What you'll learn
- Explain a digit’s value in a written number.
- Represent regrouping without changing the total.
- Explain the role of zero in a number such as 304.
Distinguish the digit from its value
A digit is a symbol; its place determines the quantity it represents within the base-ten numeral. In 352, the 3 represents three hundreds, the 5 represents five tens and the 2 represents two ones. Ask learners to connect those values with groups and with an expanded expression. Simply naming a column may hide uncertainty about quantity.
Represent 352 as 300 + 50 + 2 using labelled drawings or bundled sticks. Compare the 5 in 352 with the 5 in 523. The written symbol is the same, but it represents fifty in the first number and five hundred in the second.
Regroup while preserving the total
Regrouping changes how a quantity is organised, not how much there is. Ten ones can be exchanged for one ten, and ten tens for one hundred. Use both directions so learners do not see regrouping only as a procedure used in a written algorithm. Ask them to explain an exchange before attaching a notation to it.
Forty-two can be shown as four tens and two ones, or as three tens and twelve ones. Both equal 42. Replacing one ten with ten ones is an exchange; adding ten extra ones without removing a ten would change the total.
Explain zero as a placeholder
Zero indicates that there are no units of a particular place in the usual positional representation. In 304, the zero keeps the hundreds and ones in their correct positions. Reading the numeral as 34 loses a hundred-based grouping relationship. Use a representation with an empty tens position rather than describing zero as something that can always be ignored.
Place three hundred-groups in the hundreds column, no ten-groups in the tens column and four units in the ones column. Compare 304 and 340, asking which place is empty in each. Their totals differ even though they use the same three digits.
Diagnose the representation, not only the answer
A learner may correctly read a number from familiarity while being unable to build it. Another may understand the quantity but reverse symbols in writing. Compare spoken names, grouped objects, drawings and numerals. Use a fresh number to check whether the relationship between these forms is understood rather than memorised for one example.
Ask for 205 using groups, then ask the learner to write it. If they write 25, discuss where the two hundreds are represented. Next use 407, keeping the same relationship but changing the values, and invite an independent explanation.
Take these ideas with you.
- A digit and its positional value are different.
- Exchanging groups preserves quantity.
- Zero preserves the positional structure of the numeral.
Check your understanding
Work out each answer before opening the explanation. These checks are not scored or saved.
What is the value of 7 in 472?
Seventy: the digit 7 occupies the tens place.
Is 56 equal to four tens and sixteen ones?
Yes. 40 + 16 = 56. One of the original five tens has been exchanged for ten ones.
Why is 206 different from 26?
In 206, 2 represents two hundreds and zero holds the tens position. In 26, 2 represents two tens.
Sources and review status
Prepared for Teachers Track with AI assistance. Source and editorial audit completed on 18 October 2026. The explanations and self-checks were checked against the references below. No independent academic reviewer or official examination alignment is claimed.
- NCERT: Source Book on Assessment, Mathematics
Number representation and assessing conceptual understanding. All quantities, worked examples and self-checks in this guide are original.
English content version: lesson-place-value-v1. A Telugu translation has not yet been published. The English guide is published for general topic learning. No official examination curriculum or full practice bank is claimed.
Keep building your understanding
The three self-checks above are available now. A scored practice set for this topic has not yet been published.
Explore learning topicsOriginal explanations and fictional classroom examples. Independent topic learning; official examination alignment is not claimed. Self-checks are for reflection and are not scored or saved.
Report a correctionGuest reading is not saved.