Place Value

Write a Number in Expanded Form

Write 582 in expanded form by expressing each digit as a multiple of its place value: 5 x 100 + 8 x 10 + 2 x 1.

expanded-form Expanded form shows each digit multiplied by its place value, then added together. For 582: 5 x 100 + 8 x 10 + 2 x 1 = 500 + 80 + 2 = 582.

Example

Write 582 as hundreds, tens, and ones. Expanded form breaks a number apart by place value, showing what each digit is worth according to its position. Because our number system is built on powers of ten, a digit's column tells you how many hundreds, tens, or ones it contributes, and adding those pieces back reproduces the original number.

highlighted = computed this step

Step 1 — Set up

Start with the place-value chart.

hundredstensones582\begin{array}{c|c|c}\text{hundreds}&\text{tens}&\text{ones}\\5&8&2\end{array}
582 has hundreds, tens, and oneshundredsdigit 5100100100100100value 500tensdigit 81010101010101010value 80onesdigit 211value 2___ + ___ + ___Each column shows a different place value.

Step 2 — Hundreds term

Hundreds: 5 x 100 = 500.

hundredstensones582,5⋅100=500\begin{array}{c|c|c}\text{hundreds}&\text{tens}&\text{ones}\\5&8&2\end{array},\quad 5\cdot 100=\hl{500}
5 hundreds = 500hundredsdigit 5100100100100100value 500tensdigit 81010101010101010value 80onesdigit 211value 2500 + ___ + ___The hundreds digit 5 counts 5 groups of 100.

Step 3 — Tens term

Tens: 8 x 10 = 80.

hundredstensones582,8⋅10=80\begin{array}{c|c|c}\text{hundreds}&\text{tens}&\text{ones}\\5&8&2\end{array},\quad 8\cdot 10=\hl{80}
8 tens = 80hundredsdigit 5100100100100100value 500tensdigit 81010101010101010value 80onesdigit 211value 2500 + 80 + ___The tens digit 8 counts 8 groups of 10.

Step 4 — Ones term

Ones: 2 x 1 = 2.

hundredstensones582,2⋅1=2\begin{array}{c|c|c}\text{hundreds}&\text{tens}&\text{ones}\\5&8&2\end{array},\quad 2\cdot 1=\hl{2}
2 ones = 2hundredsdigit 5100100100100100value 500tensdigit 81010101010101010value 80onesdigit 211value 2500 + 80 + 2The ones digit 2 counts 2 single ones.

Step 5 — Expanded form

Write 582 as 5 x 100 + 8 x 10 + 2 x 1.

582=5⋅100+8⋅10+2⋅1582=5\cdot100+8\cdot10+2\cdot1
582 = 500 + 80 + 2hundredsdigit 5100100100100100value 500tensdigit 81010101010101010value 80onesdigit 211value 2500 + 80 + 2 = 582Adding the place values gives the original number.