Measuring and Units

International System of UnitsMetric systemSI Universally accepted and understood by

scientist around the world

Derived units are a combination of base units

Example: m/s

DensityDensity is a ratio that compares the mass of

an object to its volume. Density = mass/volume D=m/vUnits are

g/L g/mL g/cm3

Temperature◦C increase 1 unit at a time

Kelvin increase 1 unit at a time

Therefore to convert from ◦C to K K = 273 + ◦C

Degrees CelsiusBoiling point = 100 ◦CFreezing point = 0 ◦C

SI Unit is KelvinBoiling point = 373 KFreezing point = 273 K

Scientific NotationContains a number and then raised to a

power

The exponent tell you how many times the factor must be multiplied by ten

If the number is less then 1 the exponent is negative

If the number is greater then 1 the exponent is positive

When adding or subtracting using exponents, the exponents must be the same

If they are not the same in the problem you can change them so they are the same

When multiplying and dividing exponents the exponents do not have to be the same.

When multiplying first multiply the factors then you add the exponents

When dividing first divide the factors then you subtract the exponents

Dimensional AnalysisDimensional analysis is a method focused on

units that describe matter

Use conversion factors to convert from one unit to another

35 m = 35000 mmConversion factor 1m = 1000mm

Accuracy and PrecisionAccuracy refers to how close a measured

value is to an accepted value

Precision refers to how close a series of measurements are to each other

Percent ErrorPercent error is the ratio of error to an

accepted value.

Percent ErrorA student performs an experiment and determines

the density of an object to be 1.54 g/mL. The actual density is 1.58 g/mL. Find the students percent error.

Significant FiguresSignificant Figures (sig figs) are the digits

that carry meaning contributing to its precision.

Rules for Sig Figs1) ALL non-zero numbers (1,2,3,4,5,6,7,8,9)

are ALWAYS significant. 2) ALL zeroes between non-zero numbers are

ALWAYS significant. 3) ALL final zeroes which are to the right of

the decimal point are significant4) Zeros that act as placeholders are not

significantWhen in scientific notation if you can remove

the zeros they are not significant

ExamplesRule 1 –

456 has 3 significant figures

Rule 2 – 507 has 3 significant figures

Rule 3 – 9.70 has 3 significant figures

Rule 4 – 0.0787 has only 3 significant figures4350 has only 3 significant figures

RoundingA calculated number should only have the

number of significant figures as the data with the fewest sig figs.

Rules for Rounding1. If the digit to the immediate right of the last

significant figures is less than five, do not change the last significant figure

We need only 3 sig figs1. 3.562 3.56

2. If the digit to the immediate right of the last significant figure is greater than five, round up the last significant figure

3 sig figs

1. 4.567 4.57

3. If the digit to the immediate right of the last significant figure is equal to five and is followed by a nonzero digit, round up the last significant figure

2.5351 2.54

4. If the digit to the immediate right of the last significant figure is equal to five and is not followed by a nonzero digit, look at the last significant figure. If it is an odd digit, round it up. If it is an even digit, do not round up.

2.5350 2.54

2.5250 2.52

Adding and SubtractingWhen you add or subtract measurements,

your answer must have the same number of digits to the right of the decimal point as the value with the fewest digits to the right of the decimal point.

Example:1.24 mL + 12.4 mL = 13.84 mL – 13.8

mL

Multiplying and DividingWhen multiplying and dividing, your answer must

have the same number of sig figs as the measurement with the fewest sig figs.

3.65 cm x 3.20 x 2.05 cm = 23.944 cm3 = 23.9 cm3