Defining Significant Figures
Significant figures, often called 'sig figs,' are the digits in a number that carry meaningful contributions to its measurement resolution. They include all non-zero digits, trailing zeros only when a decimal point is present, and zeros between non-zero digits. They represent the degree of precision of a measurement, indicating how reliably a value is known.
Rules for Identifying Significant Figures
To identify significant figures, follow these rules: 1) Non-zero digits are always significant. 2) Zeros between non-zero digits (sandwich zeros) are significant. 3) Leading zeros (before non-zero digits) are never significant. 4) Trailing zeros (at the end of the number) are significant *only if* the number contains a decimal point. Scientific notation clarifies ambiguity, as all digits presented are significant.
A Practical Example of Counting
Consider the number 0.00250 grams. The leading zeros (0.00) are not significant. The '2' and '5' are non-zero and thus significant. The final '0' is a trailing zero after a decimal point, making it significant. Therefore, 0.00250 grams has three significant figures. If the number were 250 grams without a decimal, it would only have two significant figures (2 and 5), but if written as 250. grams, it would have three.
Importance in Scientific Measurement
Significant figures are crucial in science because they prevent misrepresenting the precision of data. When performing calculations with measurements, the result cannot be more precise than the least precise measurement used. Applying significant figure rules ensures that calculated values accurately reflect the uncertainty and reliability inherent in the original measurements, maintaining integrity in scientific reporting.