Significant Figures Precision Accuracy

Accuracy, Precision, and Measurement

​Accuracy vs. Precision

​Accuracy: refers to how close a measurement is to a true, accepted or target value.

​

​

​Precision: Refers to the reproducibility of a series of measurements

​

​OUR GOAL IN SCIENCE IS TO BE BOTH ACCURATE AND PRECISE.

Multiple Choice

Which target represents LOW ACCURACY (not correct) and LOW PRECISION (not close together)

• A

• B

• C

• D

Multiple Choice

Which target represents HIGH ACCURACY (correct) and LOW PRECISION (not close together)

• A

• B

• C

• D

Multiple Choice

Which target represents HIGH ACCURACY (correct) and HIGH PRECISION (close together)

• A

• B

• C

• D

Multiple Choice

Which target represents LOW ACCURACY (not correct) and HIGH PRECISION (close together)

• A

• B

• C

• D

Significant Figures

​What are significant figures?

• tell you how to round

• make measurements more readable

• makes measurements more PRECISE (close together)

​Significant Figures Rules

RULE #1

• ​Non-zero digits are ALWAYS significant

​so, any digit THAT IS NOT ZERO is BY DEFINITION Significant

​Significant Figures Rules

RULE #2

• ​Zeros that are BETWEEN other significant digits are ALWAYS significant.

​For example these zeros ARE significant

​203

​12.005

​503.00602

​Significant Figures Rules

RULE #3

• ​Trailing zeros (also called final zeros) are significant ONLY if there is a decimal point

​For example:

These trailing zeros ARE Significant:

• ​12.0

• ​156.3300

​These trailing zeros ARE NOT Significant

• ​200

• ​780

​Significant Figures Rules

RULE #4

• ​Leading zeros are NEVER significant

​

For example: These leading zeros are NOT significant

​

• ​0.25

• ​0.0007

• ​0.0567

​Significant Figures Rules: RECAP

Multiple Choice

Choose the correct number of significant figures present in the given number:

1.234 g

• 1

• 2

• 3

• 4

Multiple Choice

Choose the correct number of significant figures present in the given number:

3,702 kg

• 1

• 2

• 3

• 4

Multiple Choice

Choose the correct number of significant figures present in the given number:

0.230 s

• 1

• 2

• 3

• 4

Multiple Choice

Choose the correct number of significant figures present in the given number:

0.05 m

• 1

• 2

• 3

• 4

Multiple Choice

Choose the correct number of significant figures present in the given number:

1,200. cm

• 1

• 2

• 3

• 4

Multiple Choice

Choose the correct number of significant figures present in the given number:

8,000 m

• 1

• 2

• 3

• 4

​Measurements using Significant Digits

​When reading measurements, your reading should include ALL KNOWN digits (all you can see) and one estimated digit (your guess).

​

​For example: In the picture to the right, ALL WE CAN SEE is that the pencil is 6 cm.

​

​Now, you must ESTIMATE the last significant digit. Your guess is your guess...it cannot be marked wrong.

​6.7 cm.

​Measurements using Significant Digits

​When reading measurements, your reading should include ALL KNOWN digits (all you can see) and one estimated digit (your guess).

​

​Another example: In the picture to the right, ALL WE CAN SEE is that the paper clip is 2.3 cm.

​

​Now, you must ESTIMATE the last significant digit. Your guess is your guess...it cannot be marked wrong.

​2.35 cm

​Measurements using Significant Digits

​When reading measurements, your reading should include ALL KNOWN digits (all you can see) and one estimated digit (your guess).

​

​Another example: In the picture to the right, ALL WE CAN SEE is that the liquid measures 21 mL.

​

​Now, you must ESTIMATE the last significant digit. Your guess is your guess...it cannot be marked wrong.

​21.6 mL

Multiple Choice

Read the instruments to their limits. Include units and the correct number of significant figures. (don't forget your estimated digit)

• 40 mL

• 41 mL

• 40.0 mL

• 40.00 mL

Multiple Choice

Read the instruments to their limits. Include units and the correct number of significant figures. (don't forget your estimated digit)

• 24 mL

• 24.0 mL

• 25 mL

• 25.0 mL

Multiple Choice

Read the instruments to their limits. Include units and the correct number of significant figures. (don't forget your estimated digit)

• 21 mL

• 21.5 mL

• 22 mL

• 22.5 mL

​Adding and Subtracting with Significant digits

​Adding and Subtracting with Significant digits

​another example:

​3.12 g + 0.8 g + 1.033 g = 4.953 g = 5.0 g

​DON'T FORGET TO ROUND IF NESSESSARY!!!

​2 sig figs in the decimal

​portion.

​3 sig figs in the decimal

​portion.

​1 sig fig in the decimal

​portion.

​1 sig fig in the decimal

​portion.

​Adding and Subtracting with Significant digits

​another example:

​345.009 g - 23.009 g = 322 g = 322.000 g

​

​3 sig figs in the decimal portion

​3 sig figs in the decimal portion

​3 sig figs in the decimal portion

Multiple Choice

Subtract: 7.987 m - 0.54 m

• 7.447 m

• 7.4 m

• 7.5 m

• 7.45 m

​Multiplying and Dividing with Significant Digits

​Multiplying and Dividing with Significant Digits

​DON'T FORGET TO ROUND IF NESSESSARY!!!

​3 sig figs in the whole number

​2 sig figs in the whole number

​2 sig figs in the whole number

Multiple Choice

Solve: 0.020 cm x 50 cm x 10.0 cm = ?

• 10. cm^3

• 10 cm^3

• 10.00 cm^3

• 10.000 cm^3