# Numeration, Place Value and Whole Numbers - Link: https://thecuriosi.com/lessons/aptet-maths-numeration-place-value/ - Published: 2026-11-03T18:19:24+05:30 - Author: MAHENDRA MANCHIKALAPATI 1. [Courses](https://thecuriosi.com/courses/) 2. [APTET Maths: Numbers and Arithmetic](https://thecuriosi.com/courses/aptet-maths-numbers-arithmetic/) 3. Lesson 1 of 10 Every arithmetic question rests on a clear sense of how numbers are written and what each digit is worth. The APTET syllabus begins with **knowing about numbers**: the **Hindu-Arabic (Indian) and international systems of numeration**, **place value and face value**, **comparing and ordering numbers**, the **four fundamental operations** and **whole numbers**. Questions here are quick, but traps such as “place value of zero” and “lakh vs million” are common. ## Systems of numeration Our number system is the **Hindu-Arabic system**. It uses ten digits (0 to 9), is a **base-10** system, and uses **place value** with **zero** as a placeholder. Large numbers are grouped and read in two ways. | Indian system | Digits | International system | | 1 thousand | 1,000 | 1 thousand | | 1 lakh | 1,00,000 | 100 thousand | | 10 lakh | 10,00,000 | 1 million | | 1 crore | 1,00,00,000 | 10 million | | 10 crore | 10,00,00,000 | 100 million | | 100 crore | 1,00,00,00,000 | 1 billion | **Commas**: in the Indian system, the first comma comes after three digits from the right, then after every two digits: 5,62,34,817 (five crore sixty-two lakh thirty- four thousand eight hundred seventeen). In the international system, commas come after every three digits: 56,234,817 (fifty-six million two hundred thirty-four thousand eight hundred seventeen). Memory aid: **10 lakh = 1 million**, **1 crore = 10 million**. ## Place value, face value and comparing numbers The **face value** of a digit is the digit itself. Its **place value** is the digit × the value of its place. | In 3,47,285 | Face value | Place value | | 3 | 3 | 3 × 1,00,000 = 3,00,000 | | 4 | 4 | 4 × 10,000 = 40,000 | | 7 | 7 | 7 × 1,000 = 7,000 | | 8 | 8 | 8 × 10 = 80 | The place value of **0** is always 0, whatever its position. The **expanded form** writes a number as the sum of place values: 3,47,285 = 3,00,000 + 40,000 + 7,000 + 200 + 80 + 5. ### Comparing and ordering * A number with **more digits** is greater. * With the same number of digits, compare **from the left**; the first place where the digits differ decides. * **Ascending** order: smallest to largest; **descending**: largest to smallest. **Forming numbers from digits:** with 3, 0, 7, 5 used once each, the largest 4-digit number is **7530** (digits in descending order) and the smallest is **3057** (smallest non-zero digit first, then 0, then the rest in ascending order). **Counting numbers of a given size:** there are 9 one-digit numbers, **90** two- digit numbers (10 to 99), **900** three-digit numbers and 9,000 four-digit numbers. ## Four operations and whole numbers | Operation | Terms | | Addition | addend + addend = sum | | Subtraction | minuend − subtrahend = difference | | Multiplication | multiplicand × multiplier = product | | Division | dividend ÷ divisor = quotient, with a remainder | **Division algorithm**: Dividend = Divisor × Quotient + Remainder (remainder < divisor). Example: 434 ÷ 17 gives quotient 25 and remainder 9, because 17 × 25 + 9 = 425 + 9 = 434. **Natural numbers** are 1, 2, 3, …; **whole numbers** are 0, 1, 2, 3, …. Zero is the smallest whole number; there is no largest. Every natural number is a whole number, but 0 is not a natural number. | Property of whole numbers | Addition | Multiplication | | Closure | yes: sum is a whole number | yes | | Commutative | a + b = b + a | a × b = b × a | | Associative | (a + b) + c = a + (b + c) | (a × b) × c = a × (b × c) | | Identity | 0 (a + 0 = a) | 1 (a × 1 = a) | | Distributive | a × (b + c) = a × b + a × c | – | Whole numbers are **not closed** under subtraction (3 − 5 is not a whole number) or division (3 ÷ 5 is not). **Division by zero is not defined**. ### Exam focus * Place value vs face value; place value of 0 is 0. * Indian vs international commas and names: 10 lakh = 1 million; 1 crore = 10 million. * Number of 2-digit numbers = 90; 3-digit = 900. * Dividend = divisor × quotient + remainder. * Whole numbers: closed under + and ×, not under − and ÷. ### Example Mrs Jyothi gives Class 4 a place-value chart and bundles of sticks (ones, tens, hundreds). Children show 347 with 3 bundles of hundred, 4 of ten and 7 single sticks, then write it in expanded form. Later, newspaper figures such as “the district population is 42,15,000” become reading practice in lakhs. ## Key takeaways * The Hindu-Arabic system is base 10, with ten digits, place value and zero. * Indian commas: 3 digits, then every 2; international: every 3. * Place value = face value × place; the place value of 0 is 0. * Compare numbers by the number of digits, then from the left. * Dividend = divisor × quotient + remainder. * Whole numbers start at 0 and are closed under addition and multiplication only. ## Practice 1. The place value of 6 in 3,46,215 is: 2. * (A) 6 * (B) 600 * (C) 6,000 * (D) 60,000 3. 1 crore is equal to: 4. * (A) 10 million * (B) 100 million * (C) 1 million * (D) 1,000 million 5. The difference between the place value and the face value of 5 in 2,53,601 is: 6. * (A) 50,000 * (B) 0 * (C) 4,995 * (D) 49,995 7. The largest 4-digit number formed using the digits 4, 0, 9, 2 once each is: 8. * (A) 9,240 * (B) 9,420 * (C) 4,920 * (D) 2,049 9. How many 3-digit numbers are there? 10. * (A) 999 * (B) 900 * (C) 899 * (D) 1,000 11. 7 × (5 + 3) = 7 × 5 + 7 × 3 shows the: 12. * (A) commutative property * (B) associative property * (C) closure property * (D) distributive property 13. In a division, the divisor is 17, the quotient is 25 and the remainder is 9. The dividend is: 14. * (A) 434 * (B) 425 * (C) 443 * (D) 416 15. Seventy million in the Indian system is: 16. * (A) 70 lakh * (B) 7 lakh * (C) 7 crore * (D) 70 crore Answers and explanations (tap to show) 1. (C) In 3,46,215 the 6 is in the thousands place: 6 × 1,000 = 6,000. 2. (A) 1 crore = 1,00,00,000 = 10,000,000 = 10 million. 3. (D) The 5 is in the ten-thousands place: 50,000 − 5 = 49,995. 4. (B) Arrange the digits in descending order: 9, 4, 2, 0 → 9,420. 5. (B) From 100 to 999 there are 999 − 100 + 1 = 900 numbers. 6. (D) Multiplication is distributed over addition. 7. (A) 17 × 25 + 9 = 425 + 9 = 434. 8. (C) 70,000,000 = 7,00,00,000 = 7 crore. [Log in](https://thecuriosi.com/wp-login.php?redirect_to=https%3A%2F%2Fthecuriosi.com%2Flessons%2Faptet-maths-numeration-place-value%2F) to mark lessons complete and track your progress. [ Next lesson Factors, Multiples, Primes and Divisibility ](https://thecuriosi.com/lessons/aptet-maths-factors-primes-divisibility/) [Back to course overview](https://thecuriosi.com/courses/aptet-maths-numbers-arithmetic/) Share this