 # Measurements and Calculations

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Measurements and Calculations
Chapter 2 Measurements and Calculations

Quantitative observation. Has 2 parts – number and unit.

Technique used to express very large or very small numbers.

Using Scientific Notation
The number of places the decimal point is moved determines the power of 10. The direction of the move determines whether the power of 10 is positive or negative. Copyright © Cengage Learning. All rights reserved

Using Scientific Notation
If the decimal point is moved to the left, the power of 10 is positive. If the decimal point is moved to the right, the power of 10 is negative. Copyright © Cengage Learning. All rights reserved

Express the following numbers in scientific notation: 0.0000671; 72.
The World’s population is estimated to be 7,187,000,000 people. Express this number in scientific notation. Express the following numbers in scientific notation: ; 72. Express the following numbers in standard notation: x 10-7; 9.5 x 104. Copyright © Cengage Learning. All rights reserved

The Fundamental SI Units
Physical Quantity Name of Unit Abbreviation Mass kilogram kg Length meter m Time second s Temperature kelvin K Electric current ampere A Amount of substance mole mol Copyright © Cengage Learning. All rights reserved

Prefixes Used in the SI System

Measure of the amount of 3-D space occupied by a substance.

Measure of the amount of matter present in an object.

A gallon of milk is equal to about 4 L of milk.
Concept Check Choose the statement(s) that contain improper use(s) of commonly used units (doesn’t make sense)? A gallon of milk is equal to about 4 L of milk. A 200-lb man has a mass of about 90 kg. A basketball player has a height of 7 m tall. A nickel is 6.5 cm thick. Copyright © Cengage Learning. All rights reserved

Measurement of Length Using a Ruler

A digit that must be estimated is called uncertain.

Rules for Counting Significant Figures

Rules for Counting Significant Figures
Leading zeros are zeros that precede all the nonzero digits. These do not count as significant figures. Captive zeros are zeros between nonzero digits. These always count as significant figures. Trailing zeros are zeros at the right end of the number. They are significant only if the number contains a decimal point. Copyright © Cengage Learning. All rights reserved

Rules for Counting Significant Figures

Rules for Rounding Off If the digit to be removed is less than 5, the preceding digit stays the same. If the digit to be removed is equal to or greater than 5, the preceding digit is increased by 1. In a series of calculations, carry the extra digits through to the final result and then round off. Copyright © Cengage Learning. All rights reserved

Significant Figures in Mathematical Operations
1. For multiplication or division, the number of significant figures in the result is the same as that in the measurement with the smallest number of significant figures. Copyright © Cengage Learning. All rights reserved

Significant Figures in Mathematical Operations

Concept Check You have water in each graduated cylinder shown. You then add both samples to a beaker (assume that all of the liquid is transferred). How would you write the number describing the total volume? What limits the precision of the total volume? Copyright © Cengage Learning. All rights reserved

An impossibly regular, paved walkway mysteriously appears overnight; leading out of Seattle. Careful measurement shows this walkway to be 15,432 meters long and 0.42 meters wide. To the correct number of significant figures, what area is covered by walkway? How would this number change if the walkway were 0.41 meters wide? meters wide? By the next morning, this walkway has grown 0.42 meters. To the correct number of significant figures, how long is it now? Copyright © Cengage Learning. All rights reserved

Use when converting a given result from one system of units to another.

A golfer putted a golf ball 6. 8 ft across a green
A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent? How many centimeters? What is the volume of a 1.25 gallon jug in cubic centimeters? Cubic inches? (1 L = qts) An iron sample has a mass of 4.50 lb. What is the mass of this sample in grams? (1 kg = lbs) If an oxygen molecule is moving at 4.78 x 104 cm/s, what is its speed in mi/hr? Copyright © Cengage Learning. All rights reserved

Three Systems for Measuring Temperature

The Three Major Temperature Scales

Converting Between Scales
The normal body temperature for a dog is approximately 102oF. What is this equivalent to on the Kelvin temperature scale? At what temperature does C = F? Copyright © Cengage Learning. All rights reserved

Mass of substance per unit volume of the substance.

Measuring the Volume of a Solid Object by Water Displacement

Example A certain mineral has a mass of 17.8 g and a volume of 2.35 cm3. What is the density of this mineral? What is the mass of a 49.6 mL sample of a liquid, which has a density of 0.85 g/mL? Copper has a density of 8.96 g/cm3. If 75.0 g of copper is added to 50.0 mL of water in a graduated cylinder, to what volume reading will the water level in the cylinder rise? Copyright © Cengage Learning. All rights reserved