Mastering Rounding: Decimal Places and 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 Decimal Places (DP)

What are Decimal Places?

Decimal places are the digits that appear after the decimal point. Rounding to decimal places means keeping only a specific number of these digits.

Steps for Rounding to Decimal Places

1. Count the decimal places to where you want to round.
2. Look at the next digit (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.
3. Drop all digits after the rounding point.

Example

Round $3.4567$ to 2 decimal places

1. Identify the second decimal place: $3.4567$
2. The checking digit is 6 (5 or more), so round up
3. The rounded number is $3.46$

 

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 $0.0046$