SIGNIFICANT FIGURES & SCIENTIFIC NOTATION

Sig Figs

Scientific NotationIn science, we often come across either very large or very small numbers, so we use Scientific Notation as a way to simplify them.

Some numbers hard to work with:

Mass of one atom

= 0.000000000000000000000000000000091 kg

# atoms in 2 grams of hydrogen

= 1200000000000000000000000 atoms

Scientific NotationEasier:

Mass of one electron = 9.1 x 10-32

# atoms in 2 g hydrogen = 1.2 x 1024

In Scientific Notation, a number is written as the product of two numbers:

A coefficient, and 10 raised to a power (exponent).

The coefficient is always greater than or equal to 1, and less than 10M x 10n

M = Coefficient between 1 and 10

10 is the base

n is the exponent

Scientific Notation Worksheet

Numbers > 1 have a positive exponent

5.2 x 103

Numbers < 1 have a negative exponent

9.65 x 10-4

The Importance of MeasurementEx: 2011. converted to scientific notation:

In this case: In order for the coefficient to be between 1 and 10, the decimal

has to move 3 places to the left. The decimal moved 3 times, so the value of the exponent is 3 The number (2011) is bigger than 1, so the exponent will be

positive.(103 = 1000., so this reads 2.011 x 1000 which = 2011.)

Ex: 0.036 converted to scientific notation:In this case: In order for the coefficient to be between 1 and 10, the decimal

has to move 2 places to the right. The decimal moved 2 times, so the value of the exponent is 2 The number (0.036) is less than 1, so the exponent will be

negative.(10-2 = 0.01, so this reads 3.6 x 0.01 which = 0.036)

2.011x 10 3+

3.6 x 10 -2

The Importance of Measurement

1.420 x 10-92 x 106

Convert the following numbers from standard to scientific notation

2 000 000. 0.000 000 001 420

Convert the following numbers from scientific to standard notation7.29 x 1015

7 290 000 000 000 000.9.25 x 10-11

0.000 000 000 092 5

Practice

Significant Figures

We keep track of measurement accuracy through significant digits(Sig Digs) also called significant figures (Sig. Fig)

A measurement is considered to be more accurate if it has more significant digitsSignificant Figures = all known

digits plus one estimated digit

Significant Figures RULES

1) No zeros? All significant. 3772) All sandwich zeros significant.

3073) Leading zeros are not significant.

0.00312

4) If digits are left of a decimal then zeros right of a decimal are significant

3.005) Scientific notation indicates significant

figures when numbers end in zero

300 = 3 x 102 or 3.00 x 102

When you have to guess, zeros don’t count

Uncertainty in Measurements

Practice:Count the number of significant digits in each measurement.

0.05730 meters 8.750 x 10-2 centimeters

8765 seconds 200. yards

0.00073 milliliters 200 yards 200.0 yards

40.070 grams 101010 milliseconds

44

4

4

55

3

2 1

Uncertainty in Measurements

Accuracy is a measure of how close the measurement is to the actual, or “true value” of what was measured.

Actual blood glucose level = 94.899

mg/dL

Uncertainty in Measurements

Precision is a measure of how close your measurements are to each other.- measurements do not have to be accurate to be precise- measurements can be both precise and accurate, or neither.