Scientific Notation Converter (b×10ⁿ, E Notation, Engineering Notation)

Enter the number you want to convert. It is shown in scientific, E, engineering and decimal notation at once, with steps showing how many places the decimal point moved.

Number to convert

Besides ordinary numbers (3672.2), you can enter E notation (2.3e11) or ×10^ notation (3.5×10^-12 or 3.5x10^-12). Commas (1,568,938) are OK too. Exponents from −99 to 99 and up to 30 digits are supported.

Result

Enter a number in the field on the left and press "Calculate". The number will appear here in four forms, scientific, E, engineering and decimal notation.

[ CLOSE ]

What you can do on this page
What is this calculation used for?
How to Use
Formula
Symbols and terms
- Symbols
- Terms
Good to know before you start
How to calculate it in Excel
How to calculate it in Google Sheets
How to calculate it in Python
How to write it in LaTeX and other math languages (copy and paste)
How to have ChatGPT do the calculation
DataChef Features
Related Features
NumberChef Calculators List

What you can do on this page

Enter an ordinary number such as "3672.2" and see it in four forms at once: scientific notation (\(3.6722 \times 10^3\)), E notation (3.6722e3), engineering notation and decimal notation
You can also enter a number in exponent form, such as "2.3e11" or "\(3.5 \times 10^{-12}\)", and turn it back into an ordinary number (decimal notation)
The steps show which way and how many places the decimal point moved, so you learn how to convert by yourself
Useful for writing numbers in science and chemistry lab reports, and for reading a "2.3E+11" on a calculator or in Excel
A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page

This page handles numbers whose exponent (the power of 10) is from −99 to 99, with up to 30 digits (significant figures). 0 is shown simply as "0" (it cannot be written with a coefficient whose absolute value is at least 1 and less than 10).

What is this calculation used for?

Numbers in science and physics (the speed of light, 3×10⁸ m/s)

The speed of light is about 300000000 m per second. Just counting the zeros is hard. Science and physics textbooks write it as \(3 \times 10^8\) m/s. Comparing it with the distance around the Earth (about \(4 \times 10^7\) m), the exponents alone tell you it is about 10 times larger.
In lab reports and science records with large numbers, scientific notation is the standard rule.

Mole calculations in chemistry (Avogadro's number, 6.02×10²³)

The number of particles in 1 mole of a substance (Avogadro's number) is about \(6.02 \times 10^{23}\). Written out, it is 602000000000000000000000, a 24-digit number that invites mistakes.
Mole calculations in high school chemistry are a chain of multiplying and dividing by this number, so reading and writing scientific notation leads directly to better chemistry grades.

Reading "2.3E+11" on a calculator or in Excel

Calculators and Excel automatically show numbers with many digits as something like 2.3E+11. This is not an error but E notation for \(2.3 \times 10^{11} = 230000000000\) (230 billion).
If you can read it calmly instead of worrying about "strange letters in the cell", you can use spreadsheets with confidence, from household budgets to work reports.

Floating-point numbers in programming

In programming, number literals in E notation such as 1e9 (1 billion) and 1.5e-8 are used every day, and results are shown in forms like 3.5e-12.
If you know how E notation matches scientific notation, you can quickly check whether a large result makes sense (check its order of magnitude).

Units for the tiny world (virus sizes and nanometers)

A flu virus is about 0.0000001 m across. In scientific notation that is \(1 \times 10^{-7}\) m, and rewriting it the engineering notation way as \(100 \times 10^{-9}\) m, you can read it as "100 nm (nanometers)".
Engineering notation, with exponents that are multiples of 3, connects directly to SI prefixes such as nano, micro and milli. It helps you understand sizes in semiconductors and biology with numbers.

Formula

Scientific notation (normalized, \(1 \le |b| < 10\))

Standard notation (the usual math form)

\(N\) \(=\) \(b\) \(\times\) \(10\) \(n\)

In words (symbols replaced with words)

④ \(N\): original number \(=\) ① \(b\): coefficient (\(1 \le |b| < 10\)) \(\times\) ② \(10\): base ③ \(n\): exponent

The formula in words

① Multiply the \(b\): coefficient (the digits, adjusted so the absolute value is at least 1 and less than 10)

② by the \(10\): base

③ raised to the \(n\): exponent (that is, \(10^n\))

④ and you get back the \(N\): original number

Quick example

3672.2 in scientific notation is

original number (3672.2) \(=\) coefficient (3.6722) \(\times\) base 10 exponent (3)

\(3.6722 \times 10^{3} = 3.6722 \times 1000 = 3672.2\)

Key idea

The rule that the coefficient's absolute value must be at least 1 and less than 10 is called normalization. For a negative number, keep the minus sign on the coefficient and use its absolute value (for example, \(-5000000000 = -5 \times 10^9\): the coefficient is \(-5\), and its absolute value 5 is at least 1 and less than 10). \(36.722 \times 10^2\) has the same value, but the normalized form is unique, so you can compare the size of numbers (the order of magnitude) just by looking at the exponent \(n\). The biggest advantage of scientific notation is that you never miscount the zeros, even for very large or very small numbers.

How moving the decimal point sets the exponent

Standard notation (the usual math form)

\(n\) \(=\) \(+k\)

\(n\) \(=\) \(-k\)

In words (symbols replaced with words)

② \(n\): exponent \(=\) ① \(k\): places moved left

④ \(n\): exponent \(=\) ③ \(-k\): minus the places moved right

The formula in words

① For a large number (absolute value 10 or more), move the decimal point left until the coefficient's absolute value is at least 1 and less than 10, and use the \(k\): places moved left

② as the \(n\): exponent

③ For a small number (absolute value less than 1), move the decimal point right, and put a minus sign on the \(k\): places moved right

④ to get the \(n\): exponent

Quick example

0.0004212 in scientific notation (move the decimal point 4 places right to make the coefficient 4.212) is

exponent (−4) \(=\) minus the places moved right (4)

\(0.0004212 = 4.212 \times 10^{-4}\)

\(3672.2 = 3.6722 \times 10^{3}\)

Key idea

To remember the direction: "big number, move left, positive exponent" and "small number, move right, negative exponent". Moving the decimal point left divides by 10, and moving it right multiplies by 10, so \(10^n\) makes up for that. Thinking of it this way, you will not get the sign wrong. Also note that a number with a negative exponent (such as \(10^{-4}\)) is a small number less than 1, not a negative number.

E notation and engineering notation

Standard notation (the usual math form)

\(b\) \(\times\) \(10\) \(n\) \(=\) \(b\,\mathrm{e}\,n\)

In words (symbols replaced with words)

① \(b\): coefficient \(\times\) \(10\): base ② \(n\): exponent \(=\) ③ E notation (coefficient e exponent)

The formula in words

① Join the \(b\): coefficient

② and the \(n\): exponent with the letter e and write them on one line, as in

③ E notation (coefficient e exponent) (a capital E has the same meaning)

Quick example

3.5 × 10⁻¹² in E notation and 1.234 × 10⁸ in engineering notation are

coefficient (3.5) \(\times\) base 10 exponent (−12) \(=\) 3.5e-12

\(3.5 \times 10^{-12} = 3.5\mathrm{e}{-12}\)

\(1.234 \times 10^{8} = 123.4 \times 10^{6}\)

Key idea

The e in E notation is a separator that stands for "× 10 to the power". It is the standard way to write numbers on calculators, in Excel and in programming, where superscripts are not available (it has nothing to do with the base of the natural logarithm, \(e \approx 2.718\)). Engineering notation allows only exponents that are multiples of 3 (…, \(10^{-6}\), \(10^{-3}\), \(10^{0}\), \(10^{3}\), \(10^{6}\), …). The coefficient's absolute value is then at least 1 and less than 1000, so \(1.234 \times 10^8\) becomes \(123.4 \times 10^6\). The exponent matches a unit prefix such as k (kilo \(=10^3\)) or M (mega \(=10^6\)), so "\(123.4 \times 10^6\) Hz = 123.4 MHz".

Scientific notation writes a number as "a coefficient whose absolute value is at least 1 and less than 10 × a power of 10". If the decimal point moves \(k\) places left, the exponent is \(+k\); if it moves \(k\) places right, the exponent is \(-k\). E notation writes "× 10 to the power" with the letter e, and engineering notation uses only exponents that are multiples of 3.

Symbols and terms

Symbols

\(N\)	N (capital)	The original number. On this page, a number written the ordinary way (decimal notation), such as 3672.2.
\(b\)	b	The coefficient (also called the significand). The digits, adjusted so the absolute value is at least 1 and less than 10 (for example, 3.6722 for 3672.2, and −5 for −5000000000). It carries the actual digits of the number.
\(n\)	n	The exponent. The number of times 10 is multiplied, which carries the size of the number (the order of magnitude). If it is positive, the absolute value is 10 or more; if negative, the absolute value is less than 1.
\(10^n\)	10 to the nth power	10 multiplied \(n\) times (for example, \(10^3 = 1000\)). When \(n\) is negative, it stands for dividing by 10 (for example, \(10^{-4} = \dfrac{1}{10000} = 0.0001\)).
\(k\)	k	The number of places the decimal point moved. Moving left gives \(n = +k\), and moving right gives \(n = -k\).
\(\mathrm{e}\) (the e in E notation)	e	A separator that stands for "× 10 to the power" (for example, 3.5e-12 is \(3.5 \times 10^{-12}\)). A capital E is the same. It has nothing to do with \(e \approx 2.718\), the base of the natural logarithm.

Terms

scientific notation	A way to write a number as "a coefficient whose absolute value is at least 1 and less than 10 × a power of 10". Very large and very small numbers can be written briefly without miscounting zeros. In the UK it is also called standard form.
coefficient (significand, mantissa)	The \(b\) in \(b \times 10^n\). This page calls it the coefficient. Depending on the field, it is also called the significand or the mantissa.
exponent	The small number at the upper right of a number. It tells how many times to multiply by the same number. On this page, it tells how many times to multiply by 10 (or, if negative, how many times to divide by 10).
order of magnitude	The rough size of a number as "about 10 to what power". The exponent \(n\) in scientific notation is the order of magnitude. "Orders of magnitude larger" is used when numbers differ by one or more powers of 10.
E notation	A way of writing the \(\times 10^n\) part with the letter e (or E), for example 7e2 for \(7 \times 10^2\). It is used on calculators, in Excel and in programming, where superscripts are not available.
engineering notation	A relative of scientific notation that uses only exponents that are multiples of 3. The coefficient's absolute value is at least 1 and less than 1000. Its advantage is that it matches units that step by 1000 (SI prefixes).
SI prefix	Symbols put in front of a unit to show sizes that step by 1000, such as k (kilo \(=10^3\)), M (mega \(=10^6\)), G (giga \(=10^9\)), m (milli \(=10^{-3}\)), μ (micro \(=10^{-6}\)) and n (nano \(=10^{-9}\)). They match the exponents of engineering notation.

Good to know before you start

Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.

Multiplying by 10 or 100 and moving the decimal point (Grade 5)	Knowing that multiplying a number by 10 moves the decimal point 1 place right, and dividing by 10 moves it 1 place left Knowing that the number of times you multiply by 10 matches the number of zeros, as in 1000 = 10×10×10
Powers and exponents (Grade 6)	Knowing that "to the \(n\)th power" stands for multiplying the same number \(n\) times, as in \(10^3 = 10 \times 10 \times 10\) Knowing that any nonzero number to the power 0 is defined as 1 (\(10^0 = 1\))
Negative exponents (Grade 8)	Knowing that \(10^{-n}\) stands for "divide by \(10^n\)" (\(\dfrac{1}{10^n}\)) (you can learn this on this page)
Rounding and significant figures (high school chemistry and physics)	Knowing that measurements are often rounded to "about how much" Knowing that numbers can be read in terms of which digits can be trusted (significant figures)

How to calculate it in Excel

Copy the whole table below and paste it into cell A1 in Excel. It works as is.

Table to convert a decimal to scientific notation (E notation)

Number to convert	3672.2
E notation (TEXT function)	=TEXT(B1,"0.0000E+00")

Table to convert a coefficient and exponent to a decimal

Coefficient b	3.5
Exponent n	-12
Decimal value	=B1*10^B2

In the first table, enter a number in B1 and B2 shows it as E notation text (3.6722E+03 for 3672.2). Change the number of 0s after the decimal point in the format "0.0000E+00" to set how many decimal places the coefficient has.
Instead of a function, you can also change the cell format to Scientific (Home → Number Format → Scientific). If you want to stop Excel from showing a number as something like 2.3E+11, change the format to Number.
The second table turns a coefficient and exponent back into a decimal. B3 shows 3.5E-12, but its value is 0.0000000000035 (set the format to Number with 13 decimal places to see it as is).

How to calculate it in Google Sheets

Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.

Table to convert a decimal to scientific notation (E notation)

Number to convert	3672.2
E notation (TEXT function)	=TEXT(B1,"0.0000E+00")

Table to convert a coefficient and exponent to a decimal

Coefficient b	3.5
Exponent n	-12
Decimal value	=B1*10^B2

The same TEXT formula as in Excel works as is. Copy the whole table, paste it into cell A1, and replace B1 (B1 and B2 in the second table) with your own numbers.
You can switch the display with Format → Number → Scientific.

How to calculate it in Python

x = 3672.2                # number to convert
print(f"{x:e}")           # E notation (3.672200e+03)
print(f"{x:.4e}")         # E notation with 4 decimal places (3.6722e+03)

y = float("2.3e11")       # a string in E notation can be read as a number directly
print(f"{y:.0f}")         # back to decimal notation (230000000000)

Runs with the standard library only. The format "e" in an f-string gives E notation, and ".4e" sets the number of decimal places in the coefficient. float() turns an E notation string straight into a number, so you can also use it to check "what number is 2.3e11?". Change the number at the top and run it.

How to write it in LaTeX and other math languages (copy and paste)

Scientific notation (normalized, \(1 \le |b| < 10\))

N = b × 10ⁿ (1 ≤ |b| < 10)

N = b \times 10^{n} \quad (1 \le |b| < 10)

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>N</mi>
    <mo>=</mo>
    <mi>b</mi>
    <mo>&#xD7;</mo>
    <msup><mn>10</mn><mi>n</mi></msup>
  </mrow>
</math>

N = b * 10^n, \ 1 <= |b| < 10

ScientificForm[3672.2]

evalf(3.6722 * 10^3);

N = b * 10^n;

N = b × 10^n (1 ≤ |b| < 10)

How moving the decimal point sets the exponent

n = +k (|N| ≥ 10), n = −k (|N| < 1)

n = +k \ (|N| \ge 10), \quad n = -k \ (|N| < 1)

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>n</mi><mo>=</mo><mo>+</mo><mi>k</mi>
    <mo>,</mo>
    <mi>n</mi><mo>=</mo><mo>&#x2212;</mo><mi>k</mi>
  </mrow>
</math>

n = +k (|N| >= 10), n = -k (|N| < 1)

Floor[Log10[Abs[3672.2]]]

n := floor(log10(abs(x)));

n = floor(log10(abs(x)));

n = +k (|N| ≥ 10), n = −k (|N| < 1)

E notation and engineering notation

b × 10ⁿ = bEn

b \times 10^{n} = b\mathrm{E}n

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>b</mi>
    <mo>&#xD7;</mo>
    <msup><mn>10</mn><mi>n</mi></msup>
    <mo>=</mo>
    <mi>b</mi><mi>E</mi><mi>n</mi>
  </mrow>
</math>

b * 10^n = b E n

ScientificForm[0.0000000000035]

evalf(3.5e-12);

sprintf('%e', 3.5e-12)

b × 10^n = bEn

How to have ChatGPT do the calculation

You are a calculation assistant for converting number notation. Do the following by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing).

Convert each of the following three numbers into (a) scientific notation (a coefficient with absolute value at least 1 and less than 10 × a power of 10), (b) E notation, and (c) engineering notation (exponent a multiple of 3).
1. 3672.2
2. 0.0004212
3. 299792458 (the speed of light in m/s)

Also show which way and how many places the decimal point moved for each.
Show the code you used and the numbers from the execution result.

How to Use

1

Enter your numbers

Type the numbers you want to calculate with into the input fields
2

Calculate

Press the "Calculate" button
3

Check the result

The result appears on the spot. The same page also explains the idea behind the calculation and the formula