Expanded Form Calculator

Results

Written out

Place-value chart

What each digit is worth

• The 4 in the thousands place is worth 4000.
• The 5 in the hundreds place is worth 500.
• The 3 in the tens place is worth 30.
• The 2 in the ones place is worth 2.
• The 7 in the hundredths place is worth 0.07.

How to Use the Expanded Form Calculator

1. 1. Enter a number. Whole numbers and decimals work, up to 36 digits before the point and 30 after it. Negative numbers are written with the sign in front.
2. 2. Or enter an expanded form. Typing 4000 + 500 + 30 + 2, or 4 × 10^3 + 5 × 10^2, shows the standard form it adds up to and then writes it out all the ways below.
3. 3. Adjust the style. Tick the box to keep zero digits such as 0 × 100, tick “and” for British word form, and choose whether decimals are read as fractions (fifty-seven hundredths) or with a point (point five seven).
4. 4. Copy what you need. The words and the expanded form each have a copy button, and the chart shows what every digit is worth.

What Expanded Form Is

In our number system the value of a digit depends on its place: each place is ten times the one to its right. The number 4,532 means 4 thousands, 5 hundreds, 3 tens and 2 ones, and expanded form writes that as a sum: 4,532 = 4000 + 500 + 30 + 2. Reading and writing numbers in base-ten numerals, number names and expanded form is a Grade 2 expectation in the Common Core State Standards for Mathematics (2.NBT.A.3), and the same idea extends to decimals, where the places to the right of the point are tenths, hundredths, thousandths and so on.

Writing Numbers in Words

• Hyphenate 21 to 99 when the second digit is not zero: thirty-two, ninety-nine.
• Read in groups of three from the left, saying the group name after each: 4,532,000 is four million five hundred thirty-two thousand.
• “And.” Many US textbooks keep “and” for the decimal point only, so 305.027 is three hundred five and twenty-seven thousandths. British style adds “and” after the hundreds: three hundred and five.
• Decimals are read either as a fraction of the last place (fifty-seven hundredths) or digit by digit after “point” (zero point five seven). A decimal below 1 needs no “and”: 0.57 is just fifty-seven hundredths.
• Names run thousand, million, billion, trillion, quadrillion and on to decillion (10³³) in this calculator, using the short scale, in which a billion is a thousand million.

Two Meanings of “Standard Form”

In the United States, standard form means the ordinary numeral, 4,532, as opposed to expanded form or word form. In the United Kingdom and some other countries, “standard form” means scientific notation: a number between 1 and 10 times a power of ten, so 4,532 is 4.532 × 10³. The calculator shows both, with the second labelled as such. To convert in either direction at any size, use the Scientific Notation Converter.

Worked Example: 305.027

• Digits and places: 3 hundreds, 0 tens, 5 ones, 0 tenths, 2 hundredths, 7 thousandths.
• Expanded form, skipping the zeros: 300 + 5 + 0.02 + 0.007. With zeros shown: 300 + 0 + 5 + 0 + 0.02 + 0.007.
• Powers of ten: (3 × 10²) + (5 × 10⁰) + (2 × 10⁻²) + (7 × 10⁻³).
• In words: three hundred five and twenty-seven thousandths. Notice that the digits after the point, 027, are read as twenty-seven and named for the last place, thousandths.

Common Mistakes

• Confusing tens and tenths. The “ths” ending marks the places to the right of the point: tens is 10, tenths is 0.1.
• Dropping a zero. In 4,032 the zero in the hundreds place must stay as a placeholder; without it, 432 is a different number.
• Writing a decimal term as a whole number. The 7 in 0.07 is 7 hundredths, 0.07 — not 7.
• Reading 305.027 as “three hundred five point twenty-seven.” That says 0.27, not 0.027; the fractional reading keeps the place straight.

Frequently Asked Questions

What is the expanded form of 4,532?

4,532 = 4000 + 500 + 30 + 2. Each digit is multiplied by its place value and the products are added. In expanded notation it is (4 × 1000) + (5 × 100) + (3 × 10) + (2 × 1).

What is the difference between expanded form and expanded notation?

Expanded form is the plain sum of the place values, 400 + 50 + 3. Expanded notation shows the multiplication behind each term, (4 × 100) + (5 × 10) + (3 × 1), and sometimes uses powers of ten, (4 × 10²) + (5 × 10¹) + (3 × 10⁰). Textbooks use the names slightly differently, so follow your course.

How do you write a decimal in expanded form?

Give each digit after the point its place value: tenths are 0.1, hundredths 0.01, thousandths 0.001. So 7.35 = 7 + 0.3 + 0.05, or (7 × 1) + (3 × 0.1) + (5 × 0.01). As fractions, the last two terms are 3/10 and 5/100.

How do you say a number in word form?

Break it into groups of three digits, say each group as hundreds, tens and ones, and add the group name — thousand, million, billion. Hyphenate 21 through 99 where needed. For a decimal, say the digits after the point as a whole number followed by the name of the last place.

What is standard form?

In US classrooms, it is the usual way of writing a number with digits, such as 4,532. In the UK, standard form is scientific notation, such as 4.532 × 10³. This page shows both.

Can I enter an expanded form and get the number?

Yes. Type the terms joined by plus signs, for example 4000 + 500 + 30 + 2 or 4 × 10^3 + 5 × 10^2. The calculator adds them exactly and then writes the result every way.