Lesson 13

Definition of Scientific Notation

Lesson Narrative

In the previous few lessons, students have built familiarity with arithmetic involving powers of 10 to solve problems with very large and very small quantities. This lesson formalizes what they have learned by introducing the definition of scientific notation. A number is said to be in scientific notation if it is written as a product of two factors: the first factor is a number greater than or equal to 1, but less than 10; and the second factor is an integer power of 10. This definition does not include negative numbers for simplicity. Students must attend to precision as they decide whether or not numbers are in scientific notation and convert to scientific notation (MP6).

Learning Goals

Teacher Facing

• Identify (in writing) numbers written in scientific notation, and describe (orally) the features of an expression in scientific notation.

Student Facing

Let’s use scientific notation to describe large and small numbers.

Required Preparation

The blackline master for Scientific Notation Matching has three sets of cards. Set A is for the teacher to demonstrate the process, so only one copy of set A is needed. Cut out one set of cards (either set B or set C) for every 2 students. If possible, copy each complete set on a different color of paper, so that a stray slip can quickly be put back.

Student Facing

• I can tell whether or not a number is written in scientific notation.

Building On

Building Towards

Glossary Entries

• scientific notation

Scientific notation is a way to write very large or very small numbers. We write these numbers by multiplying a number between 1 and 10 by a power of 10.

For example, the number 425,000,000 in scientific notation is $$4.25 \times 10^8$$. The number 0.0000000000783 in scientific notation is $$7.83 \times 10^{\text-11}$$.