Decoding Significant Figures

Significant figures, in essence, are the valuable digits that contribute to the precision of a measurement. For instance, the number 24.7 contains three significant digits. It's important to note that any non-zero digit is always significant. So, the number 3.14159 has 6 significant digits, with each number providing valuable measurement information.

Implementing Significant Figures

To better understand this concept, let's establish some rules for Significant Figures:

• All non-zero digits are significant: For instance, 3.456g has four significant figures.
• Zeroes between non-zero digits are significant: 2004 kg has 4 figures.
• Leading zeros to the left of the first non-zero digits are not significant;
• Trailing zeroes that are also to the right of a decimal point in a number are significant: For example, 0.0230 mL has three significant figures.
• When a number ends in zeroes that are not to the right of a decimal point, the zeroes are not necessarily significant: 180 kilometers could have 2 or 3 significant figures.

To avoid confusion from the last rule, we can use the standard exponential representation of numbers. For instance,

4.56 × 10 ³ calories (3 significant figures)

4.056 × 10 ³ calories (4 significant figures)

Defining Exact Number