand: the deciding digit (thousands) is 4, so it rounds down to 36,70,000.
Try it
Chapter 09
Estimating sums, differences and products
An estimate is a quick, sensible approximation. We estimate when an exact answer is not needed (roughly how many buses for a school trip?), when we want to check an exact answer (is 4,862 × 29 really 1,40,998?), or when exact data does not exist (how many people were at a mela?).
A common method is to round each number to its greatest place (its leftmost digit) and then calculate. For sums and differences you can also round every number to the same place, such as the nearest hundred or thousand; choose the place that suits how accurate you need to be.
Worked example
0 / 3 steps shownEstimating a sum
Estimate 5,290 + 17,986.
Worked example
0 / 4 steps shownEstimating a product (a school trip)
632 students go on a trip and each pays ₹385. Roughly how much is collected?
Worked example
0 / 3 steps shownEstimating a difference
A town had 1,83,275 voters; 97,640 of them voted. Roughly how many did not vote?
Worked example
0 / 3 steps shownEstimating in a real context: a monsoon water tank
A school roof collects rainwater. In June it collected 38,460 litres, in July 72,915 litres, in August 64,280 litres and in September 29,740 litres. Estimate the total to the nearest ten thousand litres to plan a new tank.
Lab
Estimate first, then calculate exactly, and see how close your estimate was.
10 questions on addition, subtraction, multiplication with some word problems mixed in. Estimate first, then work it out exactly.
Get three in a row and the numbers level up!
Text version of this activity
Each of 10 rounds shows a sum, difference or product with a first number from 100 to 9,999 and a second from 10 to 999. You first enter an estimate (round each number, then calculate), then the exact answer. The game shows how far your estimate was from the exact answer. There is no timer.
Some rounds are word problems, which ask only for the exact answer, so estimate in your head first: a train with 18 coaches of 72 passengers (about 20 × 70 = 1,400; exact 1,296); a library with 4,856 books buying 1,275 more (about 5,000 + 1,000 = 6,000; exact 6,131); a farmer with 7,250 kg of rice selling 3,875 kg (about 7,000 − 4,000 = 3,000; exact 3,375).
Good estimates use numbers you can calculate in your head. They should be close enough to catch a mistake such as a missing zero.
| Situation | Estimate or exact? | Why |
|---|---|---|
| How many buses for 632 students, 50 per bus? | Estimate first, then check exactly | About 12 or 13 buses; the exact count (13, because 12 buses seat only 600) decides the booking. |
| Bill at the kirana shop | Exact | Money changes hands; every rupee counts. An estimate helps you check the total. |
| Crowd at a mela | Estimate | Nobody can count every person; a rounded figure is all that is possible. |
| Medicine dose | Exact | A small error can be harmful. |
| Is my calculator answer sensible? | Estimate | A rough check catches missing zeros and pressed-wrong keys. |
| Distance to plan a road trip | Estimate | Rounded kilometres are enough to plan fuel and time. |
Try it
Chapter 10
Roman numerals: all the rules
| Rule | Examples | Not allowed |
|---|---|---|
| Symbols: I 1, V 5, X 10, L 50, C 100, D 500, M 1,000 | MDCLXVI = 1,666 | — |
| Repeating a symbol adds it; at most three times in a row | III = 3, XXX = 30, CCC = 300 | IIII, XXXX |
| V, L and D are never repeated | X (not VV), C (not LL), M (not DD) | VV, LL, DD |
| Smaller after bigger: add | VI = 6, LX = 60, MC = 1,100 | — |
| Smaller before bigger: subtract, only for these six pairs | IV 4, IX 9, XL 40, XC 90, CD 400, CM 900 | IL, IC, XD, VX |
| V, L and D are never subtracted | 45 is XLV | VL for 45 |
| A bar over a symbol multiplies it by 1,000 | V with a bar = 5,000 | — |
Worked example
0 / 3 steps shownWriting 1,994 in Roman numerals
Write 1,994 in Roman numerals.
Worked example
0 / 3 steps shownReading CDXLVIII
What number is CDXLVIII?
Lab
Sort Roman numerals into correctly written ones and ones that break a rule.
Is each Roman numeral written correctly by the standard rules?
10 cards, 2 bins. Tap a card, then tap its bin. You can also drag, or press a bin’s number key.
Text version of this activity
Ten cards show Roman numerals; sort each into Correct or Breaks a rule.
Correct: XC (90), XLIV (44), MCM (1,900), CCCXC (390) and DCCC (800).
Breaks a rule: IC (I can only be subtracted from V and X; 99 is XCIX), XXXX (no symbol four times; 40 is XL), VX (V is never subtracted), LL (L is never repeated; 100 is C) and IL (49 is XLIX, not IL).
Try it
Try it
Chapter 11
Place value in measurement
The metric system is place value in disguise. Its units go up and down in steps of ten, and the prefixes tell you the place:
- kilo means 1,000 (1 km = 1,000 m; 1 kg = 1,000 g)
- centi means one hundredth (1 m = 100 cm)
- milli means one thousandth (1 m = 1,000 mm; 1 L = 1,000 mL)
So converting between metric units is just moving digits between places, exactly like converting thousands to ones.
| Measure | Big unit | Small unit | Example |
|---|---|---|---|
| Length | 1 km | 1,000 m | 3 km 45 m = 3,000 + 45 = 3,045 m |
| Length | 1 m | 100 cm | 2 m 7 cm = 207 cm |
| Length | 1 cm | 10 mm | 15 cm 4 mm = 154 mm |
| Mass | 1 kg | 1,000 g | 5 kg 250 g = 5,250 g |
| Capacity | 1 L | 1,000 mL | A 2 L bottle holds 2,000 mL |
Worked example
0 / 3 steps shownMetres on a railway
A train journey is 1,284 km. How many metres is that? Write it both ways.
Words to know
All maths vocabulary →Vocabulary: precise meanings
- Numeral
- A symbol or group of symbols that stands for a number, such as 47, XLVII or the word forty-seven.
- Place-value system
- A way of writing numbers in which a digit's value depends on its position. Ours is a base-ten place-value system.
- Standard form
- A number written in the usual way with digits (and commas), such as 7,04,396.
- Expanded form
- A number written as the sum of the place values of its non-zero digits.
- Example: 7,04,396 = 7,00,000 + 4,000 + 300 + 90 + 6
- Period
- A group of places marked off by commas and read with one name.
- Example: Lakhs period, millions period
- Indian system
- Place-value naming with periods ones (3 places), thousands, lakhs, crores (2 places each).
- Example: 1,23,45,678
- International system
- Place-value naming with periods of three places: ones, thousands, millions, billions.
- Example: 12,345,678
- Ascending order
- Arranged from smallest to greatest.
- Example: 12, 45, 300
- Descending order
- Arranged from greatest to smallest.
- Example: 300, 45, 12
- Greater than (>) / less than (<)
- Symbols comparing two numbers; the open side faces the bigger number.
- Example: 8 > 3 and 3 < 8
- Estimate
- A sensible approximate value, usually found by rounding before calculating.
- Example: 632 × 385 ≈ 600 × 400
- Deciding digit
- When rounding, the digit one place to the right of the rounding place. 0–4 round down, 5–9 round up.
- Kilo, centi, milli
- Metric prefixes meaning 1,000, one hundredth and one thousandth.
- Example: 1 km = 1,000 m
- Vinculum
- A bar over a Roman numeral that multiplies its value by 1,000.
Quick check
Understand check
11 questions · answer what you can, then check. Getting one wrong is useful.
Reflect
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Helps you understand
Four operationsEstimating before multiplying or dividing uses rounding to the greatest place, and carrying in column methods is regrouping between places.
Related to
Properties of numbersWhole numbers, successors and predecessors lead straight into properties such as closure and the role of 0 and 1.
Related to
Measuring and constructing anglesReading measurement scales, like a protractor or a ruler in mm and cm, relies on the same place-value thinking as metric units.
Keep this
Cheat sheet
- Place value = face value × value of the place. Face value = the digit. Place value of 0 is 0.
- Expanded form: 70,40,396 = 70,00,000 + 40,000 + 300 + 90 + 6 = 7 × 10,00,000 + 4 × 10,000 + 3 × 100 + 9 × 10 + 6 × 1.
- Names: read period by period; skip all-zero periods; lakh, crore, million stay singular.
- Commas: Indian 3 then 2s (12,34,56,789); International 3s (123,456,789).
- Key facts: 10 lakh = 1 million; 1 crore = 10 million; 10 crore = 100 million; 100 crore = 1 billion.
- n-digit numbers: smallest 10ⁿ⁻¹ written as 1 then (n − 1) zeros; largest is n nines; there are 9 × 10ⁿ⁻¹ of them.
- Compare: more digits wins; else first differing digit from the left.
- Forming: greatest = digits in descending order; smallest = ascending, but never start with 0.
- Rounding: look only at the deciding digit; 5 or more rounds up; round once from the original number.
- Estimating: round each number (often to its greatest place), then calculate; use it to plan and to check.
- Roman: I V X L C D M; repeat at most 3 times; V, L, D never repeated or subtracted; only IV IX XL XC CD CM subtract.
- Metric prefixes: kilo 1,000; centi one hundredth; milli one thousandth.
Where this comes from
Sources
Ganita Prakash, Mathematics textbook for Grade 6 — Chapter 3: Number Play (opens another website) — NCERTawaiting owner check
Supports the Class 6 treatment of numbers: comparing and ordering numbers (supercells, smallest and largest), forming numbers from given digits, digit sums, digit patterns and palindromes, and estimating with numbers of a few digits.
Ganita Prakash, Mathematics textbook for Grade 7 — Chapter 1: Large Numbers Around Us (opens another website) — NCERTawaiting owner check
Supports lakh, crore and arab; the Sanskrit origin of the words lakh and crore; reading large numbers in the Indian (3-2-2) and American/International systems; rounding to the nearest thousand, lakh or crore; and estimating with real-world large numbers.
Place value (Arithmetic) (opens another website) — Khan Academyawaiting check
Supports place value, expanded form, comparing numbers by place value and rounding whole numbers.
Indian numbering system (opens another website) — Wikipediaawaiting owner check
Supports lakh (10⁵), crore (10⁷), arab (10⁹) and kharab (10¹¹), the 3-2-2 comma grouping, lakh crore = 10¹², and the equivalences with the short-scale thousand, million and billion.
Roman Numerals (opens another website) — Math is Funawaiting owner check
Supports the seven Roman symbols, the rule not to repeat a symbol more than three times, the subtraction pairs (IV, IX, XL, XC, CD, CM) and the bar over a symbol to multiply it by 1,000.
SI prefixes (opens another website) — BIPM (International Bureau of Weights and Measures)awaiting owner check
Supports metric prefixes as powers of ten: deca 10¹, hecto 10², kilo 10³, mega 10⁶, giga 10⁹, and deci 10⁻¹, centi 10⁻² and milli 10⁻³.
Place Value (opens another website) — Math is Funawaiting owner check
Supports place value, the rule that each column on the left is ten times the column on its right, expanded form (143 = 1 × 100 + 4 × 10 + 3 × 1), and the place names from ones up to millions.
End of Understand
What you just read
- Find the place value and face value of any digit in a number up to ten crore, and write numbers in expanded form.
- Write and read number names correctly in the Indian and International systems and convert between them.
- Compare and order large numbers, and form the greatest and smallest numbers from given digits with and without repetition.
- Round to the nearest 10, 100, 1,000, 10,000 or lakh and estimate sums, differences and products sensibly.
- Read and write Roman numerals using the addition, subtraction and repetition rules.
- Next depthGo deeper: InvestigateChange conditions, predict, compare evidence and test.
- Practise83 questionsHints and a worked solution for every question — or play a 10-question round.
- Step backDiscoverGo back over the ground before this one — you can move up and down as often as you like.
- TopicAll of number systemThe whole ladder, the connections and the words to know, on one page.
The web
Explore a connection
Helps you understand
Four operationsPlace value is what makes column addition, carrying and long division work.
Helps you understand
Data handlingReading, comparing and rounding numbers comes first when you sort data and round a mean.
Related to
Number and shape patternsPlace-value charts are full of patterns: each place is ten times the one to its right.
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Revision 1 · release preview-7e1cbbcc4f · accepted 20/09/2026