Module 1: Principles of Science

 

PHYS-1315 M1L1 Significant Figures and Scientific Notation

"One accurate measurement is worth a thousand expert opinions."
— Grace Hopper


Have you ever wondered why scientists and engineers are so picky about numbers? Imagine building a bridge, launching a rocket, or even baking a cake—using the wrong number of digits could mean disaster or a delicious mess! In this lesson, you’ll discover how significant figures and scientific notation help us communicate measurements clearly, avoid costly mistakes, and make sense of the world’s tiniest and largest quantities. By the end, you’ll see how a few simple rules can make you a more confident problem-solver in science, engineering, and everyday life.

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Course Competencies and Learning Objectives

A ★ indicates that this page contains content related to that LO.

CC1.1 Solve problems related to scientific units of measurement and significant figures

LO1.1.1 Identify the terms used in scientific communication

★ LO1.1.2 Apply the rules of significant figures

LO1.1.3 Identify SI and imperial units

LO1.1.4 Match the SI prefixes with their corresponding values

LO1.1.5 Apply unit conversion

LO1.1.6 Demonstrate units displayed in the correct style

Optional Reading

Deeper Dive (Extra Enrichment)

Curious how these ideas show up in the real world? Check out these resources to see how engineers, scientists, and data analysts use significant figures and scientific notation every day.

Media

Ready to see these concepts in action? Watch these short videos and jot down anything that surprises you or makes you think differently about numbers!

Video 1: Significant Figures

Significant Figures

This video goes over the arithmetic rules of significant figures. Be sure to take note of the differences in the rules for addition vs multiplication.

  • Explains the purpose of significant figures in scientific measurement and computation.
  • Emphasizes that measurements have limited precision, and results should not claim more precision than the inputs.
  • Demonstrates how to add numbers with different precision and why only measured digits are significant.
  • Shows how to use significant figures in addition, subtraction, multiplication, and division.
  • Explains the difference between measured and exact quantities.
  • Provides worked examples and rules for rounding results to the correct number of significant figures.

Time: 11:20

ASL version of Significant Figures
Direct link to non-ASL version

Video 2: Working with Scientific Notation

Working with Scientific Notation

This video covers what scientific notation is, how to use it on a calculator, and arithmetic with it.

  • Introduces two methods for computing with scientific notation: using a scientific calculator and manual calculation.
  • Explains how to enter numbers in scientific notation on calculators and in computer programs.
  • Demonstrates manual calculation by separating numbers and exponents, performing arithmetic on each, and recombining.
  • Walks through a detailed example multiplying and dividing numbers in scientific notation.
  • Provides practice problems for students to try on their own.

Time: 4:20

ASL Version of Working with Scientific Notation
Direct link to non-ASL version

Practice and Apply - Conceptual

Sort Items

Test your instincts! Can you quickly spot which numbers have two or three significant figures? Drag and drop to find out.

Answer Bank

  • 4.2
  • 55.
  • 1.9 × 103
  • 820
  • 0.010
  • 0.0190
  • 4.20
  • 9.20 × 102
  • 1.01
  • 157

Two Significant Figures

  • 4.2
  • 55.
  • 1.9 × 103
  • 820
  • 0.010

Three Significant Figures

  • 0.0190
  • 4.20
  • 9.20 × 102
  • 1.01
  • 157

Practice and Apply - Computational

Now it's your turn to practice calculating with significant figures! Work through the problems below, and remember to pay close attention to the rules for addition and multiplication. Good luck!

Important: Strict Answer Formatting Required

Pro tip: In science, details matter! Make sure your answers follow the exact format—just like a scientist or engineer would.

  • Significant Figures: Use the correct number of significant digits. Do not add extra digits or zeros unless they are significant.
  • Scientific Notation: Enter scientific notation as 1.2*10^6 (not 1.20*10^6 unless two decimals are significant).
  • No Extra Characters: Do not include units, spaces, or unnecessary symbols unless instructed.

If your answer is not accepted, double-check your formatting!

The questions are visible, but the answers are hidden to encourage you to try solving them on your own first. When you're ready, you can reveal the answers to check your work.

Compute the following quantity with the correct number of significant figures: 11.2 × 39.18

Compute the following quantity with the correct number of significant figures: 11.2 × 39.18

The operation here is multiplication, so we can compute:

11.2 × 39.18 = 438.816

Now, we need to round to the correct number of digits. Because this is multiplication, the number of significant figures is the minimum number of significant figures of the inputs. In this problem, the first number has three significant figures (the 1, the 1, and the 2), and the second number has four significant figures (the 3, the 9, the 1, and the 8). Therefore, the number of significant figures in the result is min(3, 4) = 3; don't forget to round:

438.816 → 439.

Compute the following quantity with the correct number of significant figures: 1.2×106 + 980

Compute the following quantity with the correct number of significant figures: 1.2×106 + 980

Both numbers have two significant figures. The digits in the first number that are significant are the 1 and the 2, and the two numbers in the second that are significant are the 9 and the 8; the 0 is not significant. To perform the addition, we need to put both numbers in the same form:

1.2×106 + 0.00098×106 = 1.20098×106

Because the operation is addition, we need to look for the least precise digit. In the first number, the least precise digit is one digit past the decimal point, and in the second it is the fifth. The least precise digit in the result is the minimum of those two, which is 1. Therefore, the result is rounded to the first digit past the decimal point:

1.20098×106 → 1.2×106

Because the first number is so large and has fairly limited precision, the addition of a relatively small number has no change.

To enter this value in Canvas, you would type: 1.2*10^6

Compute the following quantity with the correct number of significant figures: 2.47 × 3.1

Compute the following quantity with the correct number of significant figures: 2.47 × 3.1

This is a multiplication problem. First, multiply the numbers:

2.47 × 3.1 = 7.657

Now, determine the correct number of significant figures. 2.47 has three significant figures, and 3.1 has two significant figures. The result should have the minimum, which is two significant figures.

7.657 → 7.7

So, the answer is 7.7.

Compute the following quantity with the correct number of significant figures: 4.0572 × 1.09

Compute the following quantity with the correct number of significant figures: 4.0572 × 1.09

Multiply the numbers:

4.0572 × 1.09 = 4.422348

4.0572 has five significant figures, 1.09 has three. The result should have three significant figures.

4.422348 → 4.42

So, the answer is 4.42.

Note: In Canvas, enter your answer as 4.42 (do not include extra digits or trailing zeros unless they are significant).