See the idea
Before you start
Count reliably and group ten objects into one bundle. A digit is a symbol; its value depends on where it appears in the number.
Words used in this guide
- Digit
- One of the symbols 0 to 9 used to write numbers.
- Place value
- The value contributed by a digit in its position.
- Expanded form
- Writing a number as the sum of its place-value parts.
Why the method works
Ten ones can be exchanged for one ten without changing the total amount. Ten tens can be exchanged for one hundred. This repeated exchange is why each place is ten times the value of the place immediately to its right. In 505, the left 5 means 500 and the right 5 means 5. The zero records that there are no additional tens between them.
Expand the number
352 = 300 + 50 + 2. Naming each amount helps when adding, subtracting or estimating. Reading only the digits can hide what they represent.
Zero keeps a place open
In 405, the zero records no tens. The number is four hundreds and five ones. Removing the zero would make 45, which is a different number.
Regroup without changing the total
One hundred can be exchanged for ten tens. So 230 can be represented as two hundreds and three tens, or twenty-three tens. Different groupings are useful in subtraction.
Worked examples, step by step
Example 1: What does the 7 represent in 274?
- The 7 is in the tens place.
- Seven tens = 70, and 274 = 200 + 70 + 4.
Example 2: Write 3,082 in expanded form.
- There are three thousands, no hundreds, eight tens and two ones.
- 3,082 = 3,000 + 80 + 2.
- The zero need not appear as an added zero, but it must stay in the standard number to hold the hundreds place.
Example 3: Represent 246 using a different number of tens and ones.
- The usual grouping is 2 hundreds, 4 tens and 6 ones. Exchange one ten for ten ones.
- It becomes 2 hundreds, 3 tens and 16 ones. Both descriptions total 246.
- Regrouping changes the description, not the amount. This exchange is used in subtraction.
Example 4: Which is larger, 4,095 or 4,509?
- Both have four thousands. Compare hundreds next: zero hundreds versus five hundreds.
- 4,509 is larger. There is no need to compare the remaining digits once this place differs.
- Compare from the largest place; the final digit alone cannot decide.
Common mistakes and how to repair them
“The value of 6 in 462 is 6.”
Its digit is 6, but it is in the tens place, so its value is 60.
“Deleting zero never changes a number.”
Removing the zero from 407 produces 47. The hundreds digit shifts into the tens place.
Check your understanding
Choose an answer for each question. You can check again after reading the explanation.
Worked answers
What is the value of 6 in 462? 60. The 6 is in the tens place.
Which number has 3 hundreds, 0 tens and 8 ones? 308. The zero holds the tens place.
Practise independently
Work these out on paper. Include a diagram or a sentence where the question asks you to explain. Open each solution after making an attempt.
3. What is the value of 8 in 5,804?
Show the reasoning
800; the 8 is in the hundreds place.
4. Write 7,000 + 300 + 9 as one number.
Show the reasoning
7,309. A zero is needed in the tens place.
5. Write 352 as 3 hundreds, some tens and 12 ones.
Show the reasoning
3 hundreds, 4 tens and 12 ones: 300 + 40 + 12 = 352.
6. Using 0, 2, 5 and 8 once each, make the smallest four-digit number.
Show the reasoning
2,058. The thousands digit cannot be zero; place the remaining digits in increasing order.
If a method still feels uncertain, revisit the closest worked example, then try a fresh problem. A correct answer copied from a solution tells you less than an explanation you can give independently.
Learn it → Try it → Explain it
Put the idea into play
Practise the place-value foundations behind reading and calculating with numbers.
Choose an available grade band. Say the value of each digit before placing it; use the whole-number levels as a warm-up for decimals.
Try Digit Drop →Free guest play has question, level and time limits. Sign in to continue or save progress. A game score is not a mastery assessment.
Questions students and parents ask
Is zero worth nothing?
A zero contributes no amount in its own place, but its position can be essential to the meaning of the other digits.
Can a number have more than nine ones?
A regrouped description can. Standard notation exchanges each group of ten, so each written place contains one digit.
Do commas change the value?
No. Grouping conventions help reading. Whether a number is grouped using thousands or lakhs, the positional values remain powers of ten.
Help at home: Trade bundles
Use straws or drawn marks. Make 23 as two bundles of ten and three singles, then trade a bundle for ten singles. Ask whether the total changed.
Move to a three-digit number only after your child can explain the exchange. If “twenty-three” is secure but 203 is not, focus on the empty tens place.
Ask the child to build a number from an unusual description, such as 1 hundred, 12 tens and 4 ones. It is 224.
Keep the conversation focused on the reasoning you can hear or see. One short activity cannot establish lasting mastery or diagnose a learning difficulty.
Would a teacher help with the next step?
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