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

Scientific Notation - dCode

Tag(s) : Mathematics

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

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

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 $

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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