Transcript Powers of Ten & Significant Figures

Unit 1 – Lecture 5
Scientific Notation
 Why use scientific notation / powers of 10?
 hard to use very large or very small numbers
 Uses Powers of Ten
 Format =
B
 A times 10

A = coefficient
B = number of places decimal moves to express A

always ONE number before the decimal.

Scientific Notation – cont’d
 A * 10
B
 positive exponent = move decimal to the right
 makes the coefficient larger
 A * 10
-B
 negative exponent = move decimal to the left
 makes the coefficient smaller
Change out of Scientific Notation
 1 * 100
 move decimal zero times
 1 with zero zeros behind it; = 1
 1* 105
 move the decimal 5x to the right
 1 with 5 zeros behind it; = 100,000
 5 * 1015
 move the decimal 15x to the right
 5 with 15 zeros after it; = 5 000 000 000 000 000
 1 * 10-2
 move decimal 2x to the LEFT
 = .01
Change into Scientific Notation
 10,000
 moving the decimal 4 places to the left
4
 = 1 * 10
 .000 000 000 000 004
 moving decimal 15x to the right
 =4 * 10
-15
 12,357
 moving decimal 4x to the left
4
 = 1.2357 x 10
 .003 675 78
 moving decimal 3x to the right
 = 3.67578 x 10
-3
200.0 * 102
moving decimal
2x to the left
= 2.000 * 104
Check Your Warm-Ups
 3427 cm =
 34.378 ml =
 3.427 x 103 cm
 3.4378 x 101 ml
 0.502 km =
 .0078 x 104 seconds =
 5.02 x 10-1 km
 78 OR
 7.8 x 101
Check Your Warm-Ups
 1 x 103 cm =
 3.787 x 102 km =
 1,000 cm
 378.7 km
 2.45 x 104 cm =
 7.0076 x 105 L =
 24,500 cm
 700,760 L
Significant Figures
 used to express the certainty of a measured value
 ex: 2, 2.0, 2.00



2 = 1-3 [+/- 1]
2.0 = 1.9-2.1 [+/- 0.1]
2.00 = 1.99-2.01 [+/- .01]
Significant Figures – 5 rules
 Always count nonzero digits
 Example: 21 has two significant figures,
while 8.926 has four
 Never count leading zeros
[zeros to the left of the first non-zero digit]
 Example: 021 and 0.021 both have
two significant figures
Sig Fig Rules – cont’d
 Always count zeros which fall between two
nonzero digits
 Example: 20.8 has three significant figures;
0.00104009 has six
Sig Fig Rules – cont’d
 Count trailing zeros if and only if the # contains a
decimal point [even if there is nothing after it]
 Example: 210 and 210000 both have two significant
figures, while 210. has three and 210.00 has five
 the difference is in how
accurately they were measured…
 210 is accurate to only the “tens” place
 210. is accurate to the “ones” place
Sig Fig Rules – cont’d
 For numbers expressed in scientific notation, ignore
the exponent and apply Rules 1-4 to the coefficient
 Example: -4.2010 x 1028 has five significant figures
Sig Fig Practice
Count the # of Sig Figs
 29000
4
 1.05 g
 two [2.9 * 10 ]
0
 three [1.05 * 10 ]
 29000.
4
 0.0003040 mm
 five [2.9000 * 10 ]
-4
 four [3.040 * 10 ]
 0.90 * 1045 L
44
 two [9.0 * 10 ]
Sig Fig Practice
Round each to 3 Sig Figs:
[find the third sig fig, then round to that number]
 77.0653
1
 77.1 [7.71 * 10 ]
 6,300,178.2
6
 6.30 * 10
 0.00023350
-4
 .000234 [2.34 * 10 ]
Homework
 Complete:
 Scientific Notation w/s
[pgs 20-21]
 Sig Figs w/s
[pgs 22]
 GO TO 3301 TOMORROW!!!