Final answer:
When performing addition or subtraction with measured quantities, round the result to the same number of decimal places as the least precise quantity. For multiplication or division, round the result to the same number of significant figures as the least precise quantity.
Step-by-step explanation:
a) Addition and Subtraction:
When performing addition or subtraction with measured quantities, the result is rounded to the same number of decimal places as the quantity with the fewest decimal places.
Example: If we add 5.623 g and 3.8 g, the result would be 9.4 g, since 5.623 g has 3 decimal places and 3.8 g has 1 decimal place.
b) Multiplication and Division:
For multiplication or division, the result is rounded to the same number of significant figures as the quantity with the fewest significant figures.
Example: If we multiply 2.51 cm by 6.47 cm, the result would be 16 cm², since 2.51 cm has 3 significant figures and 6.47 cm has 3 significant figures.
c) Rules and Considerations:
When determining the significant figures in calculations, we follow these rules:
- For addition and subtraction, consider the decimal places.
- For multiplication and division, consider the significant figures.
- Always round the final result to the appropriate number of decimal places or significant figures.
- Remember that measured quantities can only be as precise as the least precise measurement involved.