Scientific Measurement: Units, Prefixes, Significant Figures, and Scientific Notation

Scientific Measurement

Introduction

Scientific measurement is fundamental to all areas of chemistry, including general, organic, and biological chemistry. Accurate measurement allows scientists to describe quantities, compare results, and communicate findings effectively. This section covers the basics of measurement, including units, prefixes, significant figures, and scientific notation.

Quantities and Units

Physical Quantities and Their Measurement

Physical quantities are properties of matter that can be measured, such as mass, length, volume, temperature, and time. Every measurement consists of a number and a unit (e.g., 61.2 kilograms).

• Number: Indicates the magnitude of the measurement.

• Unit: Specifies the standard of comparison for the measurement.

The International System of Units (SI)

The International System of Units (SI) is the standard system used in science for consistency and clarity. It is based on seven base units, but in chemistry, the most commonly used are mass, length, volume, temperature, and time.

Quantity	SI Unit (Symbol)	Metric Unit (Symbol)	Equivalent
Mass	Kilogram (kg)	Gram (g)	1 kg = 1000 g
Length	Meter (m)	Meter (m)	1 m = 100 cm
Volume	Cubic meter (m3)	Liter (L)	1 m3 = 1000 L
Temperature	Kelvin (K)	Celsius degree (°C)	See Section 2.3 (conversion required)
Time	Second (s)	Second (s)	—

SI Prefixes

Multiples and Submultiples of Units

SI prefixes are used to express very large or very small quantities conveniently. Each prefix represents a specific power of ten.

Symbol	Base Unit Multiplied By	Example
M	1,000,000 = 10^6	1 megameter (Mm) = 106 m
k	1,000 = 10^3	1 kilogram (kg) = 103 g
h	100 = 10^2	1 hectogram (hg) = 102 g
da	10 = 10^1	1 dekaliter (daL) = 10 L
d	0.1 = 10^-1	1 deciliter (dL) = 0.1 L
c	0.01 = 10^-2	1 centimeter (cm) = 0.01 m
m	0.001 = 10^-3	1 milligram (mg) = 0.001 g
μ	0.000 001 = 10^-6	1 micrometer (μm) = 10^-6 m
n	0.000 000 001 = 10^-9	1 nanogram (ng) = 10^-9 g
p	0.000 000 000 001 = 10^-12	1 picogram (pg) = 10^-12 g
f	0.000 000 000 000 001 = 10^-15	1 femtogram (fg) = 10^-15 g

Examples of Prefix Use

• Radius of a lithium atom: approximately $1 \times 10^{-11}$ m (picometers)

• Diameter of a human hair: approximately $1 \times 10^{-7}$ m (micrometers)

• Camera resolution (iPhone X): approximately $1 \times 10^{7}$ m (megapixels, but here used as a large number for illustration)

Significant Figures

Definition and Importance

Significant figures (sig figs) are the digits in a measurement that are known with certainty plus one digit that is estimated. The last digit is considered uncertain by ±1.

• All nonzero digits are significant.

• Zeros between nonzero digits are significant (e.g., 92.065 has five significant figures).

• Leading zeros (zeros before the first nonzero digit) are not significant (e.g., 0.0834 has three significant figures).

• Trailing zeros after a decimal point are significant (e.g., 2.50 has three significant figures).

• Trailing zeros before a decimal point may or may not be significant, depending on context (e.g., 200 may have one, two, or three significant figures).

Examples

• 2.50 cm (three significant figures)

• 43 lb (two significant figures)

• 43.1 lb (three significant figures)

• 43.43 lb (four significant figures)

• 0.02040 g (four significant figures)

Practice: Counting Significant Figures

• 0.065 g: two significant figures

• 0.034 cm: two significant figures

• 200 m: one, two, or three significant figures (context needed)

Measuring with Significant Figures

When reading a measurement from a device (e.g., graduated cylinder), always record all certain digits plus one estimated digit.

• Example: If the liquid level is between 17 and 18 mL, and you estimate it as 17.6 mL, you record three significant figures.

Scientific Notation

Purpose and Format

Scientific notation is a method for expressing very large or very small numbers in the form:

$a \times 10^{n}$

• a is a number between 1 and 10 (including 1, but not 10).

• n is an integer (positive for large numbers, negative for small numbers).

Examples

• 10,000 = $1 \times 10^{4}$

• 0.00000008 = $8 \times 10^{-8}$

Converting to Scientific Notation

• Move the decimal point so that only one nonzero digit remains to the left of the decimal.

• Count the number of places the decimal was moved; this is the exponent on 10.

• If the decimal is moved to the left, the exponent is positive; if to the right, the exponent is negative.

Example Conversion

• 0.003 g = $3 \times 10^{-3}$ g

Summary Table: Significant Figure Rules for Zeros

Zero Type	Example	Significant?
Between nonzero digits	92.065	Yes
At the beginning (leading zeros)	0.0834	No
At the end and after the decimal point	2.50	Yes
At the end and before the decimal point	200	Context-dependent

Key Takeaways

• Always use the correct SI unit and prefix for clarity and precision.

• Record measurements with the correct number of significant figures.

• Use scientific notation to express very large or very small numbers efficiently.

Additional info: The above notes include inferred context and expanded explanations to ensure completeness and clarity for GOB Chemistry students.