Ones, Tens, and Hundreds

**Place value** tells us how much a digit is worth based on its position in a number. In our number system, each position has a value **10 times greater** than the position to its right: | Position | Value | Example in 253 | |----------|-------|----------------| | Hundreds | 100 | 2 hundreds = $2 \times 100 = 200$ | | Tens | 10 | 5 tens = $5 \times 10 = 50$ | | Ones | 1 | 3 ones = $3 \times 1 = 3$ | So $253 = 200 + 50 + 3$ This is called **expanded form** - writing a number as the sum of the values of each digit.

Finding the Value of Each Digit

What is the value of each digit in 472?

Identify the ones digit: The rightmost digit is 2 = $2 \times 1 = 2$

Identify the tens digit: The middle digit is 7 = $7 \times 10 = 70$

Identify the hundreds digit: The leftmost digit is 4 = $4 \times 100 = 400$

Write in expanded form: Add all values together = $472 = 400 + 70 + 2$

Answer: The 4 is worth 400, the 7 is worth 70, and the 2 is worth 2.

Building a Number from Place Values

Write the number: 6 hundreds, 0 tens, 8 ones

Find the hundreds value: 6 hundreds = $6 \times 100 = 600$

Find the tens value: 0 tens = $0 \times 10 = 0$

Find the ones value: 8 ones = $8 \times 1 = 8$

Combine all values: $600 + 0 + 8$ = $608$

Answer: The number is 608. Notice the 0 holds the tens place!

Comparing Digit Values in Different Positions

In the number 535, which 5 has a greater value - the first or the last?

Find the position of the first 5: The first 5 is in the hundreds place = $5 \times 100 = 500$

Find the position of the last 5: The last 5 is in the ones place = $5 \times 1 = 5$

Compare the values: $500$ vs $5$ = $500 > 5$

Answer: The first 5 has a greater value (500) because it is in the hundreds place. The same digit can have different values depending on its position!

Understanding place value is the foundation of all math! - **Reading numbers**: When you see 847, you know it means "eight hundred forty-seven" - **Adding and carrying**: When adding 58 + 37, you need to know that 5 and 3 are in the tens place - **Money**: A 100 dollar bill is worth ten 10 dollar bills, which is worth one hundred 1 dollar bills - **Measurement**: 1 meter = 10 decimeters = 100 centimeters Without place value, we would need a different symbol for every number - imagine memorizing millions of symbols!

Mistake: Confusing the digit with its value (saying the 5 in 350 is worth 5)

Why: The position matters! The 5 is in the tens place, so it represents 50, not 5.

Correct: Always multiply the digit by its place value: $5 \times 10 = 50$

Mistake: Forgetting zero as a placeholder (writing 608 as 68)

Why: Zero holds the position. Without the 0, the 6 would move to the tens place.

Correct: 608 means 6 hundreds, 0 tens, 8 ones. The zero keeps 6 in the hundreds place.

Money and Bills

Our money system uses place value! A 100 dollar bill equals ten 10 dollar bills or one hundred 1 dollar bills.

If you have 3 hundred dollar bills, 2 ten dollar bills, and 7 one dollar bills, you have 327 dollars total.

Addresses and House Numbers

House numbers use place value. House 253 comes after 252 and before 254.

On a street, house 100 is at the start of a block, 200 is at the next block, and so on.

Each position in a number has a value: ones (1), tens (10), hundreds (100)

The value of a digit equals the digit times its place value

Expanded form shows a number as the sum of each digit's value: $253 = 200 + 50 + 3$

Zero is a placeholder that keeps other digits in their correct positions

Q: Why do we need zero in numbers like 305?

A: Zero holds the tens place. Without it, 305 would become 35, which is a completely different number! Zero tells us there are no tens, but it keeps the 3 in the hundreds position.

Q: Why is our system called 'base 10'?

A: Because each place is worth 10 times more than the place to its right. We use 10 digits (0-9), and when we count past 9, we move to the next place. This is probably because humans have 10 fingers!

Exit Presentation

Ones, Tens, and Hundreds

1 / 11

Arithmetic / Place Value

Ones, Tens, and Hundreds

Learn how digits in different positions represent different values in our number system.

Elementary15 min

Use arrow keys or spacebar to navigate