In this lesson, students make sense of the rule that and extend the rules they have developed for working with values with exponents to include situations with negative exponents. This type of reasoning appears again in a later course when students extend the rules of exponents to make sense of exponents that are not integers.

Students develop their fluency as they mentally determine missing values from equations involving powers of 10. Next students complete a table comparing expressions written using exponents with those written as a decimal and as a fraction. The table includes both large values and values less than 1. By looking at the multiplier required to increase or decrease the exponent by 1, students correspond a power of 10 with a negative exponent to repeated multiplication by (MP8).

Students reinforce this understanding by matching a series of expressions written with negative exponents to a corresponding expression written using repeated multiplication (MP7).