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Scientific Notation

Tool to write numbers in scientific notation/form and conversely to write numbers in scientific notation with all their digits.

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Scientific Notation -

Tag(s) : Mathematics

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# Scientific Notation

## Decimal writing from scientific notation

$$a \times 10^b \qquad \underbrace{1.234}_{a} \cdot 10{\underbrace{^5}_{b}} \qquad \underbrace{3.456}_{a} e \underbrace{7}_{b}$$

### How to write a number in scientific notation?

Any number written in decimal can be written in the form $a \times 10^n$ (a number multiplied by a power of 10), called scientific notation.

By default, the value $a$ is a relative integer (integer or decimal) such as $1 \leq a < 10$

$a$ is called the mantissa and $n$ is called the exponent.

This notation has the advantage of getting rid of the integer part and the decimal part of numbers and standardizes their format in order to be able to easily compare them, especially in terms of order of magnitude, indeed scientific notation displays directly in the exponent the number of digits before or after the decimal point, which is useful for very large or very small numbers.

Example: $$123 = 1.23 \times 10^2 \\ -456000 = -4.56 \times 10^5 \\ 0.000789 = 7.89 \times 10^{-4}$$

### How to write a number in decimal notation?

From a number in scientific form writing, decimal writing consists of shifting the comma according to the value of the exponent: a negative exponent shifts the decimal to the left, a positive exponent to the right.

Example: Rewriting the number $N = 1.234 \times 10^2$ in decimal form is to take $1.234$ and shift the comma by $2$ to the right, so $N = 123.4$

Example: Rewriting the number $N = 1.234 \times 10^{-1}$ in decimal form is to take $1.234$ and shift the comma by $1$ to the left, so $N = 0.1234$

### What is the calculator scientific notation?

On calculators, the exponent symbol is sometimes noted e or E.

Example: 1.23e+4 is read $1.23 \times 10^4$

Example: 5.678E09 is read $5.678 \times 10^9$

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Scientific Notation on dCode.fr [online website], retrieved on 2023-09-27, https://www.dcode.fr/scientific-notation

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