Ch. 2 Notes Day 1 Metric Ladder

Objectives SWBAT convert between different metric units using the ladder method SWBAT identify questions that cannot be converted because suffixes don’t match.

Aim: What is the metric system, and why do we use it? Do Now: On your paper 30ºC = 86 ºF 35 km = 21 miles Notes are in Yellow.

What Type of Measurement do we Normally Use in the USA? The “English System” Why don’t we use this system in science? Too complicated, no logic

How Complicated Is It? 12 inches in a foot 3 feet in a yard 16 ½ feet in a rod 120 feet in a furlong 2 pints in a quart 4 quarts in gallon 2 gallons in a peck 4 pecks in a bushel

WTFudge? There is no logic so you can’t guess the relationship. If you want to use the English System, you have to memorize the relationships and multiply or divide to do conversions Luckily, the metric system is MUCH easier!!!

How is the Metric System Easier? In the metric system, everything is based on units of 10. Every type of measurement uses the same beginning prefixes. We can do conversions WITHOUT doing math, just by moving the decimal point right or left.

What is the Basic Unit for Length? Meter abbreviated as m How long is a meter? A meter is about a yard. (39.37 inches - a yard is 36 inches)

What is the Basic Unit for Volume? Liter abbreviated as L How much is a liter? A liter is about a quart. (1.06 quarts)

What is the Basic Unit for Mass/Weight? Gram abbreviated as g How much is a gram? A gram is very light – about the weight of a paperclip! (0.035 ounces)

Using the Metric System Would a meter stick be good enough unit to measure a hair? No, it’s too big If you wanted to measure the distance from the earth to the sun, would a meter stick be a good way to measure the distance? No, it’s too shorteed smaller and larger units

Use Prefixes to Make Units Bigger or Smaller Centi – what does this mean? 1/100 or 0.01 -makes unit smaller Milli – what does this mean? 1/1000 or 0.001 -makes unit smaller Kilo – what does this mean? 1000 - makes unit larger

Conversions are EASY! Let’s Practice! 0.009 A) 9 0 g = _____ kg B) 3.0 L = _____ mL C) 5.0 m = _____ cm 0 0 0 . 0 0 0

Conversions are EASY! Let’s Practice! 0.009 A) 9 0 g = _____ kg B) 3 0 L = _____ mL C) 5.0 m = _____ cm 0.0 0 0 0 0 0 0 0 . 3000 0 0 0 .

Conversions are EASY! Let’s Practice! 0.009 A) 9 0 g = _____ kg B) 3 0 L = _____ mL C) 5 0 m = _____ cm 0.0 0 0 0 0 0 0 0 . 3000 0 0 0 0 0 0 . 0 0 0 . 500

Metric Ladder Review

Scientific Notation (106) (103) (102) (101) (100) (10-1) (10-2) (10-3) (105) (104) (103) (102) (101) (100) (10-1) (10-2) (10-3) (10-4) (10-5) (10-6)

Ch. 2 Notes Day 2 Scientific Notation

Objectives SWBAT convert long form numbers into scientific notation

A short-hand way of writing large numbers without Scientific Notation A short-hand way of writing large numbers without writing all of the zeros.

The Distance From the Sun to the Earth 93,000,000 miles

Move the decimal so there is only one number in front of it. Step 1 Move the decimal so there is only one number in front of it. 93,000,000. = 9.3000000

Step 2 Write number without zeros 9.3000000= 9.3

Step 3 Count how many places you moved the decimal. Multiply your number by 10. Take 10 to a power equal to the number of places you moved. If you moved left, the power is POSITIVE. If you moved right, the power is NEGATIVE. 93,000,000 = 9.3 x 10 7

The power of ten is 7 because the decimal moved 7 places. 93,000,000 = 9.3 x 10 7

93,000,000 --- Standard Form 9.3 x 107 --- Scientific Notation

Practice Problem Write in scientific notation. Decide the power of ten. 9.85 x 107 98,500,000 = 9.85 x 10? 64,100,000,000 = 6.41 x 10? 279,000,000 = 2.79 x 10? 4,200,000 = 4.2 x 10? 6.41 x 1010 2.79 x 108 4.2 x 106

More Practice Problems On these, decide where the decimal will be moved. 734,000,000 = ______ x 108 870,000,000,000 = ______x 1011 90,000,000,000 = _____ x 1010 Answers 3) 9 x 1010 7.34 x 108 2) 8.7 x 1011

Complete Practice Problems Write in scientific notation. 50,000 7,200,000 802,000,000,000 Answers 1) 5 x 104 2) 7.2 x 106 3) 8.02 x 1011

Scientific Notation to Standard Form Move the decimal to the right 3.4 x 105 in scientific notation 3.40000 --- move the decimal ---> 340,000 in standard form

Move the decimal to the right. Write in Standard Form Move the decimal to the right. 6.27 x 106 9.01 x 104 6,270,000 90,100

Scientific Notation in the Negative STEP ONE Move decimal Right Leave only one number in front of decimal 0.00076= 0007.6 STEP TWO Write number without zeros 7.6

Scientific Notation in the Negative Count how many places you moved decimal Make that your power of ten 7.6 x10-4 The negative exponent indicates that your standard notation is smaller than 1

Ch. 2 Notes Day 3 Significant Figures

Objectives Define accuracy Define precision Compare accuracy & precision Use significant figures

Accuracy Accuracy refers to how closely a measurement matches the true or actual values To be accurate only requires the true value (bulls eye) & one measurement (for the arrow to hit the target) Highly accurate data can be costly and difficult to acquire

Precision Precision refers to the reproducibility of the measurement and exactness of description in a number. To decide on precision, you need several measurements (notice multiple arrow holes), and you do not need to know the true value (none of the values are close to the target but all the holes are close together.)

Accuracy & Precision In order to be accurate and precise, one must pay close attention to detail to receive the same results every time as well as “hit the target”.

Comparing Accuracy & Precision Notice the difference in these pictures. To win the tournament the archers must hit the target the most times. The winner must show accuracy & precision. The 1st archer has _____ accuracy & ____ precision. The 2nd archer has _____ accuracy & ____ precision. The 3rd archer has _____ accuracy & ____ precision. The 4th archer has _____ accuracy & _____ precision BAD BAD BAD GOOD GOOD GOOD GOOD BAD

Example 1 A sample is known to weigh 3.182 g. Jane weighed the sample five different times with the resulting data. Which measurement was the most accurate? 3.200 g 3.180 g 3.152 g 3.189 g

Example 2 Consider the data (in cm) for the length of an object as measured by three students. The length is known to be 14.5 cm. Which student had the most precise work, and which student had the most accurate work? Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Student A 14.8 14.7 Student B 14.2 14.6 Student C 14.4 14.5

Solution Most precise: Student A (0.1 cm difference) Most accurate: Student C (2 were true value, rest within 0.1 cm) Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Student A 14.8 14.7 Student B 14.2 14.6 Student C 14.4 14.5

Significant Figures Why are significant figures necessary? True accuracy is no better than the measurement obtained by the least precise method. We use significant digits so we are not exaggerating our precision.

What is a significant figure? There are 2 kinds of numbers: Exact: the amount of money in your account. Known with certainty.

What is a significant figure? Approximate: weight, height—anything MEASURED. No measurement is perfect.

When to use Significant figures When a measurement is recorded only those digits that are dependable are written down.

Rules of Significant Digits All digits 1 through 9 are significant. 9.342 mg = 4 Sig. Digits 233,124 = 6 sig. digits

Rules of Significant Digits 2. Zero is significant when it is between two non‐zero digits 2.06 = 3 SD 206 = 3 SD 100,001 = 6 SD

Rules of Significant Digits 3. A zero to the right of a decimal point in a number greater than or equal to one is significant. 1.000 (4 SD) 30.00 (4 SD) 205.0 (4 SD) 2.00000 (6 SD) 10.0 (3 SD)

Rules of Significant Digits 4. A zero to the right of a decimal point (in a number less than one) but to the left of nonzero digit is not significant. 0.001020 (4 SD) 0.00024200 (5 SD)

Rules of Significant Digits 5. Zeros used only to space the decimal point (placeholders) are not significant. - 1000 (1 SD) - 1010 (3 SD) -78,000 (2 SD)

Counting SDs How many significant digits are in the following numbers? 1235 2020 235.0 0.0270 235. 0.00010900 65,100 19,620,000,000 102,800

Estimated to the tens place Estimated to the tenths place Why are S.F.s Important? When reporting a measurement the number of digits indicates the precision of an instrument. 100 ml Estimated to the tens place 99.9 mL Estimated to the tenths place

Why are S.F.s Necessary? When you divide 5.0 /0.87 = 5.7471… (Actual Answer: 5.7) S.F.s will provide a way to determine how many numbers to report in a measurement or calcualtion!

Example 1: How would you record this measurement? 1.37 cm

Example 2: Provide the measurements for each example. B.

How many significant digits would be recorded? 10 20 30 40 50 60 70 B. 10 20 30 40 50 60 70 C. 10 20 30 40 50 60 70

How many significant digits would be recorded? 48 cm (2 sfs) A. 10 20 30 40 50 60 70 B. 48 cm (2 sfs) 10 20 30 40 50 60 70 C. 48.0 cm (3 sfs) 10 20 30 40 50 60 70