Identifying Place Value

What is the value of the digit 6 in the number $2{,}643$?

Find the position of 6: Reading right to left: 3 is in ones, 4 is in tens, 6 is in hundreds = 6 is in the hundreds place

Calculate the value: $6 \times 100$ = $600$

Verify: $2{,}643 = 2{,}000 + 600 + 40 + 3$ = The 6 represents 600

Answer: The digit 6 in $2{,}643$ has a value of $600$.

Writing in Expanded Form

Write $5{,}809$ in expanded form.

Identify each digit's place: 5 (thousands), 8 (hundreds), 0 (tens), 9 (ones) = Four digits, four places

Write each digit times its place value: $5 \times 1{,}000$, $8 \times 100$, $0 \times 10$, $9 \times 1$ = $5{,}000 + 800 + 0 + 9$

Simplify (remove the zero): $5{,}000 + 800 + 9$ = Expanded form complete

Answer: $5{,}809 = 5{,}000 + 800 + 9$

Comparing Numbers Using Place Value

Which is greater: $3{,}472$ or $3{,}427$?

Compare thousands: Both have 3 in thousands place: $3{,}000 = 3{,}000$ = Same, move to next place

Compare hundreds: Both have 4 in hundreds place: $400 = 400$ = Same, move to next place

Compare tens: First has 7 tens ($70$), second has 2 tens ($20$) = $70 > 20$

Conclusion: Since $70 > 20$ in the tens place = $3{,}472 > 3{,}427$

Answer: $3{,}472$ is greater than $3{,}427$

Mistake: Confusing the digit with its value (saying 5 instead of 500)

Why: Students forget that position matters. The digit 5 in 1,523 is worth 500, not 5.

Correct: Always ask: What place is this digit in? Then multiply: digit × place value = value

Mistake: Reading digits from left to right when identifying places

Why: Place values are named from the right (ones, tens, hundreds...). Reading from the left can cause confusion.

Correct: Start from the rightmost digit (ones place) and work left: ones → tens → hundreds → thousands

Mistake: Forgetting zeros in expanded form

Why: In a number like 4,507, the 0 in the tens place is a placeholder and represents 0 × 10 = 0.

Correct: Zeros matter! 4,507 = 4,000 + 500 + 0 + 7 (though we often write 4,000 + 500 + 7)

Money and Place Value

Our money system uses place value. Each larger bill is worth 10 times the smaller one.

If you have 3 hundred-dollar bills, 4 ten-dollar bills, and 7 one-dollar bills, you have 347 dollars.

Odometers in Cars

Car odometers show distance traveled using place value. Each digit represents a different unit.

If an odometer shows 12,345 km, the car has traveled 12 thousand kilometers, plus 345 more.

Q: Why do we use place value instead of different symbols for each number?

A: Using place value with just 10 digits (0-9) lets us write any number, no matter how large! Without place value, we would need infinite symbols.

Q: What comes after the thousands place?

A: After thousands comes ten thousands, then hundred thousands, then millions. Each place is still 10 times greater than the one before it.

Q: Why is zero important in place value?

A: Zero acts as a placeholder. In 305, the zero shows there are no tens. Without it, we would write 35, which is a different number!