Significant Figures Describing Scientific Measurements Density UNIT 1: DATA ANALYSIS Significant Figures Describing Scientific Measurements Density

Significant Figures

Scientific Notation (LET’s REVIEW QUICKLY) 65,000 kg → 6.5 × 104 kg Converting into Sci. Notation: Move decimal until there’s 1 digit to its left. Places moved = exponent. Large # (>1) ⇒ positive exponent Small # (<1) ⇒ negative exponent Only include sig figs.

Scientific Notation Practice 2.4 × 106 μg 2,400,000 μg 0.00256 kg 7 × 10-5 km 6.2 × 104 mm 2.56 × 10-3 kg 0.00007 km 62,000 mm

What are significant figures? Indicate precision of a measurement. Recording Sig Figs Sig figs in a measurement include the known digits plus a final estimated digit 2.35 cm

Counting Significant Figures: USE ARROW METHOD 1. ZEROS AT THE END AND NO DECIMAL: -Draw an arrow through the zeros from right to left until you hit a nonzero number. Count every number after the arrow as significant 2. ZEROS AT THE BEGINNING : -Draw an arrow through the zeros from left to right until you hit a nonzero number. Count every number after the arrow as significant. 3. ZEROS AT THE END WITH A DECIMAL: -Count EVERY number as significant

Examples: 0.000458 0.23080000 101,000 3,050 300,000,000 102 2.00 X 109 3.02 X 10-23

Practice: Count the number of sig figs in the following: 23.50 4 sig figs 402 3 sig figs 5,280 3 sig figs 0.080 2 sig figs

Math with Significant Figures Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm3)(23.3cm3) = 324.103g 4 SF 3 SF 3 SF 324 g

Math with Significant Figures Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer. 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL 7.85 mL 224 g + 130 g 354 g 224 g + 130 g 354 g → 7.9 mL → 350 g

MATH PRACTICE: Calculate the following and report your answer to the correct number of sig figs 1. 0.2020 + 3.25 4. 38/2 2. 2.0 – 0.03 5. (6.022 X 1023)/(3.25 X 1026). 3. 8 X 2.0 6. (200 X 0.05) + 23.0 (Round the following numbers to 3 SF) 1. 887 3. 5.6879 X 103 2. 2.2350 4.1000

Reading instruments in the lab When you are reading equipment in a lab, you must report your answers to correct sig figs. Report every number you know FOR sure and then take a guess for the last one. Record units. Hint: the less “lines”, the fewer numbers you know for sure.

Uncertainty Measurements should include all certain digits plus the first uncertain digit. Ex. Reading thermometer, buret, balance, etc. (On digital devices, the last digit shown is uncertain) So what is the reading from this graduated cylinder? How many decimals are acceptable here? The reading should be 52.8 ml where the 8 is the estimated digit.

You should be able to use and read these pieces of equipment.

Describe Scientific Measurements

Types of information Qualitative-non-numerical data The sample of copper is shiny Quantitative-numerical data The sample of copper has a mass of 4.7 grams

Qualitative or quantitative? The liquid floats on water Qualitative The liquid has a temperature of 55.6°C Quantitative The metal is malleable

Measurements: Number & unit! Measurements represent quantities such as volume or length. Measurements must include a number and unit!

Accuracy and Precision Which is which??

Accuracy and Precision Accuracy-measurement is close to the “right” or accepted value Precision-a set of measurements are close to each other

DENSITY

M V D = 1 cm3 = 1 mL Derived Units Combination of base units. Volume (mLor cm3) length × length × length 1 cm3 = 1 mL D = M V Density (g/mL or g/cm3) mass per volume

Density Example 1 V = 825 cm3 M = DV D = 13.6 g/cm3 An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass. GIVEN: V = 825 cm3 D = 13.6 g/cm3 M = ? WORK: M = DV M = (13.6 g/cm3)(825cm3) M = 11,200 g

Density Example 2 D = 0.87 g/mL V = M V = ? M = 25 g V = 25 g A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: D = 0.87 g/mL V = ? M = 25 g WORK: V = M D V = 25 g 0.87 g/mL V = 29 mL

Practice: Density 1. A student finds a rock on the way to school.  In the laboratory he determines that the volume of the rock is 22.7 mL, and the mass in 39.943 g.  What is the density of the rock? 2.The density of silver is 10.49 g/cm3.  If a sample of pure silver has a volume of 12.993 cm3, what is the mass?  

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