Expanded form is a way of writing a number as the sum of the values of its digits. Each digit is multiplied by its place value, so 4072 = 4000 + 70 + 2, or 4 × 1000 + 7 × 10 + 2 × 1. It shows what every digit is worth. Zeros add nothing, so they are usually left out.
In Spanish
forma desarrollada
Also called
expanded notation, expanded form of a number, writing a number as a sum of place values
Each digit becomes its value: digit times place. Adding the values gives back the number: 4000 + 70 + 2 + 0.5 = 4072.5.
Formal definition and notation
A number written in base ten with digits dk … d1d0 has the expanded form dk × 10k + ⋯ + d1 × 10 + d0 × 1. For decimals the sum continues with negative powers of ten: d−1 × 110 + d−2 × 1100 + …. Terms whose digit is 0 may be omitted, because their value is 0.
Symbol
Read it as
Meaning
4000 + 70 + 2
four thousand plus seventy plus two
expanded form using the value of each digit
4 × 1000 + 7 × 10 + 2 × 1
four times one thousand plus …
expanded form with each digit times its place value
4 × 103 + 7 × 101 + 2 × 100
four times ten to the third plus …
expanded form with exponent powers of ten (grade 5 and up)
Key facts
Three forms of the same number: standard form 4,072; expanded form 4,000 + 70 + 2; word form four thousand seventy-two.
A digit’s value is the digit times its place: the 7 in 4,072 is worth 7 × 10 = 70.
Skip zeros: 5,006 is 5000 + 6, not 5000 + 0 + 0 + 6 (both are correct, but the zeros add nothing).
Decimals continue to the right: 3.58 = 3 + 0.5 + 0.08 = 3 + 510 + 8100.
Use the arrows to change any digit, or select a digit to see its value. The readout writes the number in expanded form as you go. Try putting a 0 in the middle.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Expanded Form examples, step by step
Example 1: A four-digit number
Warm-up
Write 6,385 in expanded form.
6 is in the thousands place: 6,000.
3 is in the hundreds place: 300.
8 is in the tens place: 80, and 5 is in the ones place: 5.
Add the values: 6000 + 300 + 80 + 5.
Answer:6385 = 6000 + 300 + 80 + 5
Example 2: Zeros in the middle
Core
Write 50,409 in expanded form, both with values and with multiplication.
No hundreds, ones or tenths appear, so those places hold 0.
Add: 3000 + 60 + 0.08 = 3060.08.
Answer: The number is 3,060.08.
Common mistakes
✗ Mistake5406 = 5 + 4 + 0 + 6
✓ Instead5406 = 5000 + 400 + 6
Expanded form adds the value of each digit, not the digits themselves. The 5 is worth 5,000 because it sits in the thousands place.
✗ Mistake2070 = 2000 + 7
✓ Instead2070 = 2000 + 70
The 7 is in the tens place, so it is worth 70. Read the place of each digit from the right: ones, tens, hundreds, thousands.
✗ Mistake0.36 = 0.3 + 0.6
✓ Instead0.36 = 0.3 + 0.06
The 6 is in the hundredths place, the second place after the decimal point, so it is worth 6 hundredths.
Not to be confused with
Expanded Formvs.Standard form
Standard form is the usual way of writing a number with digits, 4,072. (In algebra, standard form also names a way to write equations, which is a different idea.)
Scientific notation writes a number as one product, 4.072 × 103; expanded form writes it as a sum of place values.
Quick check: 3 questions
Question 1 of 3
Which is the expanded form of 7,305?
Show answer and explanation
Answer: C. 7 thousands, 3 hundreds, 0 tens and 5 ones: 7000 + 300 + 5. The first adds digits instead of values, the second shifts every place down, and the last treats the 5 as tens.
Question 2 of 3
What number is 60,000 + 2000 + 9?
Show answer and explanation
Answer: B. 6 ten-thousands, 2 thousands, no hundreds or tens, and 9 ones: 62,009. The zeros hold the hundreds and tens places.
Question 3 of 3
Which shows 4.25 in expanded form?
Show answer and explanation
Answer: D. 2 is in the tenths place (0.2) and 5 is in the hundredths place (0.05), so 4.25 = 4 + 0.2 + 0.05. The first choice puts the 5 in the tenths place.
Expanded Form: frequently asked questions
What is the difference between expanded form and standard form?
Standard form is the compact way you usually write a number, like 8,316. Expanded form breaks it into the value of each digit and adds them: 8000 + 300 + 10 + 6. Both name the same number; expanded form just shows what each digit is worth, which helps with place value, regrouping and mental math.
Do you include zeros in expanded form?
Usually not. A zero digit has a value of 0, so adding it changes nothing: 905 = 900 + 5. Some teachers ask for every place, 900 + 0 + 5, to show the empty tens place, and that is also correct. Either way, the zero in standard form is still needed to hold the place.
How do you write a decimal in expanded form?
Keep going to the right of the decimal point with tenths, hundredths and thousandths. 12.407 = 10 + 2 + 0.4 + 0.007, or with fractions 10 + 2 + 410 + 71000. The hundredths digit is 0, so that term is skipped. Each place to the right is worth one tenth of the place before it.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 2.NBT.A.3, CCSS 4.NBT.A.2, CCSS 5.NBT.A.3.a
Cite this entry
Effortless Math Team. “Expanded Form.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/expanded-form/
Flashcard
TermExpanded Form4,072 = ?
DefinitionA number written as the sum of its digits’ values: 4072 = 4000 + 70 + 2.
Place ValuePlace value is the value of a digit based on its position in a number. In 3,507 the 5 is worth 500, because it sits in the hundreds place. Each place is worth 10 times the place to its right: ones, tens, hundreds, thousands, and after the decimal point, tenths and hundredths.Number System · Grade 3, Grade 4, Grade 5NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2PowerA power is a number written as a base with an exponent, such as 53, or the value that results, 53 = 5 × 5 × 5 = 125. We say 125 is the third power of 5, or “5 to the third power”. The second power is called the square and the third power the cube.Number System · Grade 5, Grade 6, Grade 7ExponentAn exponent tells how many times to use a base as a factor. It is the small raised number to the upper right of the base: in 53, the base is 5 and the exponent is 3, so 53 = 5 × 5 × 5 = 125. Any nonzero number with an exponent of 0 equals 1.Algebra · Grade 6, Grade 7, Grade 8Standard FormStandard form of a number is the usual way of writing it with digits, such as 4,306, with each digit in its place-value position. It is the short form you get from expanded form (4,000 + 300 + 6) or from word form (four thousand, three hundred six). Zeros hold any empty places.Number System · Grade 2, Grade 3, Grade 4Word FormWord form is a way of writing a number using words instead of digits, as you would say it aloud: 4,306 is written “four thousand, three hundred six”. Read each three-digit period, then say its name (million, thousand). For decimals, say “and” at the decimal point: 6.25 is “six and twenty-five hundredths”.Number System · Grade 2, Grade 3, Grade 4RegroupingRegrouping is trading 10 of one place value for 1 of the next larger place, or 1 for 10 of the next smaller place, so that column addition or subtraction works. In 47 + 38, the 15 ones become 1 ten and 5 ones; in 52 − 27, 1 ten becomes 10 ones. It is also called carrying and borrowing.Operations · Grade 1, Grade 2, Grade 3Distributive PropertyThe distributive property says that multiplying a number by a sum gives the same result as multiplying it by each term and then adding: a(b + c) = ab + ac. It multiplies a factor by each term inside parentheses, so 3(x + 4) = 3x + 12. It works with subtraction too, and using it backward is factoring.Algebra · Grade 6, Grade 7, Grade 8MultiplicationMultiplication is the operation that combines equal groups to find a total. The fact 4 × 6 = 24 means 4 groups of 6, or 6 + 6 + 6 + 6. The numbers you multiply are called factors, and the result is the product. Order does not matter: 6 × 4 is also 24.Operations · Grade 2, Grade 3, Grade 4TenthsTenths are the parts you get when one whole is split into 10 equal parts; each part is one tenth, written 110 or 0.1. The tenths place is the first digit to the right of the decimal point, so in 4.7 the 7 means 7 tenths, or 0.7.Number System · Grade 3, Grade 4, Grade 5HundredthsHundredths are the parts you get when one whole is split into 100 equal parts; one hundredth is 1100 or 0.01. The hundredths place is the second digit to the right of the decimal point, so in 3.47 the 7 means 7 hundredths. One cent is one hundredth of a dollar.Number System · Grade 4, Grade 5, Grade 6Decimal PointA decimal point is the dot that separates the whole-number part of a number from its fractional part. Digits to its left are ones, tens and hundreds; digits to its right are tenths, hundredths and thousandths. In 46.25 the point sits between 6 ones and 2 tenths, and you read it aloud as “and”.Number System · Grade 4, Grade 5, Grade 6Whole NumberA whole number is 0 or a positive counting number: 0, 1, 2, 3, and so on. Whole numbers do not include fractions, decimals, or negative numbers, so 12 is a whole number but 8.5, 34 and −3 are not. Every whole number is also an integer.Number System · Grade 3, Grade 4, Grade 5Scientific NotationScientific notation writes a number as a value from 1 to less than 10 times a power of 10, such as 5.4 × 103 for 5,400. The exponent records how far the decimal point moved: positive for large numbers and negative for numbers between 0 and 1, as in 0.0062 = 6.2 × 10−3.Number System · Grade 8, Algebra 1DigitA digit is one of the ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 that we use to write every number. The number 507 has three digits: 5, 0 and 7. What a digit is worth depends on its place: in 507, the 5 stands for 5 hundreds, or 500.Number System · Grade 1, Grade 2, Grade 3DecimalA decimal is a number written with a decimal point to show parts of a whole. Decimals use place value to represent tenths, hundredths, thousandths and more: in 3.14, the 1 means 1 tenth and the 4 means 4 hundredths. So 0.75 = 75100, and 0.5 is one half.Number System · Grade 4, Grade 5, Grade 6RoundingRounding replaces a number with a nearby number that is easier to use, to a chosen place value. Look at the digit immediately to the right of that place: 5 or more rounds up, 4 or less rounds down. So 47 rounds to 50 to the nearest ten, and 3.68 rounds to 3.7 to the nearest tenth.Number System · Grade 3, Grade 4, Grade 5SumA sum is the result you get when you add two or more numbers. In 8 + 5 = 13, the numbers 8 and 5 are the addends and 13 is the sum. The order does not change it: 5 + 8 is also 13. Word problems ask for a sum with words like total, in all and altogether.Operations · Grade 1, Grade 2, Grade 3