Here's a breakdown:
* Scientific notation: A way to represent numbers as a product of a number between 1 and 10 (the coefficient) and a power of 10.
* Example: 1,234,000 can be written in scientific notation as 1.234 x 10^6.
* Mantissa: The part of the scientific notation that represents the significant digits of the number. In the example above, the mantissa is 1.234.
In simpler terms:
Imagine a number like 123.45. In scientific notation, it becomes 1.2345 x 10^2. The mantissa here is 1.2345. It's the part that tells us the actual value of the number, while the power of 10 (10^2) indicates its scale (how large or small it is).
Importance of the mantissa:
* Precision: The mantissa determines the accuracy of the number. A larger mantissa with more digits means greater precision.
* Range of representation: The mantissa allows us to represent very large or very small numbers within a limited range.
Note: The term "mantissa" is often used in the context of floating-point numbers, which are a way to represent numbers in computers. In this context, the mantissa represents the significant digits of the number, while the exponent (the power of 10) represents its scale.