addition and subtraction of significant figures. rule 1 before performing an addition or subtraction...
TRANSCRIPT
Addition and Subtraction of significant figures
Addition and Subtraction of significant figures
Rule 1Rule 1
• Before performing an addition or subtraction operation, round off numbers to the least amount of decimal points (this is different from multiplication were after performing multiplication or division round off the result to least amount of significant figures)
• Before performing an addition or subtraction operation, round off numbers to the least amount of decimal points (this is different from multiplication were after performing multiplication or division round off the result to least amount of significant figures)
Rule 1Rule 1
• The rounding off before performing an addition or subtraction operation ensures that the result will have no more reliability than the quantity read from the measuring device.
• The rounding off before performing an addition or subtraction operation ensures that the result will have no more reliability than the quantity read from the measuring device.
Rule 2Rule 2
• The final result of the addition and subtraction of significant figures should have the same number of Decimal places as the quantity with the least number of decimal places that was used in the calculations.
• The final result of the addition and subtraction of significant figures should have the same number of Decimal places as the quantity with the least number of decimal places that was used in the calculations.
Example of addition of sig figs
Example of addition of sig figs
• Measurements have been made on three different pieces of string. Each measure was made with three different measurement devices (each with their own number of sig figs). What is the total length of the string we have.
• Measurements have been made on three different pieces of string. Each measure was made with three different measurement devices (each with their own number of sig figs). What is the total length of the string we have.
Example of addition of sig figs
Example of addition of sig figs
• Here are the three lengths of strings • 23.1 m• 0.546 m• 1.45 m
• The total length without considering sig figs is 25.093 m but that’s the wrong answer.
• Here are the three lengths of strings • 23.1 m• 0.546 m• 1.45 m
• The total length without considering sig figs is 25.093 m but that’s the wrong answer.
Example of addition of sig figs
Example of addition of sig figs
• Because I only measured the 23.1 m length to 1/10th of a meter, the length could have been 23.14m or 23.05m or any number in between. Even if I did measured the other pieces of string to 1/100th and 1/1000th meters it does me no good. I need to round to the least number of decimal places.
• Because I only measured the 23.1 m length to 1/10th of a meter, the length could have been 23.14m or 23.05m or any number in between. Even if I did measured the other pieces of string to 1/100th and 1/1000th meters it does me no good. I need to round to the least number of decimal places.
Example of addition of sig figs
Example of addition of sig figs
23.1 stays 23.1 0.546 rounds .5 1.45 rounds 1.5 25.096 25.1
wrong right
23.1 stays 23.1 0.546 rounds .5 1.45 rounds 1.5 25.096 25.1
wrong right