One of the most powerful ways to represent numbers is through Scientific Notation. This system is especially useful for handling very large or very small numbers, making it ideal for computer science, where precise storage within limited memory is essential.
Let’s break it down using the number 128 as an example:
1. How Do Floating-Point Numbers Work?
Floating-point numbers are typically divided into two main parts:
✅ Mantissa (or significand): This represents the actual number, usually between 1 and 10.
✅ Exponent: This indicates how many times the decimal point needs to be shifted to the left or right.
For example, the number 128 can be written as:
128 = 1.28 × 10²
✔ 1.28 is the mantissa
✔ 10² (i.e., 10 raised to the power of 2) is the exponent
2. How Is This Equal to 128?
We know that:
10² = 100
So,
1.28 × 100 = 128
3. Why Is This Method Important?
🔹 Efficient storage of large numbers
Example: 123,000,000 can be easily written as 1.23 × 10⁸
🔹 Small numbers can also be represented precisely
Example: 0.00000456 becomes 4.56 × 10⁻⁶
🔹 Improves computational accuracy
According to the IEEE 754 floating-point standard, this method is used for representing decimal numbers in computer systems.
Have You Ever Faced Floating-Point Precision Errors or Worked with the IEEE 754 Standard?
Share your experience in the comments below!
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