Warm up: Mass of Object 24.46 g Volume of Water 12.5 mL Objective: Perform Calculations to the correct number of digits. The density of an object was found by using water displacement. The following data was collected (this is in packet). Determine the volume of the object. Calculate the density of the object. Mass of Object 24.46 g Volume of Water 12.5 mL Volume of Water and Object 16.3 mL

RULES FOR DETERMINING SIGNIFICANT FIGURES Rule #1: Nonzero digits always count as significant figures:  Examples: 438 g _____ sig fig 26.42 m _____ sig fig 1.7 cm _____ sig fig 2.653 L _____ sig fig

Examples: 0.8 g _____ sig fig Rule #2: Captive zeros always count as significant figures: Examples: 506 dm _____ sig fig 1005 mL _____ sig fig 900.43 kg _____ sig fig 20.006 cm _____ sig fig Rule #3: Leading zeros do not count as significant figures: 0.8 g _____ sig fig 0.06 g _____ sig fig 0.0047 L _____ sig fig

Rule #4: Trailing zeros are significant only if the number contains a decimal point: Examples: 60 g _____ sig fig 4830 km _____ sig fig 8.0 dm _____ sig fig 1.60 sec _____ sig fig 35.000 L _____ sig fig 0.002450 kg _____ sig fig

RULES FOR ROUNDING NUMBERS If the digit immediately to the right of the last significant figure you want to retain is: Less than 5 ------ the last significant digit should stay the same. Example: Round 17.32 m to 3 significant figures. Since the 2 is less than 5, you should round to __________ m

Round 42.68 g to 3 significant figures. 5 or greater --------- the last significant figure should increase by 1. Example: Round 42.68 g to 3 significant figures. Since 8 is greater than 5, you should round to __________ g

What Do You Think? Determine the number of significant figures in each of the following: a. 12.045 d. 12.0 b. 0.0028 e. 0.500 c. 6500 f. 16.002070 Round each of the following to 2 significant figures. 5.2836 b. 0.06382 c. 3196 Explain how the measurement 6.2 cm is different from 6.20 cm.

CALCULATIONS WITH MEASUREMENTS Rule #1: Whenever you add or subtract measurements, your answer should have as many DECIMAL PLACES as the measurement with the LEAST number of DECIMAL PLACES. EXAMPLE: 23.445 g + 7.83 g = 31.275 g 31.28 g

Rule#2: Whenever you multiply or divide measurements, your answer should have as many SIGNIFICANT FIGURES as the measurement with the LEAST number of SIGNIFICANT FIGURES. EXAMPLE: 1.342 cm × 5.5 cm = 7.381 cm2 7.4 cm2

Its Your Turn! Perform the following calculations and record your answer to the correct number of digits. a. 14.025 – 6.49 = b. 142.38 x 3.050 = c. 59.968 / 0.07628 =

Scientific Notation Short hand for writing very large or small numbers Two parts: Coefficient and Power of 10 A number between 1 and 10 (can include 1 but not 10). Exponent: + exponent  - exponent

Practice Write the following numbers in scientific notation: 41,000 0.0029 60,007,000 0.000 000 132 123,000,000

One Minute Paper You have one minute to answer these two questions concerning significant figures and calculations with measurements. What was the most important thing you learned? What is still muddy? 13