The Expanded Form Calculator provided by Hesapstan breaks an integer or decimal into place-value parts and shows additive expanded form, factor form, and powers-of-10 exponential form.
Expanded form writes a number as the sum of its place values
Expanded form shows what each digit contributes to a number. For example, 342 becomes 300 + 40 + 2, so the hundreds, tens, and ones places are visible instead of hidden inside the compact number.
This calculator shows three related forms: additive expanded form, factor form, and powers-of-10 form. They describe the same number from different place-value angles.
Expanded form is a way to write a number as the sum of the values of its digits.
Additive form shows the place-value parts as a sum
In additive form, every nonzero place-value part is written as a separate term. The number 4523 becomes 4000 + 500 + 20 + 3.
This form is useful when learning place value because it makes the size of each digit visible. The digit 4 in 4523 is not just 4; it contributes 4000.
Factor form writes each digit multiplied by its place value
Factor form explains where the additive terms come from. Instead of writing 4000 + 500 + 20 + 3 directly, it writes 4×1000 + 5×100 + 2×10 + 3×1.
This is different from prime factorization. The word factor here means digit × place value, not decomposing the whole number into prime factors.
This calculator expands numbers by place value. It does not find prime factors such as 84 = 2²×3×7.
Exponential form uses powers of 10 for each place
In the decimal number system, each place corresponds to a power of 10. Ones are 10⁰, tens are 10¹, hundreds are 10², and thousands are 10³.
So 4523 can be written as 4×10³ + 5×10² + 2×10¹ + 3×10⁰. This is an expanded powers-of-10 form, not the same as scientific notation.
Scientific notation usually rewrites the whole number as one coefficient times a power of 10. Expanded exponential form writes each place separately.
Decimals use tenths, hundredths and negative powers of 10
Digits to the right of the decimal point represent fractional place values. The first digit after the decimal point is tenths, the second is hundredths, and the third is thousandths.
For 5.07, the additive form is 5 + 0.07, the factor form is 5×1 + 7×0.01, and the powers-of-10 form is 5×10⁰ + 7×10⁻².
The content contract says decimal comma and decimal dot are accepted. For example, 5.07 and 5,07 represent the same decimal value depending on locale.
The calculator is for notation, not algebraic factoring
This tool expands a number by place value. It does not factor algebraic expressions, find prime factors, or convert numbers between bases such as binary and hexadecimal.
If you want a table showing digit, place name, and place value, use the Place Value Calculator. If you want the number written as sums and powers of 10, this expanded form calculator is the right page.
Examples show that all three forms describe the same number
For 342, expanded form is 300 + 40 + 2, factor form is 3×100 + 4×10 + 2×1, and powers-of-10 form is 3×10² + 4×10¹ + 2×10⁰.
For 5.07, expanded form is 5 + 0.07, factor form is 5×1 + 7×0.01, and powers-of-10 form is 5×10⁰ + 7×10⁻². The zero helps position the hundredths place even if it does not add a nonzero term.
Related calculators help with place value and decimal operations
Use the Place Value Calculator for a row-by-row digit table, the Decimal Operations Calculator for arithmetic with decimals, and the Integer Calculator for integer practice. The Scientific Notation Calculator is useful when you need compact powers-of-10 notation instead of expanded place-value notation.
Frequently Asked Questions
What is expanded form?
Expanded form writes a number as the sum of its place-value parts. For example, 342 is 300 + 40 + 2.
What is factor form?
Factor form writes each digit multiplied by its place value, such as 3×100 + 4×10 + 2×1 for 342.
What is exponential form here?
It is the expanded powers-of-10 form: each place is written with a power of 10, such as 3×10² + 4×10¹ + 2×10⁰.
Is this the same as scientific notation?
No. Scientific notation usually uses one coefficient times 10 to a power. This calculator writes each place-value part separately.
Can I expand decimals?
Yes. According to the contract, the calculator supports integers and decimals, including decimal comma and decimal dot input.
Does this calculator support negative numbers?
Negative-number support is not promised by this content contract. The page is written for the place-value expansion of ordinary integers and decimals, not signed-number operations.
Does this find prime factors?
No. Expanded form is not prime factorization. It breaks a number into place-value terms, not into prime factors.
How is this different from the Place Value Calculator?
The Place Value Calculator gives a digit-by-digit table. This calculator writes the whole number in additive, factor, and powers-of-10 expanded forms.