In this activity students identify expressions written in scientific notation and practice converting numbers into scientific notation. Students make use of structure to determine if a number is written in scientific notation (MP7).

The purpose of this discussion is to identify what a number written using scientific notation looks like. Begin by inviting students to share which speeds were not written using scientific notation and how they rewrote those expressions.

If necessary, emphasize that a number is said to be in scientific notation when 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 — for example 1.2, 8, 6.35, or 2.008.
• The second factor is an integer power of 10 — for example , , or .

Make sure that students understand how to rewrite an expression that is a multiple of a power of 10 but is not in scientific notation. Consider asking these questions using the speed of light through diamond as an example:

• “Why is not written in scientific notation?” (The first factor is not between 1 and 10.)
• “How can the first factor be rewritten so that it is between 1 and 10?” (124 can be rewritten as 1.24.)
• “Why can’t we simply change it to ?” (That would change the value of the expression.)
• “How can we rewrite 124 as an equivalent expression that has 1.24 in it?” (Write it as or )
• “What is the equivalent expression in scientific notation?” ( , which is .)

If time allows, ask students to come up with at least two examples of numbers that are not in scientific notation. Select responses that highlight the fact that the first factor must be between 1 and 10 and other responses that highlight that one of the factors must be an integer power of 10.

In this partner activity, students take turns matching a decimal value to an equivalent expression written as a multiple of a power of 10. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).

Once all groups have completed the Card Sort, discuss: 

• “Which matches were tricky? Explain why.”
• “Did you need to make adjustments in your matches? What might have caused an error? What adjustments were made?”
• “Which cards were written in scientific notation? How do you know?” (The cards written in scientific notation have a factor that is between 1 and 10 and a factor that is a power of 10.)