Understanding Significant Figures

Significant figures, also known as significant digits, are the digits in a number that carry meaningful precision. They include all digits from the first non-zero digit to the last digit (which is estimated or presumed to be the last digit known).

Rules for Significant Figures

Here are the basic rules to determine the number of significant figures:

• Non-zero digits are always significant.
• Zeros between non-zero digits are always significant (e.g., 507 has 3 significant figures).
• Leading zeros (zeros to the left of the first non-zero digit) are never significant. They are placeholders (e.g., 0.0052 has 2 significant figures: 5 and 2).
• Trailing zeros (zeros at the end of a number) are significant only if the number contains a decimal point.
  • Example 1: 12.00 has 4 significant figures (1, 2, 0, 0).
  • Example 2: 1200 has 2 significant figures (1, 2). The trailing zeros are placeholders.
  • Example 3: 1200. has 4 significant figures (1, 2, 0, 0). The decimal point makes the trailing zeros significant.

Applying Rules to 2.308 cm

Let's analyze the number 2.308 based on these rules:

1. 2: This is a non-zero digit, so it is significant.
2. .: The decimal point is present.
3. 3: This is a non-zero digit, so it is significant.
4. 0: This zero is between non-zero digits (2 and 8), making it significant.
5. 8: This is a non-zero digit, so it is significant.

The number 2.308 contains the digits 2, 3, 0, and 8. All of these are significant digits according to the rules.

Counting Significant Figures in 2.308 cm

By applying the rules:

• The first digit '2' is non-zero and significant.
• The digit '3' is non-zero and significant.
• The digit '0' is a captive zero (between two non-zero digits) and is significant.
• The digit '8' is non-zero and significant.

Therefore, there are 4 significant figures in the measurement 2.308 cm.