Chapter 5

Measurements & Calculations

Content by: Ms. SandersTranscribed by: Brian Gardas

Picking them ApartA measured value has 3 parts - the numerical quantity, the unit, and the name of the

substance. Practice: For the following terms, identify the numerical quantity, unit, and name of

the substance. a) 10 lb sugar b) 5 kg potatoes c) 2 L cola d) 1 gal milk e) 500 mg vitamin C Quantity: 10 5 2 1 500 Unit: Pounds Kilograms Liters Gallon Milligrams Name: Sugar Potatoes Cola Milk Vitamin C

Measurements…• Are quantitative observations• Include three pieces of information(magnitude, unit, uncertainty)• Are not numbers(numbers are obtained by counting or by definition;

measurements are obtained by comparing an object with a standard “unit”/Numbers are exact; measurements are inexact. Math is based on numbers; science is based on measurement.

Numbers and Measurements

• Quantitative vs Qualitative

• Mass vs Weight

• Precision vs Accuracy

Scientific Notation• A number written as a product of two numbers: a coefficient and a power of ten

• For numbers larger than 10, the decimal must be moved to the left• For numbers between 0 and 1, the decimal must be moved to the right

• In standard scientific notation, only one number is to the left of the decimal Practice: Write the numbers indicated in standard scientific notation

0.0541 5.41 x 10-2

102 x 10-4

1.02 x 10-2

4326 4.33 x 103

148,600,000,000 1.49 x 1011

90.2 x 102

9.02 x 103

0.0000027 2.7 x 10-6

Significant Figures

In scientific work, most numbers are measured quantities and thus are not exact. All measured

quantities are limited in significant figures by the precision of the instrument used to make the

measurement. The measurement must be recorded in such a way as to show the degree of

precision to which it was made. Calculations based on the measured quantities can have no

more (or no less) precision than the measurements themselves.

Sig Fig GuidelinesRule #1: To determine the number of significant figures in a measurement, read the number left to

right and count all digits, starting with the first digit that is not zero. Rule #2: When adding or subtracting numbers, the number of decimal places in the answer should be

equal to the number or decimal places in the number with the fewest places. Rule #3: In multiplication or division, the number of significant figures in the answer should be the

same as that in the quantity with the fewest significant figures Rule #4: When a number is rounded off, the last digit to be retained is increased by one if the following

digit is 5 or greater Rule #5: Zeros

1) Zeros between nonzero numbers are significant2) Zeros at the end of a number to the right of the decimal are significant3) Zeros in numbers like 0.00032 are not significant (they are just place holders)4) Zeros at the end of a number but to the left of the decimal point may or may not be significant

Sig Fig PracticeHow many significant figures in each of the following:

a) 14.356 b) 6.03 c) 125.580 d) 7.5 e) 0.00368 f) 0.0368 5 3 6 2 3 3

g) 6100 h) 400. i) 400 j) 6.90 k) 10.0670 l) 65.0 x 10 9

2 3 1 3 6 3Perform the following calculations:

a) 146.20g + 24.5g + 337g b) 11.2cm x 8.0cm x 0.0093cm 508 0.83

c) (860. x 106) (0.00543 x 10-2)/0.03952 1180000

Dimensional Analysis

1) Identify the unknown2) Identify what is known or given3) Plan a solution (write conversion factors)4) Do the calculations5) Finish up

• Make sure the units cancel• Make sure your conversion factors are correct• Make sure your answer has the correct ratio of

units

Dim. Analysis Practice

1) 165 mm_____in 2) 1200.ml___qt 3)145lbs______kg 6.50in 1.268qt 65.8kg4) 1.50ft______cm 5) 275g_____lb 6)55.0mi______km 45.7cm .606lb 88.5km7) Shaquille O’Neal weighs 310. lb. What is his mass in

kilograms? 141. kg8) Michael Jordan is 6.5ft tall. What is his height a) in meters c) in cm? 2.0m 200.cm

Density

Density is an important characteristic of matter. When one speaks of how “light” or how

“heavy” something is, one is actually referring to the density of the item. Density is defined as mass per unit volume. Densities for solids are reported in grams per cubic centimeters

(g/cm3) and densities for liquids are expressed in grams per milliliter (g/mL). The formula for

calculating density is D=m/V.

Density Practice

1) The density of a certain substance is 0.732 g/mL. What mass does 23.4 mL of the substance have?

17.1g2) A flask filled to the 25.0 mL mark contained

27.42 g of a salt-water solution. What is the density of the solution?

1.10g/mL3) The density of a certain substance is 1.74 g/mL.

What volume does 32.2 grams of the substance occupy? 18.5mL