what is a significant digit

A significant digit (also called a significant figure) is a digit that carries meaning in a number. It provides information about the precision or accuracy of the measurement or calculation.

To determine the significant digits in a number, follow these rules:

1) Non-zero digits are always significant. For example, in the number 345, all three digits (3, 4, and 5) are significant.

2) Any zeros between non-zero digits are also significant. For example, in the number 505, all three digits (5, 0, and 5) are significant.

3) Leading zeros (zeros to the left of the first non-zero digit) are not significant. They indicate the position of the decimal point but do not contribute to the precision of the value. For example, in the number 0.03, only one digit (3) is significant.

4) Trailing zeros (zeros to the right of the last non-zero digit) are significant if they are after the decimal point. For example, in the number 5.00, all three digits (5, 0, and 0) are significant. However, in the number 500, only one digit (5) is significant.

5) Trailing zeros without a decimal point are ambiguous and can be made significant by using scientific notation or stating that they are significant. For example, the number 5000 written as 5.0 x 10^3 indicates that all three digits are significant.

Understanding significant digits is important because they help convey the precision and accuracy of measurements or calculations. They are especially significant when performing mathematical operations, including addition, subtraction, multiplication, and division with numbers that have different amounts of significant digits.