Do you know how to take a measurement

Do you know how to take a measurement?

Do you know how to work with the measurements you take?

Chapter 2 Significant Digits

Taking Measurements • All measurements involve one estimation. • If the measuring device is digital it will take the estimation for you.

Electronic Measuring Devices • Digital readout measuring diameter of 1. 0420 inches. • The last zero is the estimated digit.

Taking Measurements • All measurements involve one estimation. • If the measuring device is scaled you must take the estimation yourself.

Scaled Measuring Devices

Scaled Measuring Devices • Bottom ruler gives a measurement of 8. ? cm.

Scaled Measuring Devices • Measure the length of the metal using the top ruler.

How to read a meniscus. .

How to read a meniscus. ml

Read the Volume in m. L

Significant Digits

Rules for Significant Digits • • All non-zero digits are significant. “Trailing” zeros after the decimal point ARE significant. Zeros between significant digits are significant. All other zeros are NOT significant unless indicated to be so by having a bar placed over them.

How to Determine Significant Digits • Underline the leftmost nonzero digit. • Use the rules for significant digits to determine the rightmost significant digit. • Every digit in between the leftmost and rightmost significant digits are significant as well.

Counting or Exact Numbers Counting numbers: If there are 10 people in a room there are not 9. 5 or 10. 76 people in the room. Counting numbers are exact. Ones in Conversion Factors: 1 kilometer = 1000 meters. Exactly 1 km is equal to exactly 1000 m. The 1 is considered to be an exact number and so is the 1000. • Since Counting numbers and metric conversions are exact they have an infinite number of significant digits.

Determine the Significant Digits (Examples in Notebook) • • • • 70. 12 L 0. 000800 mg 82. 003 µm 27. 0 km 50 people 1. 002 cm 200 kg • -270. 8 ºC • 1000 m. L • 42, 729. 00 cm • 225 beans • 99. 294 dm • 0. 06900 m • 3, 200, 000 µL

Determine the Significant Digits (Examples in Notebook) • • • 70. 12 L 4 0. 000800 mg 3 82. 003 µm 5 27. 0 km 3 50 people infinite • 1. 002 cm 4 • 200 kg 2 • -270. 8 ºC 4 • 1000 m. L 1 • 42, 729. 00 cm 7 • 225 beans infinite • 99. 294 dm 5 • 0. 06900 m 4 • 3, 200, 000 µL 5

Are Significant Figures Important? • A student was given an assignment and a budget of $50 to complete it. Get a cube of metal which has a mass of 83 grams. He knew the density of the metal was 8. 67 g/m. L, and used this to calculate the cube's volume.

Are Significant Figures Important? • Believing significant figures were invented just to make life difficult for chemistry students and had no practical use in the real world, he calculated the volume of the cube to be about 9. 573 m. L.

Are Significant Figures Important? • He then calculated that the edge of the cube had to be 2. 097 cm. He took his plans to the machine shop where his friend had the same type of work done the previous year. The shop foreman said, "Yes, we can make the cube according to your specifications. "

Are Significant Figures Important? • "That's OK, " replied the student. "It's important. " • He knew his friend has paid $35, and he had been given $50 out of the school's research budget to get the job done.

Are Significant Figures Important? • He returned the next day, expecting the job to be done. "Sorry, " said the foreman. "We're still working on it. Try next week. " • Finally the day came, and our friend got his cube. It looked very, very smooth and shiny and beautiful in its velvet case.

Are Significant Figures Important? • Seeing it, our hero had a premonition of disaster and became a bit nervous. But he summoned up enough courage to ask for the bill.

Are Significant Figures Important? • "$500, and cheap at the price. We had a terrific job getting it right -- had to make three before we got one right. "

Are Significant Figures Important? • "But--but--my friend paid only $35 for the same thing!" • "No. He wanted a cube 2. 1 cm on an edge, and your specifications called for 2. 097 cm.

Are Significant Figures Important? • We had yours roughed out to 2. 1 that very afternoon, but it was the precision grinding and lapping to get it down to 2. 097 which took so long and cost the big money.

Are Significant Figures Important? • The first one we made was 2. 089 on one edge when we got finshed, so we had to scrap it. The second was closer, but still not what you specified. That's why the three tries. " • "Oh! I see. I should have paid attention to sig figs in science class. Guess I am going to pay now instead. "

Math Operations with Significant Digits • When multiplying and/or dividing your answer must reflect the smallest number of significant digits.

Math Operations with Significant Digits • When multiplying and/or dividing your answer must reflect the smallest number of significant digits. • (17. 3 cm)(28 cm) = 484. 4 cm 2

Math Operations with Significant Digits • When multiplying and/or dividing your answer must reflect the smallest number of significant digits. • (17. 3 cm)(28 cm) = 484. 4 cm 2 = 480 cm 2

Math Operations with Significant Digits • When multiplying and/or dividing your answer must reflect the smallest number of significant digits. • (17. 3 cm)(28 cm) = 484. 4 cm 2 = 480 cm 2 • 708 g ÷ 4. 700 ml = 150. 63829 g/ml =

Math Operations with Significant Digits • When multiplying and/or dividing your answer must reflect the smallest number of significant digits. • (17. 3 cm)(28 cm) = 484. 4 cm 2 = 480 cm 2 • 708 g ÷ 4. 700 ml = 150. 63829 g/ml = 151 g/ml

Addition and/or Subtraction reflects the fewest decimal places. • 24. 6 cm − 17. 01 cm = 7. 59 cm

Addition and/or Subtraction reflects the fewest decimal places. • 24. 6 cm − 17. 01 cm = 7. 59 cm = 7. 6 cm

Addition and/or Subtraction reflects the fewest decimal places. • 24. 6 cm − 17. 01 cm = 7. 59 cm = 7. 6 cm • 8. 5 g + 1. 32 g + 0. 18 g =

Addition and/or Subtraction reflects the fewest decimal places. • 24. 6 cm − 17. 01 cm = 7. 59 cm = 7. 6 cm • 8. 5 g + 1. 32 g + 0. 18 g = 10 g

Addition and/or Subtraction reflects the fewest decimal places. • 24. 6 cm − 17. 01 cm = 7. 59 cm = 7. 6 cm • 8. 5 g + 1. 32 g + 0. 18 g = 10. 0 g

Homework Worksheet – Significant Digits & Rounding.