Unit 7, Lesson 8
Representing Large Numbers on the Number Line
Accelerated 7
8.1
Warm-up
Base-Ten Representations Matching
Match each expression to one or more diagrams that could represent it. For each match, explain what the value of a single small square would have to be.
2 large squares each composed of 100 blocks, 10 by 10, 4 small squares each 1 block.
2 large squares each composed of 100 blocks, 10 by 10, 4 rectangles composed of 10 blocks, 10 by 1.
2 rectangles composed of 10 blocks, 10 by 1, 4 small squares, each 1 block.
Student Lesson Summary
Suppose we want to compare the number of pennies the U.S. Mint made in 2020, about 7,600,000,000, to the number of one dollar bills printed by the U.S. Bureau of Engraving and Printing in the same year (about 1.6 billion). There are many ways to do this.
We could write 1.6 billion as a decimal value, 1,600,000,000, and then we can tell that in 2020 there were more pennies made than one dollar bills printed.
Or we could use powers of 10 to write these numbers:
Since both numbers are written using the same power of 10, we can compare 7.6 to 1.6 and confirm that there were more pennies made than one dollar bills printed in 2020.
We could also plot these two numbers on a number line. We would need to carefully choose our end points to make sure that both numbers can be plotted. Here is a number line with the two values plotted:
A number line, 11 tick marks, 0, 1 times 10 to the power 9, 2 times 10 to the power 9, 3 times 10 to the power 9, 4 times 10 to the power 9, 5 times 10 to the power 9, 6 times 10 to the power 9, 7 times 10 to the power 9, 8 times 10 to the power 9, 9 times 10 to the power 9, 10 to the power 10. A point labeled People is between 7 times 10 to the power 9, and 8 times 10 to the power 9. A point labeled Pennies is just to the left of 9 times 10 to the power 9.
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