U1D8: Scientific Notation: How to write very large and very small numbers Agenda: 1.Complete Al Foil Lab data collection (15 minutes) 2.Significant figure.

1

U1D8: Scientific Notation: How to write very large and very small numbers

Agenda: 1. Complete Al Foil Lab data collection (15 minutes)2. Significant figure Review WS and Checkpoint 3. You will be able to write very large and very small

numbers proficiently.4. Review

Do Now: 1. Density Lab out: Complete Measures.2. Complete Density Lab Do Now (turn over when done)

5

Aluminum Foil Lab

• Due Monday (Day 11)…Don’t Forget…• People still owe Measurement Lab , Safety

Lab and Sci Method Lab

6

What is the rule if…..1. 0.03 kg = 3 x 10 -2 kg2. 15 000 000 m = 1.5 x 10 7 m3. 435 000 L = 4.35 x 10 5 L4. 0. 000 000 973 g = 9.73 x 10 -7 g

Rule: Pos exponent = large numberNeg exponent = small number (less than 1)# btwn 1 and 10 (w/ approp sig fig)Base number = 10

7

Scientific Notation

• Scientists like to be ‘efficient’, and have an easier way to express those loooong numbers

8

Scientific Notation• SCIENTIFIC NOTATION:

Expressing a number as a multiple of a power of ten.

Used to take looooong numbers and compress them so that they can be more easily calculated.

• 300 000 000 m/s 3 x 108 m/s

9

Handling Large Numbers

• Take the significant figures from the number, put them into the form N.NNN X 10x

x, – Place a decimal so the # is between 1 and 10– “x” represents the number of decimal places moved

• Include ALL OF THE SIG FIGS!

10

.So…World Population: 7 042 000 000 peopleIn sci notation: _____________________Practice: Sci Notation1. 5400 2. 9 076 0003. 1005004. 7 00Ō 000

11

What if you’re given Sci. Not.????

Put in decimal form..1. 5.4 x 10 5

2. 7.06 x 10 7

3. 1.5 x 10 3

4. 9.800 x 10 9

* remember rules of Sig Figs

12

Handling small numbers• Sig figs written as a number between 1 and 10• Exponent is NEGATIVE x 10 –x (moved from the left)

Practice: Sci Notation1. 0.00060 2. 0.03043. 0.000 000 000 154. 0.000 070 040

13

Handling small numbers

• 0.0020 • 2.0 (must include the 0 because it is a sig fig)• Count from the 2 back to the 0 in the one’s

place…. Three places• The 3 will be negative and we get…• 2.0 x 10-3

14

Converting to decimals• Reverse procedure• 8 x 10-3

• 8 is 3 places from the ones place• 0.008Put in decimal form..1. 1.7 x 10-3 ________________________2. 1.004 x 10 -5 _______________________3. 17.0 x 10 -8 ________________________4. 0.43 x 10 -9 ________________________ * remember rules of Sig Figs

15

Lets play; “Which number is larger?!”

A: 2.0 x 102 or B: 2.0 x 10-2

• Positive exponents are larger than negative ones (they’re decimals!)

A: 1.3 x 103 or B: 1.3 x 105 • For positives, the bigger the exponent, the

bigger the numberA: 2.6 x 10-1 or B: 2.6 x 10-6

• For negatives, the smaller the exponent, the larger the number

16

Right or Wrong? What’s the error??

1. 0.00567 5.7 x 10 -3

2. 9037000 9.037000 x 10 6

3. 23 000 23.0 x 10 -3

4. 4.90 x 10 5 490 000.5. 1.056 x 10 -6 0.0000010566. 7.000 x 10-2 0.07

17

Complete Scientific Notation WS

• Have me check your answers when done, then move onto Practice #4

18

Take out Practice Packet

Number Scientific Notation

250.

200 000

0.000 55

602 300 000 000 000 000 000 000

0.000 000 000 000 000 000 160

A) Convert each of the following into scientific notation:

19

Scientific Notation

Standard Decimal Notation

7.982 X 1011

7.02 X 10-4

2.030 X 10-18

4.3 X 10-5

B) Convert each of the following into standard decimal notation:

20

C) Ksp is a measurement of the solubility of a salt. The larger the value of Ksp is, the more salt can dissolve in water.

1)4.3 X 10-6 2) 5.7 X 10-7

3) 9.8 X 10-8 4) 3.2 x 10-9

a) Which of the following Ksp values would indicate the salt with the highest solubility? _______

b) Which of the following Ksp values would indicate

the salt with the lowest solubility? _______

c) Explain how you answered a and b.

21

Tonight: Complete WS: Scientific Notation!Density Lab due Day 11