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Chapter 1: Summary

Scientists use the Système International d’Unités, also known as the metric system of measurement. Examples of metric units are meters, kilograms, and seconds.

In these systems, units that measure the same property, for example units for mass, are related to each other by powers of ten. Unit prefixes tell you how many powers of ten. For example, a kilogram is 1000 grams and a kilometer is 1000 meters, while a milligram is one one-thousandth of a gram, and a millimeter is one-thousandth of a meter.

Numbers may be expressed in scientific notation. Any number can be written as a number between 1 and 10, multiplied by a power of ten. For example, 875.6 = 8.756×102.

A standard is an agreed-on basis for establishing measurement units, like defining the kilogram as the mass of a certain platinum-iridium cylinder that is kept at the International Bureau of Weights and Measures, near Paris. A physical constant is an empirically measured value that does not change, such as the speed of light.

In the metric system, the basic unit of length is the meter; time is measured in seconds; and mass is measured in kilograms.

Sometimes a problem will require you to do unit conversion. Work in fractions so that you can cancel like units, and make sure that the units are of the same type (all are units of length, for instance).

When you need to do arithmetic using scientific notation, remember to deal with the leading values and the exponents separately. For multiplication, multiply the leading values and add the exponents. For division, divide the leading values and subtract the exponents. When adding or subtracting, first make sure the exponents are the same and then perform the operation on the leading values. In all cases, if the leading value of the result is not between one and 10, adjust the result. For example, 0.12×10−2 becomes 1.2×10−3.

The Pythagorean theorem states that the square of the hypotenuse of a triangle is equal to the sum of the squares of the two legs.

c2 = a2 + b2

Trigonometric functions, such as sine, cosine and tangent, relate the angles of a right triangle to the lengths of its sides.

Radians (rad) measure angles. The radian measure of an angle located at the center of a circle equals the arc length it cuts off on the circle, divided by the radius of the circle.

Dimensional analysis is a useful tool for analyzing physical situations and checking whether calculations make sense. In dimensional analysis, dimensions are treated algebraically. We use the symbols L, T, and M to represent the dimensions of length, time, and mass. The volume of a cube, for instance, has dimensions L×L×L or L3.



giga (G) = 109

mega (M) = 106

kilo (k) = 103

centi (c) = 10–2

milli (m) = 10–3

micro (μ) = 10–6

nano (n) = 10–9

Pythagorean Theorem

c2 = a2 + b2

Trigonometric functions

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

Radian measure

Angle = arc length / radius = s/ r

360° = 2π rad


1.  The following variables are commonly seen in equations. The name of the quantity represented by each variable, and its dimension(s), are also shown.
x distance (L); t time (T); m mass (M); a acceleration (L/T2); v speed (L/T);

F force (ML/T2)
Using the information above, check the boxes of the equations that are dimensionally correct. Select all that apply.
F = ma; v2 = 2ax; v = at2; F/v = m/t

2. The dimensions for force are the product of mass and length divided by time squared. Newton's second law states that force equals the product of mass and acceleration. What are the dimensions of acceleration?
T2   T2/L  L/T2   L/T

3.  Multiply 3.65×1023 by 4.12×10154 by 1.11×10−11 and express the answer in scientific notation

4.  A drug company has just manufactured 50.0 kg of acetylsalicylic acid for use in aspirin tablets. If a single tablet contains 500 mg of the drug, how many tablets can the company make out of this batch?

5.  Newton's second law states that the net force equals the product of mass and acceleration. A boat's mass of is 9.6×105 kg and it experiences a net force of 1.5×104 kg·m/s2. State its acceleration.

YOU DO (#1, due 8.31.15)

1.  Sara has lived 18.0 years. How many seconds has she lived? Express the answer in scientific notation. Use 365.24 days per year for your calculations.

2.  The world's tallest man was Robert Pershing Wadlow, who was 8 feet, 11.1 inches   tall. There are 2.54 centimeters in an inch and 12 inches in a foot. How tall was   Robert in meters?

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