Significant Figures A Reflection of Accuracy Accuracy and

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Significant Figures A Reflection of Accuracy

Significant Figures A Reflection of Accuracy

Accuracy and precision l Measurements in science should be made with accuracy and precision

Accuracy and precision l Measurements in science should be made with accuracy and precision l Accuracy – being close to the actual value l Precision – measurements should be consistent

A graphic example

A graphic example

How to take measurements l When measuring you can estimate the last digit l

How to take measurements l When measuring you can estimate the last digit l So when using a meter stick ¡The smallest mark is a millimeter ¡You can estimate to the tenth of a millimeter l Your measurement should be 14. 45 cm

Another example l When reading a graduated cylinder you read from the bottom of

Another example l When reading a graduated cylinder you read from the bottom of the meniscus l What is the accurate and precise reading for this volume?

Significant Figures l They reflect the accuracy of the measurements l Includes all digits

Significant Figures l They reflect the accuracy of the measurements l Includes all digits that are known to be precise plus one last digit that is estimated.

Rules for Determining Significant Figures (Know all of these) l All non-zero digits are

Rules for Determining Significant Figures (Know all of these) l All non-zero digits are significant l Zeros to the left of non-zero digits are never significant l Zeros between non-zero digits are significant l Zeros to the right of non-zero digits are significant only if decimal point is shown

How Many Significant Figures l 234. 0 l 23400. 0 l 2304 l. 00234

How Many Significant Figures l 234. 0 l 23400. 0 l 2304 l. 00234 l 2. 345 l. 00405 l 3 l 4 l 3 l 6 l 4 l 3 l 4 l 1 l 3

Special Cases l There are two instances where measurements have unlimited significant figures ¡Exactly

Special Cases l There are two instances where measurements have unlimited significant figures ¡Exactly defined quanties l 60 minutes = 1 hour • Conversion factors l. Counting exact number • Example if you are counting 20 people in a room, then that number has unlimited significant figures.

Why is this of any importance l Your answer in when doing calculations can

Why is this of any importance l Your answer in when doing calculations can only be as accurate as your least accurate measurement l For example ¡ If you measure a stick as 7. 9 cm. How many how many inches is that ? 1 inch = 2. 54 cm l 7. 9 cm x 1 inch/2. 54 cm = 3. 11023622 l This answer implies accuracy beyond normal laboratory equipment l Round to the least significant figures. ¡ 7. 9 has 2 sig figs so the answer is 3. 1 inches