Place value

Where a digit sits matters

The digit 4 can be worth 4, 40 or 400. It depends on its place in the number. That idea is called place value.

In 347:

So 347 means 3 hundreds, 4 tens and 7 ones: 300 + 40 + 7.

Each place is ten times bigger

Moving one place to the left makes a digit worth ten times as much:

• 10 ones make 1 ten.
• 10 tens make 1 hundred.
• 10 hundreds make 1 thousand.

That’s why we call our system "base ten".

Base-ten blocks

Base-ten blocks let you see place value:

To show 235, use 2 flats, 3 rods and 5 cubes.

The job of zero

Zero holds a place when there’s nothing in it. In 305 there are no tens, but we still need the 0 so the 3 stays in the hundreds place. Without it, 305 would become 35.

Value vs digit

Be clear about two different questions:

• "What digit is in the tens place of 347?" → 4
• "What is the value of the 4 in 347?" → 40

Worked examples

Example 1: In 347, what is the value of the 4?

The 4 is in the tens place, so its value is 40.

Example 2: What number has 6 hundreds, 0 tens and 2 ones?

600 + 0 + 2 = 602.

Example 3: How many tens are in 90?

90 = 9 tens. Answer: 9.

Common mistakes

• Saying the digit’s name instead of its value. The 4 in 347 is worth 40, not 4.
• Leaving out zero as a placeholder: writing 52 for "5 hundreds and 2 ones" instead of 502.
• Reading digits in the wrong order. The hundreds come first, on the left.

Try it yourself

1. What is the value of the 8 in 582?
2. Which digit is in the hundreds place of 719?
3. Write the number: 4 hundreds, 5 tens, 0 ones.
4. Write 263 as hundreds, tens and ones.

Answers: 1) 80 2) 7 3) 450 4) 2 hundreds, 6 tens, 3 ones

Quick recap

• Place value: a digit’s value depends on its position.
• Ones, tens, hundreds: each place is worth ten times the place to its right.
• Zero holds an empty place.