Place value
Place value is the idea the whole number system rests on: the same ten digits mean different amounts depending on where they sit. A child who has it can read 4,732 without counting; a child who has not is memorising number names one at a time, and everything built on top — column addition, rounding, decimals — has nothing to stand on.
Start the levels Print a worksheet
What a digit is worth
What is the 7 in 4,732 worth?
- Find the 7. Counting from the right: 2 is ones, 3 is tens, 7 is hundreds.
- The 7 sits in the hundreds place, so it stands for 7 hundreds.
- 7 hundreds is 700.
- The 7 is worth 700.
Worth knowing. The answer is 700, not 7. "Which digit" and "what is it worth" are different questions, and swapping them is the most common mistake on this topic by a distance.
Reading a number apart
4,732
- 4 is in the thousands place, so it is worth 4,000.
- 7 is in the hundreds place, so it is worth 700.
- 3 is in the tens place, so it is worth 30.
- 2 is in the ones place, so it is worth 2. Together: 4,000 + 700 + 30 + 2.
Worth knowing. Writing a number out this way is called expanded form, and it is worth doing out loud a few times. It makes the point that a number is a sum, not a string of symbols.
Where it usually goes wrong
- Answering "7" to "what is the 7 in 4,732 worth?" — that is the digit, not its value.
- Counting places from the left instead of the right, so the thousands and the ones swap.
- Ignoring a zero, so 4,072 is read as though the 7 were in the hundreds place.
The Professor reads long numbers from the right, in threes. Ones, thousands, millions. The commas are there to help, so he lets them.
Practise it
All level pathsQuestions teachers and parents ask
When is place value taught?
It starts in grade 1 with tens and ones (1.NBT.B.2), reaches three digits in grade 2 and multi-digit numbers in grade 4 (4.NBT.A.1). It is revisited every year because each new topic — regrouping, rounding, decimals — leans on it.
Why does a zero matter so much?
Because it holds a place open. Without the 0 in 4,072 the number would read 472, and the 4 would drop from four thousands to four hundreds. A zero is doing a job even though it adds nothing to the total.
What is expanded form for?
It makes the addition inside a number visible: 4,732 is 4,000 + 700 + 30 + 2. Children who can write that tend to find column addition and regrouping easier, because carrying a ten stops being a rule and becomes something they can see.
Are the commas part of the number?
No, they are punctuation, and they mark groups of three from the right. Some countries use spaces or full stops instead. They are worth using because they turn a long string of digits into three or four readable chunks.
Where this shows up
Standards
- K.NBT · Number and operations in base ten
- 1.NBT · Number and operations in base ten
- 2.NBT · Number and operations in base ten
- 3.NBT · Number and operations in base ten
- 4.NBT · Number and operations in base ten
- 5.NBT · Number and operations in base ten
- CCSS.MATH.CONTENT.1.NBT.C.4 — Add within 100, including a two-digit number plus a one-digit number or a multiple of 10.
- CCSS.MATH.CONTENT.1.NBT.C.6 — Subtract multiples of 10 in the range 10 to 90.
- CCSS.MATH.CONTENT.1.NBT.B.2 — Understand that the two digits of a two-digit number stand for tens and ones.
- CCSS.MATH.CONTENT.1.NBT.C.5 — Given a two-digit number, mentally find 10 more or 10 less without having to count.
- CCSS.MATH.CONTENT.2.NBT.B.7 — Add and subtract within 1000, relating the strategy to a written method.
- CCSS.MATH.CONTENT.2.NBT.A.1 — Understand that the three digits of a three-digit number stand for hundreds, tens and ones.
- CCSS.MATH.CONTENT.2.NBT.A.3 — Read and write numbers to 1000 in numerals, number names and expanded form.
- CCSS.MATH.CONTENT.3.NBT.A.3 — Multiply one-digit whole numbers by multiples of 10 from 10 to 90.
- CCSS.MATH.CONTENT.4.NBT.A.1 — Recognise that a digit in one place is worth ten times what the same digit is worth one place to its right.
- CCSS.MATH.CONTENT.4.NBT.A.2 — Read, write and compare multi-digit whole numbers using numerals, number names and expanded form.
- CCSS.MATH.CONTENT.5.NBT.A.1 — Recognise that a digit in one place is worth ten times what it is worth to its right and a tenth of what it is worth to its left.
- CCSS.MATH.CONTENT.5.NBT.A.2 — Explain the pattern in the zeros of a product when multiplying by a power of 10, and use whole-number exponents to write powers of 10.
- CCSS.MATH.CONTENT.5.NBT.A.3 — Read, write and compare decimals to thousandths, using numerals, number names and expanded form.