Chapter 2: Problem 30

State the rules governing the number of significant figures that result from each of the following operations. a. addition and subtraction b. multiplication and division

Short Answer

Expert verified

For addition and subtraction, use the number with the fewest decimal places. For multiplication and division, use the number with the fewest significant figures.

Step by step solution

Title - Addition and Subtraction Rules

When performing addition or subtraction, the result should have the same number of decimal places as the number with the fewest decimal places in the original numbers. For example, if you add 12.34 and 4.5, the result should be rounded to one decimal place because 4.5 has only one decimal place.

Title - Multiplication and Division Rules

When performing multiplication or division, the result should have the same number of significant figures as the number with the fewest significant figures among the original numbers. For example, if you multiply 2.34 (3 significant figures) by 0.56 (2 significant figures), the result should be rounded to 2 significant figures.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

addition and subtraction significant figures

When dealing with addition and subtraction in significant figures, it's essential to focus on decimal places. The rule is simple: your result should have the same number of decimal places as the number in your original set with the fewest decimal places. This ensures your answer maintains the same precision as the least precise measurement.

For instance, if you add 12.34 and 4.5, you notice that 4.5 has only one decimal place. So, your result should also be rounded to one decimal place, making the sum 16.8. This rule helps keep numerical accuracy consistent across your calculations.

multiplication and division significant figures

For multiplication and division, the emphasis shifts from decimal places to significant figures. The resulting value should have the same number of significant figures as the number with the fewest significant figures in your original numbers.

Consider multiplying 2.34 (which has 3 significant figures) by 0.56 (which has 2 significant figures). After multiplying, you get 1.3104. However, since 0.56 has only 2 significant figures, your final answer should be rounded to 2 significant figures, making it 1.3. This rule ensures that the precision of your result aligns with the least precise measurement involved.

decimal places rounding rules

Rounding is important for maintaining precision and accuracy in your results. When rounding decimal places, follow these simple rules:

If the number to the right of your rounding digit is 5 or greater, round up the rounding digit by 1.
If the number to the right of your rounding digit is less than 5, keep the rounding digit as it is.

For example, if you need to round 2.346 to two decimal places, you look at the third decimal place (6). Since 6 is greater than 5, you round 4 up to 5, making the number 2.35. Proper rounding ensures your calculations are as accurate and reliable as possible.

Recommended explanations on Chemistry Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

State the rules governing the number of significant figures that result from each of the following operations. a. addition and subtraction b. multiplication and division

Short Answer

Step by step solution

Title - Addition and Subtraction Rules

Title - Multiplication and Division Rules

Key Concepts

addition and subtraction significant figures

multiplication and division significant figures

decimal places rounding rules

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Chemistry Textbooks

Chemical Analysis

Making Measurements

Kinetics

Ionic and Molecular Compounds

Organic Chemistry

The Earths Atmosphere

Study anywhere. Anytime. Across all devices.