Rules of Signification of Figures

 Rules of Signification of Figures

The "Rules of Signification of Figures" refer to the principles and guidelines used in mathematical notation and representation of numbers. These rules help ensure that numbers are properly interpreted and manipulated in various mathematical operations. Here are some key rules of signification of figures along with examples

 1. Leading Zero Rule:

   - A decimal number should not start with a leading zero, except when it represents a value between 0 and 1.

   - Example 1: 0.123 (Correct)

   - Example 2: 007.456 (Incorrect)

2. Trailing Zero Rule:

The presence of trailing zeros after the decimal point is significant.

   - Example 1: 5.200 (The zeros after the decimal point are significant)

   - Example 2: 3.0 (The zero after the decimal point is significant)

3. Non-Zero Digit Rule:

   - Every non-zero digit is always significant.

   - Example: 456.78 (All digits are significant)

4. Leading Zero in Whole Numbers Rule:

   - In whole numbers, leading zeros are not significant.

   - Example 1: 0056 (56 is significant)

   - Example 2: 00000123 (123 is significant)

5. Trailing Zero in Whole Numbers Rule:

   - Trailing zeros in whole numbers without a decimal point are not significant.

   - Example 1: 1200 (12 is significant)

   - Example 2: 45000 (45 is significant)

 6. Counted Numbers Rule:

- Counted numbers, such as those representing individual items or people, are considered to have an infinite number of significant figures.

   - Example: There are 7 apples in the basket. (Infinite significant figures)

7. Exact Numbers Rule:

   - Exact numbers, like integers or defined constants, have an infinite number of significant figures.

   - Example 1: There are 100 centimeters in 1 meter. (Infinite significant figures)

   - Example 2: The speed of light in a vacuum is exactly 299,792,458 meters per second. (Infinite significant figures)

8. Operations Rule:

   - When performing mathematical operations, the result should be rounded to match the least number of significant figures in the operands.

   - Example 1: 3.14 * 2.1 = 6.594 (rounded to 6.6 based on the least significant figures)

   - Example 2: 25.0 / 5.00 = 5.000 (rounded to 5.0 based on the least significant figures)

9. Scientific Notation Rule:

   - Scientific notation is used to express numbers in the form of a coefficient multiplied by a power of 10. The coefficient contains all significant figures.

   - Example: 6.02 x 10^23 (The coefficient, 6.02, contains the significant figures)

• Point to be noted:

Remember that these rules are essential for maintaining precision and accuracy in scientific and mathematical calculations. Adhering to these rules ensures that the significance of figures is preserved when performing calculations and expressing numerical values.