Ch. 2 - Sigfigs & Dimensional Analysis

Name the symbol, meaning, and conversion factor for:

tera-

• T

• trillion (remember: t for trillion)

• 1Tm = 1E12m

Name the symbol, meaning, and conversion factor for:

giga-

• G

• billion (remember: giga = biba)

• 1Gm = 1E9m

Name the symbol, meaning, and conversion factor for:

mega-

• M

• million (remember: mega-million lotto = million-million)

• 1Mm = 1E6m

Name the symbol, meaning, and conversion factor for:

kilo-

• k

• thousand

• 1km = 1E3m

Name the symbol, meaning, and conversion factor for:

hecto-

• h

• hundred

• 1hm = 1E2m

Name the symbol, meaning, and conversion factor for:

deca-

• da

• ten

• 1dam = 1E1m

Name the symbol, meaning, and conversion factor for:

deci-

• d

• tenth

• 1dm = 1E-1m

Name the symbol, meaning, and conversion factor for:

centi-

• cm

• hundredth

• 1cm = 1E-2m

Name the symbol, meaning, and conversion factor for:

milli-

• mm

• thousandth

• 1mm = 1E-3mm

Name the symbol, meaning, and conversion factor for:

micro-

• μ (Greek for “m”)

• millionth (remember: micro = millionth)

• 1μm = 1E-6m

Name the symbol, meaning, and conversion factor for:

nano-

• n

• billionth

• 1nm = 1E-9m (remember: nano-negative-nine)

Name the symbol, meaning, and conversion factor for:

pico-

• p

• trillionth (remember: pee (pi) on a tree (tri))

• 1pm = 1E-12m

Name the symbol, meaning, and conversion factor for:

femto-

• f

• quadrillionth

• 1fm = 1E-15m

1 in =

2.54 cm

1 mi =

5280 ft

True or false: Conversion factors have unlimited sigdigs

True

estimated vs certain digit

• Estimated - ALWAYS LAST reported digit in all measure (number that flickers back and forth on scale)

• Certain - all other digits, except for placeholders (0)

List all digits that are significant:

1. Nonzero digits (1-9)

2. Interior zeros (remember: sandwich between 2 #’s)

3. Trailing zeros after decimal point

4. Trailing zeros after nonzero digit IF has decimal point

List all digits that are NOT significant:

1. Leading zeros; left of first nonzero number (placeholder to locate decimal point)

2. Trailing zeros at end of a number + before implied decimal point are AMBIGUOUS

exact numbers

• Unlimited significant figures

• Ex.

  • Exact counting of objects

  • Exact conversion factors

  • Defined quantities

How many sigfigs?

0.0035

2

How many sigfigs?

1.080

4

How many sigfigs?

2371

4

How many sigfigs?

2.9 × 10^5

2

How many sigfigs?

1 dozen = 12

unlimited

How many sigfigs?

100.00

5

How many sigfigs?

100,000

ambiguous

Unit system for science measurements

International System of Units (SI units), based on metric system

SI unit for length

meter (m)

SI unit for mass

kilogram (kg)

SI unit for time

second (s)

SI unit for temperature

kelvin (K) *bc no negatives

Mass vs. weight

• mass - measure of quantity of matter within it

• weight - measure of the gravitational pull on that matter

Rules for Rounding:

Use only the ____ (or _____most) digit being dropped to decide in which direction to round— ignore all digits to the ___ of it.

• last; left; right

Round to 3 sigfigs:

• 10,776.522

• 0.0000344988

• 10,800

• 0.0000345

Multiplication and Division Rule:

The result of multiplication or division has the same # of sigfigs as the factor with the ____ sigfigs

fewest

Addition and Subtraction Rule:

In + or - calculations, the result has the same # of decimal places as the quantity with the _____ decimal places.

fewest

Both multiplication/division and addition/subtraction:

• Do steps in the ____ first

• Determine correct # of sigfigs in intermediate answer without _____ (you should underline the estimated digit)

• Do remaining steps

• parentheses

• rounding