acalculator

What is it in standard form?

Type a number as a decimal, in E notation, as a × 10ⁿ, or as a sum such as 100 + 30 + 8. The standard form calculator writes it in standard form a × 10ⁿ, in standard notation, and in expanded form.

Your numbers

Standard form (a × 10ⁿ)
1.5437 × 10²

154.37 in standard form is 1.5437 × 10².

Standard notation
154.37
Expanded form
100 + 50 + 4 + 0.3 + 0.07
Expanded form with powers of ten
1 × 10² + 5 × 10¹ + 4 × 10⁰ + 3 × 10⁻¹ + 7 × 10⁻²
E notation
1.5437e2
Exponent n
2

Standard form (a × 10ⁿ): 1.5437 × 10². 154.37 in standard form is 1.5437 × 10².

How to calculate

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.

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

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.

  • 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).

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Number 154.37 gives Standard form (a × 10ⁿ) 1.5437 × 10², Standard notation 154.37, Expanded form 100 + 50 + 4 + 0.3 + 0.07, Expanded form with powers of ten 1 × 10² + 5 × 10¹ + 4 × 10⁰ + 3 × 10⁻¹ + 7 × 10⁻², Exponent n 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. Number 2,780,418 gives Standard form (a × 10ⁿ) 2.780418 × 10⁶, E notation 2.780418e6, Expanded form 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. Number 0.00000000000047 gives Standard form (a × 10ⁿ) 4.7 × 10⁻¹³, Standard notation 0.00000000000047, Expanded form 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. Number 100 + 30 + 8 gives Standard notation 138, Standard form (a × 10ⁿ) 1.38 × 10², Expanded form with powers of ten 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. Number 4.5 × 10^-4 gives Standard notation 0.00045, Standard form (a × 10ⁿ) 4.5 × 10⁻⁴, Expanded form 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. Number 154.37, Round to significant figures 3 gives Standard form (a × 10ⁿ) 1.54 × 10², Standard notation 154, Expanded form 100 + 50 + 4, E notation 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. Number -3050 gives Standard form (a × 10ⁿ) −3.05 × 10³, Standard notation −3,050, Expanded form −(3,000 + 50).

How it works

The number is read as exact decimal digits, so nothing is rounded by binary floating point. It can be typed as:

  • a decimal, with or without thousands commas (154.37, 2,780,418, -3050);
  • E notation (4.5e-4);
  • a × 10ⁿ (4.5 × 10^-4, 4.5 x 10^-4, 4.5 × 10⁻⁴);
  • a sum of such numbers joined by + (100 + 30 + 8, 1 × 10^2 + 3 × 10^1 + 8), whose terms are added exactly.

An empty box counts as 0. Anything else has no answer: "Type a number such as 154.37, 4.5e-4, 4.5 × 10^-4, or 100 + 50 + 4."

The significant digits are the digits from the first non-zero digit; trailing zeros of a whole number written without a decimal point are not kept (3,050 has the digits 305), and trailing zeros after a decimal point are kept. With Round to significant figures set (1 to 30), the digits are rounded to that many: more than half rounds up, less rounds down, and exactly half rounds to the even digit (2.45 → 2.4); asking for more figures pads with zeros.

The calculator shows:

  • Standard form (a × 10ⁿ): a with one non-zero digit before the point and the rest of the digits after it, then × 10 and n in superscript digits (1.5437 × 10², 4.7 × 10⁻¹³). A negative number starts with − (the minus sign U+2212). Zero is 0 × 10⁰.
  • Standard notation: every digit written out, with thousands commas in the whole part (2,780,418, 0.00045, −3,050), for n from −30 to 30; not shown beyond.
  • Expanded form: each non-zero digit times its place value, largest first, joined by +: a place of 10^p for p ≥ 0 is the digit followed by p zeros, with thousands commas; for p < 0 it is 0. then −p − 1 zeros and the digit. A negative number is written −(…). Zero is 0. Shown for n from −30 to 30.
  • Expanded form with powers of ten: the same terms as digit × 10 with p in superscript digits.
  • E notation: a e n with a plain hyphen (1.5437e2, -3.05e3, 0e0).
  • Exponent n.

Worked examples by hand

154.37. The point moves 2 places left: 1.5437 × 10². Expanded: 100 + 50 + 4 + 0.3 + 0.07, or 1 × 10² + 5 × 10¹ + 4 × 10⁰ + 3 × 10⁻¹ + 7 × 10⁻².

2,780,418. 6 places left: 2.780418 × 10⁶; expanded 2,000,000 + 700,000 + 80,000 + 400 + 10 + 8 (the zero digit is left out).

0.00000000000047. 13 places right: 4.7 × 10⁻¹³; expanded 0.0000000000004 + 0.00000000000007.

154.37 to 3 significant figures. The dropped digits 37 are less than half of 100, so the digits are 154: 1.54 × 10², standard notation 154, expanded 100 + 50 + 4.

100 + 30 + 8. The sum is 138, which is 1.38 × 10².

4.5 × 10⁻⁴. 4 places left: 0.00045; expanded 0.0004 + 0.00005.

−3,050. −3.05 × 10³; expanded −(3,000 + 50).

Other questions people ask

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.