WorksheetsAbout this worksheet
Place value means that a digit is worth more or less depending on where it stands. In 4,318 the 3 is worth 300; in 4,381 it is worth 300 too, but the 8 has changed from 8 to 80. Expanded form asks the child to break a number into such parts: 4,318 = 4,000 + 300 + 10 + 8.
Numbers follow the Indian system here: ones, tens, hundreds, thousands, ten thousands, lakhs, with commas as 1,00,000.
What this skill is
Our number system uses only ten digits, 0 to 9, and lets the position do the rest. Each place is worth ten times the place on its right. In the Indian system the places are ones, tens, hundreds, thousands, ten thousands, lakhs, ten lakhs and crores, and commas are put after the hundreds and then after every two digits.
A worked example
Take 3,05,472.
- Read the places from the left: 3 lakhs, 0 ten thousands, 5 thousands, 4 hundreds, 7 tens, 2 ones.
- Expanded form: 3,00,000 + 5,000 + 400 + 70 + 2. The ten thousands place holds 0, so it adds nothing and is not written.
- The value of the digit 5 is 5,000, because it stands in the thousands place.
The zero is not empty decoration. Without it the number would be 35,472, which is far smaller.
Tips for parents and teachers
- Draw a place value chart (Th, H, T, O) on top of the sheet and let the child write the digits in it first.
- Zeros need care: 4,008 is 4,000 + 8. There are no hundreds and no tens to write.
- Mix both types over a week. Expanded form builds the idea; the underlined digit checks it.
How to use this sheet at home and in class
- At home: let the child build numbers with paper slips marked 1, 10, 100 and 1,000, then write what was built. Seeing 3 hundreds and 4 ones makes 304 clear.
- In class: start with "Expanded form" at 3 digits. Move to "Value of the underlined digit" once expanded form is steady, then raise the number of digits.
- Read every number aloud before working on it. A child who can say "forty-two thousand, three hundred and six" has already done most of the work.
Mistakes to watch for
- Leaving out the zero when writing a number from its parts: 4,000 + 8 written as 48.
- Giving the digit instead of its value: saying that the value of 3 in 4,318 is 3.
- Putting commas in the Western way (305,472) when the school uses the Indian way (3,05,472). Both show the same number; use the one the school uses.
What to try next
- Number names worksheets: writing the same numbers in words.
- Comparing numbers worksheets: place value put to use.
- Rounding numbers worksheets: looking at one place at a time.
Ready settings by class
Common questions
What is the difference between face value and place value?
The face value of a digit is the digit itself. The place value is the digit multiplied by the value of its place. In 4,318 the face value of 3 is 3 and its place value is 300.