In which equation is the value of the largest? Explain your reasoning.
How many times the size of 0.81 is 810?
5.2
Activity
Fractionally Speaking: Powers of Ten
Work with a partner. One partner finds the values of the expressions labeled “Partner A” and the other does the same for the expressions labeled “Partner B.” Then compare your results.
Find each product or quotient. Be prepared to explain your reasoning.
Partner A
Partner B
Use your work in the previous problems to find and . Explain your reasoning.
Pause here for a class discussion.
Find each product. Show your reasoning.
5.3
Activity
Fractionally Speaking: Multiples of Powers of Ten
Select all expressions that are equivalent to . Be prepared to explain your reasoning.
Find the value of . Show your reasoning.
Find the value of each product by writing equivalent expressions. Show your reasoning.
Student Lesson Summary
We can use fractions like and to reason about the location of the decimal point in a product of two decimals.
Let’s take as an example. There are several ways to find the product:
We can interpret it as 24 groups of 1 tenth (or 24 tenths), which is 2.4.
We can think of it as , which is equal to (and also equal to 2.4).
Because multiplying by has the same result as dividing by 10, we can also think of it as, which is equal to 2.4.
Similarly, we can think of as 7 tenths times 9 hundredths, and write:
We can rearrange the whole numbers and fractions:
This tells us that .
Here is another example: To find , we can think of 1.5 as 15 tenths and 0.43 as 43 hundredths. We can write the tenths and hundredths as fractions and rearrange the factors.
Multiplying 15 and 43 gives us 645, and multiplying and gives us . So is , which is 0.645.
Glossary
None
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