Calculations Notes

Multiplication and Division

Number of the sig. figs. is the result of the measurement with the smallest number of sig. figs. (least accurate)

Ex 1: 4.63 m x 7.5 m Ex. 2: 8.460 m2 / 2.1 m

35 m2 4.0 m

3sf 2sf

34.725 m2

4sf 2sf

4.02857143 m

Addition and Subtraction

Align the decimal points and carry out the calculation. First column from the left with an uncertain digit determines the number of sig. figs. in your answer (Chop & round at the GAP)

Ex 1: 6.341 g + .789 g + 4.2 g Ex. 2: 6.799 m - 2.41 m

6.341 .7894.2

11.330

GAP11.3 g 6.799

2.414.389

GAP4.39 m

Scientific Notation and Multiplication and Division

Multiplication – Multiply coefficients, ADD exponents, multiply units, round to proper S.F.

Division - Divide coefficients, SUBTRACT exponents, divide units, round to proper S.F.

Ex 1: (1.00 x 103 m)(3.2 x 102 m) Ex. 2: (3.00 x 104 g)/(1.0 x 102 cm3)

3.2 x 105 m2 3.0 x 102 g/cm3

Scientific Notation and Addition and Subtraction

must be in the same power of ten and same unit before you add or subtract coefficients, convert to larger exponent

Ex 1: 3.0 x 1023 m + 1.0 x 1022 m 1

3.0 x 1023 m + .10 x 1023 m

3.0 .103.10

GAP 3.1 x 1023 m

Element Buddies

• ADD PRACTICE

Problem Solving and Dimensional Analysis

Conversion factor – ratio of two parts of the statement that relates the two units

Equivalence Statement – true statement in fraction form

Dimensional Analysis – when used properly all units will cancel out except the desired unit

2.54 cm = 1 inch

100 cm = 1 m

2.54 cm 1 inch

1 inch2.54 cm

100 cm 1 m

1 m 100 cm

or or

x ______________Desired UNIT

Wanted UNIT

#

#

x ________________

Wanted UNIT

#

#

Given UNIT

Given with UNITS=

Ex. 1: 250 m = ___________ km

Ex. 2: 3.54 g = ___________ mg

Ex. 3: 0.542 kg = __________ mg

x ___________km

1000

1

m

250 m = .25 km

x ___________mg

1

1000

g

3.54 g = 3540 mg

x __________mg

g

1000

1x ________g

1

1000

kg

0.542 kg = 542000 mg

Determining Error

___________________value - correct value based on reliable references

___________________value - value measured in the lab

Error = experimental value – accepted value(Note: error can be positive or

negative) You will take the ___________ value of this when you calculate percent error.

accepted

experimental

absolute

Determining Percent (%) Error

Percent error = absolute value of error divided by accepted value and multiplied by 100%

% error = experimental value – accepted value x 100%accepted value

Example: You take three temperature readings of a beaker of boiling water and record: 91.3oC, 90.9oC, and 91.1oC. Evaluate accuracy, precision, and error. Accurate? No, water boils at 100oC

Precise? Yes, values are close to each other

1. Find average experimental data

2. Use formula

Error

(91.3oC + 90.9oC + 91.1oC)/3 = 91.1oC

% error = (91.1 oC – 100 oC) x 100%100 oC

= 8.90 %