Writing a Three-Digit Number in Expanded Form

Write $485$ in expanded form.

Identify each digit's place value: 4 is in hundreds, 8 is in tens, 5 is in ones = Places identified

Write the value of the hundreds digit: $4 \times 100 = 400$ = $400$

Write the value of the tens digit: $8 \times 10 = 80$ = $80$

Write the value of the ones digit: $5 \times 1 = 5$ = $5$

Connect with addition signs: $400 + 80 + 5$ = Expanded form complete

Answer: $485 = 400 + 80 + 5$

Writing a Four-Digit Number in Expanded Form

Write $6{,}203$ in expanded form.

Identify each digit's place value: 6 is thousands, 2 is hundreds, 0 is tens, 3 is ones = Places identified

Write the value of the thousands digit: $6 \times 1{,}000 = 6{,}000$ = $6{,}000$

Write the value of the hundreds digit: $2 \times 100 = 200$ = $200$

Handle the zero in the tens place: $0 \times 10 = 0$ (skip this, it adds nothing) = Skip

Write the value of the ones digit: $3 \times 1 = 3$ = $3$

Connect with addition signs: $6{,}000 + 200 + 3$ = Expanded form complete

Answer: $6{,}203 = 6{,}000 + 200 + 3$

Converting from Expanded Form to Standard Form

Write $7{,}000 + 400 + 50 + 2$ in standard form.

Identify the place values: $7{,}000$ (thousands), $400$ (hundreds), $50$ (tens), $2$ (ones) = All places identified

Add the values together: $7{,}000 + 400 = 7{,}400$ = $7{,}400$

Continue adding: $7{,}400 + 50 = 7{,}450$ = $7{,}450$

Add the ones: $7{,}450 + 2 = 7{,}452$ = Standard form complete

Answer: $7{,}000 + 400 + 50 + 2 = 7{,}452$

Mistake: Writing just the digit instead of its value (e.g., writing $3 + 5 + 2 + 7$ for $3{,}527$)

Why: Each digit has a different value based on its position. The 3 in 3,527 is not worth 3, it's worth 3,000!

Correct: Multiply each digit by its place value: $3{,}527 = 3{,}000 + 500 + 20 + 7$

Mistake: Including zero values (e.g., writing $405 = 400 + 0 + 5$)

Why: Adding zero doesn't change the sum, so we typically skip it to keep expanded form clean.

Correct: Just write $405 = 400 + 5$ (skip the zero in the tens place)

Mistake: Mixing up place values (e.g., thinking tens come before hundreds)

Why: Place values go right to left: ones, tens, hundreds, thousands, etc.

Correct: From right to left: ones (1), tens (10), hundreds (100), thousands (1,000)

Counting Money

When you count money, you naturally use expanded form thinking.

If you have 2 hundred-dollar bills, 3 ten-dollar bills, and 4 one-dollar bills, that's $200 + 30 + 4 = 234$ dollars.

Reading Large Numbers

Expanded form helps you understand large numbers like distances or populations.

A city has a population of $25{,}430$. That's $20{,}000 + 5{,}000 + 400 + 30$ people.

Q: Do I need to include zeros in expanded form?

A: No! Since adding zero doesn't change the sum, we skip zeros. For example, $305 = 300 + 5$ (not $300 + 0 + 5$).

Q: What's the difference between expanded form and standard form?

A: Standard form is the regular way we write numbers (like $2{,}345$). Expanded form breaks it down to show each digit's value ($2{,}000 + 300 + 40 + 5$).

Q: How do I remember the place values?

A: Start from the right! The rightmost digit is always ones, then tens, hundreds, thousands, and so on. Each place is 10 times the one before it.