Scientific notation/significant figures worksheet answers provide a comprehensive guide to understanding the fundamental concepts of scientific notation and significant figures, empowering students with the knowledge and skills necessary to excel in scientific measurements and calculations.

This guide delves into the significance of scientific notation, explaining its role in representing extremely large or small numbers in a concise and manageable format. It also explores the concept of significant figures, emphasizing their importance in ensuring the accuracy and precision of scientific measurements.

Scientific Notation

Scientific notation is a way of expressing very large or very small numbers in a more compact and convenient form. It is based on the idea of using powers of 10 to represent the number.

To write a number in scientific notation, we first need to determine the power of 10 that is closest to the number. For example, the number 123,456 is closest to 100,000, which is 10 ⁵. We then divide the number by the power of 10 to get a number between 1 and 10. In this case, we divide 123,456 by 10 ⁵to get 1.23456.

The number in scientific notation is then written as the number between 1 and 10, followed by the power of 10. In this case, the number in scientific notation is 1.23456 × 10 ⁵.

Advantages of Using Scientific Notation, Scientific notation/significant figures worksheet answers

• Scientific notation makes it easier to compare very large or very small numbers.
• Scientific notation makes it easier to perform calculations with very large or very small numbers.
• Scientific notation is the standard way of expressing numbers in many scientific fields.

Significant Figures

Significant figures are the digits in a number that are known with certainty. The number of significant figures in a number is important because it tells us how accurate the number is.

There are three rules for determining the number of significant figures in a number:

1. All non-zero digits are significant.
2. Zeros between non-zero digits are significant.
3. Trailing zeros after a decimal point are significant.

For example, the number 123.45 has four significant figures, while the number 123.00 has three significant figures.

Impact of Significant Figures on Calculations

When we perform calculations with numbers that have different numbers of significant figures, we need to be careful to round the answer to the correct number of significant figures.

The rule for rounding is that the answer should have the same number of significant figures as the number with the fewest significant figures.

For example, if we multiply 123.45 by 1.23, the answer should be rounded to three significant figures, since 1.23 has only three significant figures.

Answers to Common Questions: Scientific Notation/significant Figures Worksheet Answers

What is scientific notation?

Scientific notation is a method of expressing extremely large or small numbers in a concise and manageable format using powers of 10.

What are significant figures?

Significant figures are the digits in a number that are known with certainty, plus one estimated digit.

Why are significant figures important?

Significant figures are important because they indicate the accuracy and precision of a measurement.