Units and Significant Figures in Data

Study Guide - Smart Notes

Tailored notes based on your materials, expanded with key definitions, examples, and context.

Units and Significant Figures in Data

Introduction

Understanding units and significant figures is fundamental in General Chemistry, as they ensure that measurements and calculations are meaningful and accurate. This topic covers the rules for determining significant figures, their importance in scientific data, and how they affect calculations.

Rules for Significant Figures

Definition of Significant Figures

Significant figures are the digits in a measurement that are known with certainty plus one digit that is estimated. They reflect the precision of a measured value.

Non-zero digits: Always significant. (e.g., 1, 2, 3, 4, 5, 6, 7, 8, 9)
Zero digits: Significance depends on their position.
- Leading zeros: Zeros that precede all non-zero digits are not significant. (e.g., 0.0025 has two significant figures)
- Captive zeros: Zeros between non-zero digits are always significant. (e.g., 1002 has four significant figures)
- Trailing zeros: Zeros at the end of a number are significant only if the number contains a decimal point. (e.g., 100.0 has four significant figures; 100 has one significant figure)

Exact Numbers

Exact numbers are values that are counted or defined, not measured. They have an infinite number of significant figures. Examples include:

Counting objects (e.g., 12 eggs)
Defined quantities (e.g., 1 inch = 2.54 cm)

Significant Figures in Calculations

Multiplication and Division

For multiplication and division, the result should have the same number of significant figures as the measurement with the fewest significant figures.

Addition and Subtraction

For addition and subtraction, the result should have the same number of decimal places as the measurement with the fewest decimal places.

Examples and Applications

Example 1: (Result has two significant figures, matching the least precise measurement)
Example 2: (Result has one decimal place, matching the least precise measurement)

Units in Measurement

SI Units

The International System of Units (SI) is used for scientific measurements. Common SI units include:

Length: meter (m)
Mass: kilogram (kg)
Time: second (s)
Temperature: kelvin (K)

Prefixes

SI prefixes indicate multiples or fractions of units. Examples:

Milli- (m):
Micro- (μ):
Kilo- (k):

Practice Questions

What are the SI units for mass, length, time, and temperature?
Which SI unit and prefix would be most appropriate for measuring a person's body mass?
Which SI unit and prefix would be most appropriate for measuring the radius of an atom?
A basketball player is 2.11 m tall. Determine his height in cm.
A car's mass is 1,360,000 g. Determine the car's mass in kg.
A laser pulse is 0.15 ns long. Determine how long this pulse is in ps.
Determine how many μs there are in 1 s.
Specify the number of significant figures in each of the following:
- 0.1012
- 0.0125
- 1.00 × 102
- 0.00700
When expressed in scientific notation, the number -0.00297 becomes:
A scientist obtained the number 1290.3750 from a calculator. If this number actually has five (5) significant figures, show how it is written.
Report the total mass of three people weighing 53.0 kg, 60.4 kg, and 77.47 kg. Explain the rationale for the number of significant figures in your answer.
Calculate the number of significant figures in 0.00402 and 0.0402.
Calculate the number of significant figures in a graduated cylinder with marks at every mL, and a thermometer with marks at every 0.1°C. Indicate the estimated digit of the container, and explain the rationale for the number of significant figures.
What is the difference between 1.0 mL and 1.00 mL in terms of significant figures?
To verify the precision of a ruler, measure the length of a rod and explain the rationale for your answer.
The length of a human head for a student was approximately 24.5 cm. Write the estimated digit and explain the rationale for the number of significant figures in your answer.

Summary Table: Significant Figure Rules

Type of Digit	Significance	Example
Non-zero digits	Always significant	123 (3 significant figures)
Leading zeros	Never significant	0.0025 (2 significant figures)
Captive zeros	Always significant	1002 (4 significant figures)
Trailing zeros (with decimal)	Significant	100.0 (4 significant figures)
Trailing zeros (without decimal)	Not significant	100 (1 significant figure)

Additional info:

Significant figures are crucial for reporting scientific data accurately and for understanding the limitations of measurements.
SI units and prefixes are standardized to facilitate clear communication in science.