Chapter 2Section 3

Using Scientific Measurements

ObjectivesDistinguish between accuracy and

precisionDetermine the number of significant

figures Perform mathematical operations involving

significant figuresConvert measurements into scientific

notationDistinguish between inversely and directly

proportional relationships

Accuracy and Precision(i) Accuracy: refers to how close an answer is to the “true” value

Generally, don’t know “true” value Accuracy is related to systematic error

(ii) Precision: refers to how the results of a single measurement compares from one trial to the next

Reproducibility Precision is related to random error

Low accuracy, low precision Low accuracy, high precision

High accuracy, low precision High accuracy, high precision

Significant Figures

• Non-zero numbers are always significant.

For example, 352 g has 3 significant figures.• Zeros between non-zero numbers are always significant.

For example, 4023 mL has 4 significant figures.• Zeros before the first non-zero digit are not significant.

For example, 0.000206 L has 3 significant figures. • Zeros at the end of the number after a decimal place are

significant.

For example, 2.200 g has 4 significant figures.• Zeros at the end of a number before a decimal place are

ambiguous (e.g. 10,300 g).

Multiplying & Dividing

Least # of sig figs in valueExample: 4.870

x 3.21 15.6

Adding & Subtracting

Least precise number--usually determined by Least # of decimal places

Examples: 2.345 2500. + 0.1__ + 27.3 2.4 2527.

Rounding Rules

If the first digit to be removed is 5 or greater, round UP, 4 or lower, round DOWN.

Example: 2.453 rounded to 2 sig figs is 2.55.532 rounded to 3 sig figs is 5.53

Percent Error

Percent Error:Measures the accuracy of an experiment

Can have + or – value

%100accepted

lexperimetaaccepted

Example

Measured density from lab experiment is 1.40 g/mL. The correct density is 1.36 g/mL.

Find the percent error.

%94.210036.1

1.40-1.36 error %

Used to characterize substances (a measure of “compactness”) and is an intensive property.

Defined as mass divided by volume:

Units: g/cm3. Sometimes this is written as g • cm–3.

NOTE: cm3 = mL

Frequently used as a conversion factor (mass to volume)

Density

volumemass

Density Mass and volume are extensive properties,they are dependant on the amount of substance.

Bromine is one of two elements that is a liquid at room temperature (mercury is the other). The density of bromine at room temperature is 3.12 g/mL. What volume of bromine is required if a chemist needs 36 g for an experiment?

Solution: 11.53 mL

Sig fig

12 mL

d

mV

mLg

gV

/12.3

36

What volume is occupied by 461 g of mercury when it’s density is 13.6 g/ mL?

  Volume from Mass and Density

Solution

Here we can express the inverse of density as a ratio, 1.00 mL/13.6 g, and use it as a conversion factor.

V = 461 g x ––––– = 3.9 mL1 mL13.6 g

A metal ball was found to have a mass of 0.085 kg and a volume of 3.1 mL. Calculate the density of the metal ball in units of g/mL.

The density of liquid mercury is 13.55 g/cm3. A mercury thermometer contains exactly 0.800 mL of liquid mercury. Calculate the mass of the liquid mercury contained in the thermometer.

A glass container weighs 48.462 g. A sample of 4.00 mL of antifreeze solution is added, and the container plus the antifreeze weigh 54.51 g. Calculate the density of the antifreeze solution.