स्थानीय मान और संख्यांक
Place Value and Numerals
Place value is the value a digit gets from its position in a number. In 5,834 the digit 8 has a face value of 8 but a place value of 800. Every operation a primary child learns — carrying, borrowing, comparing, rounding — rests on this one idea.
Face value and place value
Place value = face value x value of the place
- Face value never changes. In 4,725 the face value of 7 is 7, wherever it stands.
- Place value changes with position. In 4,725 the place value of 7 is 700; in 4,275 it is 200 for 2 and 70 for 7.
- The place value of 0 is always 0, whatever place it occupies. This one line answers a question that appears very often.
The Indian and international systems
| Indian system | International system |
|---|---|
| Ones, Tens, Hundreds | Ones, Tens, Hundreds |
| Thousands, Ten Thousands | Thousands, Ten Thousands |
| Lakhs, Ten Lakhs | Hundred Thousands, Millions |
| Crores, Ten Crores | Ten Millions, Hundred Millions |
| Commas after 3, then every 2 digits | Commas after every 3 digits |
So 3,45,678 in the Indian system is written 345,678 in the international system. One lakh equals one hundred thousand, and one crore equals ten million.
Numerals and number names
- Hindu-Arabic numerals use ten digits, 0 to 9, and are positional — the same digit means different amounts in different places.
- Roman numerals are additive and have no zero and no place value: I, V, X, L, C, D, M. A smaller value before a larger one is subtracted, so IV is 4 and IX is 9.
- Roman rules worth remembering: I, X, C can be repeated up to three times; V, L, D are never repeated; V, L, D are never subtracted.
Comparing, ordering and rounding
To compare, first count the digits — the number with more digits is greater. If the count is equal, compare from the leftmost place. To round 4,738 to the nearest hundred, look at the tens digit: 3 is less than 5, so it becomes 4,700.
✗ The place value of 0 in 407 is 7. | ✓ The place value of 0 is 0; the face value of 7 is 7 and its place value is 7.
संकेत: अंकित मान (face value) अंक स्वयं; स्थानीय मान (place value) = अंक × स्थान का मान।
Place value gives 1-2 questions in the Maths section and reappears in Maths pedagogy as the classic misconception topic. Expect direct items such as the difference between the place value of two digits in one number, or conversion between Indian and international systems. The most repeated trap is asking for the place value of 0. A second trap uses a Roman numeral rule — remember V, L and D are never repeated and never subtracted.
Frequently asked questions
What is the difference between face value and place value?
Face value is the digit itself and never changes. Place value is the digit multiplied by the value of the position it occupies, so in 4,725 the face value of 7 is 7 while its place value is 700.
How many zeros are there in one crore?
Seven. One crore is written as 1,00,00,000 in the Indian system and equals ten million, that is 10,000,000, in the international system.
What is the place value of zero in any number?
Always zero. Because place value is the digit multiplied by the value of its place, and zero multiplied by anything is zero, no matter which position the zero occupies.
60-second recap
- Place value = face value x value of the place; face value never changes.
- Place value of 0 is always 0.
- Indian system: lakh and crore; international: hundred thousand and million.
- Roman numerals have no zero and no place value; V, L, D never repeat or subtract.
- Compare by digit count first, then from the leftmost place.