How Place Tells a Digit's Value
Lumi stands at a colorful market stall stacked with crates of apples, boxes of ten apples, big bins of one hundred apples, and giant warehouse pallets holding one thousand apples, pointing excitedly at each group to show how the piles grow ten times as many at every step.
- Identify the value of a digit based on its position in a multi-digit number.
- Explain why moving one place to the left makes a digit worth ten times as much.
- Compare the value of the same digit in different place positions.
- Determine the place value of each digit in a four-digit number.
- Predict how a digit's value changes when its position moves one place to the left.
Key terms
- Digit
- A single number symbol from 0 to 9.
- Place value
- What a digit is worth by its spot.
- Ones place
- The spot on the far right.
- Thousands place
- The spot four steps from the right.
Where a Digit Sits
A digit is just one number symbol, like 3 or 7. But the same digit can mean different amounts! It all depends on where the digit sits in the number. That spot is called its place value. A 3 in the ones place means just 3. A 3 in the tens place means 30. The spot tells you the real value, so always look at where the digit is sitting.
Ten Times Bigger
Here is the cool pattern. Each place to the left is worth ten times as much as the place right next to it. One ten equals ten ones. One hundred equals ten tens. One thousand equals ten hundreds. It is just like apples sold in bigger and bigger boxes! Every time you move one spot left, the value gets ten times larger. That is how big numbers are built, step by step.
Worked examples
Find the value of the 7 in 2,750.
- Find where the 7 sits: it is in the hundreds place.
- The hundreds place means the digit times 100.
- So 7 times 100 equals 700.
Answer: 700
Activity
Drag each digit card into its correct place-value column to build the number 4,672, then check what each digit is worth.
Practice
In the number 4,318, what is the value of the 3?
Which number has a 5 that means 5,000 apples?
Common mistakes to avoid
- A digit always means itself.No. A 4 can mean 4, 40, 400, or more by its place.
- Each place is just one more.No. Each place to the left is ten times bigger, not one bigger.
Check your understanding
In the number 4,672, what is the value of the digit 6?
How many times as great is the value of the 5 in 500 than the value of the 5 in 50?
Which number has a 3 that stands for 3,000?
Recap
Every digit has a value that comes from its place in the number. Each place to the left is worth ten times as much as the place to its right, from ones to tens to hundreds to thousands.
Reflect
Why is it helpful to know what each digit in a number is worth?