NumbersPlace value and face value
In our number system the same digit can stand for different amounts. The 5 in 50 means fifty. The 5 in 500 means five hundred. What a digit is worth depends on where it sits. That worth is its place value. The digit itself, wherever it sits, is its face value.
The two ideas
- Face value is the digit as it looks. The face value of 7 is always 7.
- Place value is the digit multiplied by the value of its place: ones, tens, hundreds, thousands and so on.
An example: 4,68,253
| Digit | Place | Face value | Place value |
|---|---|---|---|
| 4 | Lakhs | 4 | 4,00,000 |
| 6 | Ten thousands | 6 | 60,000 |
| 8 | Thousands | 8 | 8,000 |
| 2 | Hundreds | 2 | 200 |
| 5 | Tens | 5 | 50 |
| 3 | Ones | 3 | 3 |
Adding the place values gives the number back: 4,00,000 + 60,000 + 8,000 + 200 + 50 + 3 = 4,68,253. That sum is the expanded form.
Three facts children are asked
- The place value of 0 is always 0, whatever its place. Its face value is also 0. But zero still matters: it holds a place open. Without the zero, 405 would look like 45.
- In the ones place, place value and face value are equal. The 3 in 4,68,253 has both equal to 3.
- A digit one place to the left is worth ten times as much. In 3,33,333 each 3 is worth ten times the 3 on its right.
Typical questions, solved
Find the difference between the place value and the face value of 6 in 4,68,253. The place value is 60,000 and the face value is 6. The difference is 59,994.
Find the difference between the place values of the two 7s in 27,574. The first 7 is in the thousands place: 7,000. The second is in the tens place: 70. The difference is 6,930.
Write the greatest and the smallest 4-digit numbers using 3, 0, 8, 5 once each. Greatest: put the digits in falling order, 8530. Smallest: rising order would start with 0, which is not allowed in the first place, so put the smallest non-zero digit first and then the rest in rising order: 3058.
Place value in the two systems
The place value of a digit is the same number in the Indian and the international system. Only the name of the place differs. In 4,68,253 the 4 is in the lakhs place in the Indian system and the hundred thousands place in the international one. Either way its place value is 4,00,000. The place value chart shows both sets of names side by side.
Place value after the decimal point
To the right of the decimal point the places are tenths, hundredths and thousandths. In 6.25 the 2 has place value 2 tenths, or 0.2, and the 5 has place value 5 hundredths, or 0.05. The pattern is the same: each step to the right is worth a tenth as much.
Why this matters
Carrying in addition, borrowing in subtraction, long multiplication and long division are all place value at work. When a child writes 27 + 5 = 212, the trouble is not addition. It is place value. Time spent on this idea in classes 2 to 5 pays back in every later chapter.
The converter shows the place value of every digit of any number you type. For practice, see the place value worksheets on our Worksheets site.