Rounding: Significant Figures

Understanding Rounding

Rounding is all about making numbers simpler to work with while keeping them close to their original value. When rounding, we decide how many decimal places or significant figures we want and follow specific rules to keep our numbers accurate.

Rounding to Significant Figures (SF)

What are Significant Figures?

Significant figures (SF) are the digits that carry meaning in a number, starting from the first non-zero digit. Rounding to significant figures helps when we want an approximate value with the most meaningful digits.

Steps for Rounding to Significant Figures

1. Find the first non-zero digit—this is your starting point.
2. Count the number of significant figures you want to keep.
3. Use the checking digit to decide if you need to round up or stay the same:
   • If the checking digit is 5 or more, round up.
   • If the checking digit is 4 or less, keep the previous digit the same.
4. Replace any extra digits with zeros if they appear to the left of the decimal point.

Examples

1. Round $4567$ to 2 significant figures

   • First significant figure: $4$
   • Second significant figure: $5$, with the next checking digit $6$ (5 or more), so round up
   • The answer is $4600$
2. Round $0.004567$ to 2 significant figures.
   • First significant figure: $4$
   • Second significant figure: $5$, with the next checking digit $6$ (5 or more), so round up
   • The answer is $0.0046$