Unit 1 · Lesson 1b

1bScientific Method and Measurement

Master the steps of the scientific method, design controlled experiments, and record measurements with proper SI units and significant figures.

Every experiment in physics — and every other science — relies on the scientific method and precise measurement. Without these tools, results cannot be trusted, compared, or built upon.

Lesson Overview

Science advances through a systematic process of observation, questioning, and testing. In this lesson you will learn the steps of the scientific method, how to design a controlled experiment, and how to record measurements using SI units and significant figures — the language of all quantitative science.

Key Concepts

Observation

Noticing a phenomenon using the senses or instruments

Hypothesis

A testable, falsifiable prediction about a phenomenon

Controlled Experiment

An experiment that changes one variable while holding all others constant

Independent Variable

The variable deliberately changed by the experimenter

Dependent Variable

The variable measured as a result of the experiment

SI Units

The International System of Units used worldwide in science

Significant Figures

Digits in a measurement that carry meaningful precision

Scientific Notation

A way to express very large or small numbers as a × 10ⁿ

Example 1

A student notices that plants near a window grow taller than plants in a dark corner. She hypothesizes: 'Plants that receive more light will grow taller.' Identify the independent and dependent variables.

Answer:Independent variable: amount of light received. Dependent variable: height of the plant. All other factors (water, soil, temperature, pot size) are controlled variables.
Example 2

A physicist measures the length of a lab bench as 1.847 m. How many significant figures does this measurement contain?

Answer:4 significant figures: 1, 8, 4, and 7. All non-zero digits are significant, and the trailing 7 after the decimal is also significant.
Example 3

Express the speed of light, 300,000,000 m/s, in scientific notation.

Answer:3.00 × 10⁸ m/s. Move the decimal 8 places to the left; the exponent is +8.
Example 4

A student measures the mass of a sample five times and gets: 12.3 g, 12.4 g, 12.3 g, 12.4 g, 12.3 g. Are these results precise? Accurate? (True value = 15.0 g)

Answer:Precise — the values cluster tightly together (range of 0.1 g). Not accurate — they are consistently far from the true value of 15.0 g. This indicates systematic error.
Example 5

Round 0.004 506 to 3 significant figures.

Answer:0.004 51. Leading zeros are not significant. The first three significant figures are 4, 5, 0. The next digit is 6 ≥ 5, so round up: 0.004 51.
Guided Problem 1

List the steps of the scientific method in order.

Hint: Start with an observation and end with communicating results.

Guided Problem 2

A student tests whether salt concentration affects the boiling point of water. Identify the independent variable, dependent variable, and two controlled variables.

Hint: What is being changed? What is being measured? What must stay the same?

Guided Problem 3

How many significant figures are in the measurement 0.00720 kg?

Hint: Leading zeros are never significant; trailing zeros after a decimal point are.

Guided Problem 4

Write 0.000 000 045 m in scientific notation.

Hint: Count how many places you move the decimal to get a number between 1 and 10.

Guided Problem 5

Explain the difference between a hypothesis and a theory in science.

Hint: Think about the amount of evidence supporting each.

Key Vocabulary

Hypothesis

A testable, falsifiable prediction that explains an observation.

Example: 'Increasing temperature will increase the rate of a chemical reaction' is a hypothesis.

Controlled Variable

A factor kept constant throughout an experiment so it does not affect the results.

Example: Keeping the same amount of water for all plant groups is a controlled variable.

Significant Figures

The meaningful digits in a measured or calculated value, indicating precision.

Example: 12.30 cm has 4 significant figures; the trailing zero is significant.

SI Units

The International System of Units — the globally accepted standard for scientific measurement.

Example: The SI unit of length is the metre (m); of mass, the kilogram (kg).

Interactive Practice — 5 Questions

1

Which step of the scientific method comes immediately after forming a hypothesis?

2

How many significant figures are in 0.00340?

3

In an experiment testing how temperature affects reaction rate, what is the dependent variable?

4

Which of the following correctly expresses 56,200 in scientific notation with 3 significant figures?

5

A set of measurements is accurate but not precise. This means:

Independent Practice

1

Design a controlled experiment to test whether the height from which a ball is dropped affects the height of its bounce. Identify all variables.

2

A student records a mass as 0.005 060 kg. How many significant figures does this value have? Explain your reasoning.

3

Convert 9.81 × 10⁻² km to metres using SI prefixes. Show your work.

4

Explain the difference between accuracy and precision using a dartboard analogy.

5

★ A scientist repeats an experiment 30 times and gets consistent results, but another lab cannot reproduce them. What does this suggest about the original experiment? What should be done next?

Challenge
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Common Mistakes

Counting leading zeros as significant figures (e.g., saying 0.0045 has 4 sig figs).

Leading zeros only locate the decimal point — they are never significant. 0.0045 has 2 sig figs.

Confusing the independent variable with the dependent variable.

The independent variable is what you change; the dependent variable is what you measure as a result.

Writing scientific notation with a coefficient greater than 10 (e.g., 56 × 10³).

The coefficient must be between 1 and 10: 5.6 × 10⁴.

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Math Tips

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To count sig figs: ignore leading zeros; count all other digits including trailing zeros after a decimal point. For 0.004 50: sig figs are 4, 5, 0 → 3 sig figs.

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For scientific notation, count how many places you move the decimal. Moving left → positive exponent; moving right → negative exponent.