Significant figures

Significant figures are the digits in a number that are reliable and necessary to indicate the precision of the number.

Rules for Determining Significant Figures:

Non-Zero Digits: All non-zero digits are significant.

• Example: 123 has three significant figures.

Leading Zeros: Zeros that precede all non-zero digits are not significant.

• Example: 0.0025 has two significant figures.

Captive Zeros: Zeros between non-zero digits are significant.

• Example: 1002 has four significant figures.

Trailing Zeros: Zeros at the end of a number and to the right of a decimal point are significant.

• Example: 45.00 has four significant figures.

Trailing Zeros Without a Decimal Point: Zeros at the end of a number without a decimal point are not significant.

• Example: 1500 has two significant figures (unless specified otherwise with scientific notation).

Rules for Calculations with Significant Figures:

Addition and Subtraction:

• The result should be rounded to the least number of decimal places in any of the numbers being added or subtracted.

• Example: 12.11 + 0.34 = 12.45 (two decimal places).

Multiplication and Division:

• The result should have the same number of significant figures as the number with the least significant figures in the calculation.

• Example: 4.56 × 1.4 = 6.4 (two significant figures).