Measurements & Significant Figures

Measurement Accuracy and Precision Significant Figures Significant figures in calculations Unit Conversions

standard

an unchanging body of each unit to serve as a primary reference

international system or si system

• uses a different unit for each quantity

• two types of SI units: fundamental and

derived

length

meter

(m)

mass

kilogram

(kg)

temperature

kelvin

(K)

time

second

(s)

amount of substance

mole

(mol)

electric current

ampere

(A)

luminous intensity

candela

(cd)

derived s.i. units

are composed of 2 or more base units

e.g) volume

• The volume of a regular-shaped solid can be found by using the volume formula of the shape

• L x W x H

dimensional analysis steps

1. identify the given value: write down the quantity you are given, including its unit.

2. identify the desired unit: determine the unit you want to convert to

3. find conversion factors: Locate the relationship between the given unit and the desired unit

4. set up the conversion:

   • write the given value as a fraction (put it over 1 if it's a single number)

   • set up a conversion factor as a fraction with the unit you want to cancel in the denominator and the unit you want in the numerator

   • if needed, continue to add more conversion factors to complete the chain of conversions

5. cancel units: cross out units that appear in both the numerator and the denominator

6. perform the calculation: multiply the numbers in the numerator and divide by the numbers in the denominator

7. final answer: the remaining unit should be the desired unit, and the calculated number is your final answer

density

mass/volume

units raised to a power rule

raise both the number and the unit to the power

scientific notation

all scientific notation is based around a number multiplied by a power of ten

e.g) 0.000072 is 7.2 × 10⁻⁶

precision

refers to the degree of uncertainty in a measurement

is the ability of a measurement to be consistently reproduced

• standard deviation is calculated to evaluate the precision of data

accuracy

accuracy refers to the proximity of a measurement to the true value of a quantity

• percent error is calculated to evaluate the extent of deviation

certain digits

values that are marked on the measuring device

uncertain digit

the last digit which is always estimated

significant figures

the number of digits used to express a measured or calculated quantity

significant figures rules

1. non-zero digits count (123 → 3 sig figs)

2. zeros between non-zeros count (101 → 3 sig figs)

3. leading zeros don’t count (0.004 → 1 sig fig)

4. trailing zeros count if decimal shown (12.00 → 4 sig figs)

Multiplication/division → round to least sig figs

Addition/subtraction → round to least precise decimal places

• e.g) 12.11 + 18.0 = 30.1 (1 decimal place)

exact numbers

are assumed to have an infinite number of significant figures

e.g)

1. Counted quantities: quantities not measured

2. Defined numbers: a dozen = 12.00000000...

how does conversion between units affect number of significant figures?

converting units doesn’t change the certainty/uncertainty of the measurement → doesn’t change the number of significant figures