# What is it in standard form?

Writes a number in standard form a × 10ⁿ, in standard notation with all its digits, and in expanded form, from a decimal, E notation, a × 10ⁿ, or a sum such as 100 + 30 + 8.

- Page: https://www.acalculator.org/math/standard-form-calculator
- JSON spec: https://www.acalculator.org/math/standard-form-calculator.json
- Version: 89bd5afe6e25

## Default answer

Example with the default inputs (Number 154.37): 154.37 in standard form is 1.5437 × 10².

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| n | Number | The number: a decimal such as 154.37 or 0.00045, E notation such as 4.5e-4, a × 10ⁿ such as 4.5 × 10^-4, or a sum such as 100 + 50 + 4. |
| sf | Round to significant figures | Optional: how many significant figures to keep, from 1 to 30. Leave empty to keep them all. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| standard | Standard form (a × 10ⁿ) | The number as a × 10ⁿ with one non-zero digit before the point of a: standard form in the UK, scientific notation in the US. |
| decimal | Standard notation | The number with all its digits written out, as in US school standard form, for powers from 10⁻³⁰ to 10³⁰. |
| expanded | Expanded form | Each non-zero digit times its place value, added up. |
| powers | Expanded form with powers of ten | Each non-zero digit times its power of ten, added up. |
| e | E notation | The standard form as calculators and spreadsheets write it: a e n means a × 10ⁿ. |
| exponent | Exponent n | The power of ten in a × 10ⁿ. |

## Method

Standard form: a × 10ⁿ with 1 ≤ |a| < 10, where n counts the places the decimal point moves (left is positive). Expanded form: each non-zero digit times its place value.

## Assumptions

- In the UK, standard form means a × 10ⁿ; in US schools, standard form means the number written with digits, which this page calls standard notation.
- Digits are exact as typed: nothing is rounded through binary floating point.
- Leading zeros are never significant; trailing zeros of a whole number without a decimal point are not kept in a.
- Rounding to significant figures rounds an exact half to the even digit (2.45 → 2.4).

## Worked examples

1. n = 154.37 gives standard = 1.5437 × 10², decimal = 154.37, expanded = 100 + 50 + 4 + 0.3 + 0.07, powers = 1 × 10² + 5 × 10¹ + 4 × 10⁰ + 3 × 10⁻¹ + 7 × 10⁻², exponent = 2. Source: OpenStax, Algebra and Trigonometry 2e, section 1.2 Exponents and Scientific Notation (a × 10ⁿ with 1 ≤ |a| < 10; 2,780,418 = 2.780418 × 10⁶), https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-2-exponents-and-scientific-notation, retrieved 2026-10-02; OpenStax, Prealgebra 2e, section 1.1 Introduction to Whole Numbers (standard form 138 and expanded form 100 + 30 + 8), https://openstax.org/books/prealgebra-2e/pages/1-1-introduction-to-whole-numbers, retrieved 2026-10-02.
2. n = 2,780,418 gives standard = 2.780418 × 10⁶, e = 2.780418e6, expanded = 2,000,000 + 700,000 + 80,000 + 400 + 10 + 8. Source: OpenStax, Algebra and Trigonometry 2e, section 1.2 Exponents and Scientific Notation (a × 10ⁿ with 1 ≤ |a| < 10; 2,780,418 = 2.780418 × 10⁶), https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-2-exponents-and-scientific-notation, retrieved 2026-10-02, example: 2,780,418 = 2.780418 × 10⁶.
3. n = 0.00000000000047 gives standard = 4.7 × 10⁻¹³, decimal = 0.00000000000047, expanded = 0.0000000000004 + 0.00000000000007. Source: OpenStax, Algebra and Trigonometry 2e, section 1.2 Exponents and Scientific Notation (a × 10ⁿ with 1 ≤ |a| < 10; 2,780,418 = 2.780418 × 10⁶), https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-2-exponents-and-scientific-notation, retrieved 2026-10-02, example: 0.00000000000047 = 4.7 × 10⁻¹³.
4. n = 100 + 30 + 8 gives decimal = 138, standard = 1.38 × 10², powers = 1 × 10² + 3 × 10¹ + 8 × 10⁰. Source: OpenStax, Prealgebra 2e, section 1.1 Introduction to Whole Numbers (standard form 138 and expanded form 100 + 30 + 8), https://openstax.org/books/prealgebra-2e/pages/1-1-introduction-to-whole-numbers, retrieved 2026-10-02, example: 100 + 30 + 8 is 138 in standard form.
5. n = 4.5 × 10^-4 gives decimal = 0.00045, standard = 4.5 × 10⁻⁴, expanded = 0.0004 + 0.00005. Source: OpenStax, Algebra and Trigonometry 2e, section 1.2 Exponents and Scientific Notation (a × 10ⁿ with 1 ≤ |a| < 10; 2,780,418 = 2.780418 × 10⁶), https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-2-exponents-and-scientific-notation, retrieved 2026-10-02.
6. n = 154.37, sf = 3 gives standard = 1.54 × 10², decimal = 154, expanded = 100 + 50 + 4, e = 1.54e2. Source: OpenStax, Algebra and Trigonometry 2e, section 1.2 Exponents and Scientific Notation (a × 10ⁿ with 1 ≤ |a| < 10; 2,780,418 = 2.780418 × 10⁶), https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-2-exponents-and-scientific-notation, retrieved 2026-10-02.
7. n = -3050 gives standard = −3.05 × 10³, decimal = −3,050, expanded = −(3,000 + 50).

## FAQ

### What is standard form?

It depends on where you learned it. In the UK and in science, standard form is a × 10ⁿ with 1 ≤ a < 10, the same as US scientific notation: 2,780,418 is 2.780418 × 10⁶. In US schools, standard form is the number written with digits, such as 138, as opposed to expanded form or words. This page shows both.

### How do I write a number in standard form a × 10ⁿ?

Move the decimal point until one non-zero digit is in front of it, and count the places. Moving left gives a positive n, moving right a negative n. 154.37 becomes 1.5437 × 10² (2 places left), and 0.00000000000047 becomes 4.7 × 10⁻¹³ (13 places right).

### What is expanded form?

The number as the sum of each digit times its place value. 154.37 is 100 + 50 + 4 + 0.3 + 0.07, or 1 × 10² + 5 × 10¹ + 4 × 10⁰ + 3 × 10⁻¹ + 7 × 10⁻². Zero digits are left out: 3,050 is 3,000 + 50.

### How do I turn expanded form back into standard form?

Add the parts. Type 100 + 30 + 8 and the calculator gives 138, which is 1.38 × 10² in a × 10ⁿ form.

### How do I convert a × 10ⁿ to a normal number?

Move the decimal point n places: right when n is positive, left when it is negative, filling with zeros. 4.5 × 10⁻⁴ is 0.00045. Type 4.5 × 10^-4 or 4.5e-4 to see it.

### Is standard form the same as scientific notation?

In the UK, yes: both mean a × 10ⁿ. In the US, standard form means the plain number and scientific notation means a × 10ⁿ. The scientific notation calculator also gives engineering notation and counts significant figures.

## Sources

- OpenStax, Algebra and Trigonometry 2e, section 1.2 Exponents and Scientific Notation (a × 10ⁿ with 1 ≤ |a| < 10; 2,780,418 = 2.780418 × 10⁶; 0.00000000000047 = 4.7 × 10⁻¹³), CC BY 4.0, retrieved 2026-10-02. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-2-exponents-and-scientific-notation
- OpenStax, Prealgebra 2e, section 1.1 Introduction to Whole Numbers (standard form 138; expanded form 100 + 30 + 8), CC BY 4.0, retrieved 2026-10-02. https://openstax.org/books/prealgebra-2e/pages/1-1-introduction-to-whole-numbers