Section 1.5: Critical thinking and number sense: What do these figures mean?
Magnitudes
Example 1: How many millions are in a trillion?
Example 2 (Using powers of 10): In the 1980s, one of the book’s authors owned a
microcomputer that had a memory of 64 kilobytes. The computer on his desk today has 4
gigabytes of memory. Is the memory of today’s computer tens, hundreds, or thousands of
times as large as the old computer’s memory?
Example 3 (Understanding large numbers): As of January 2009, the national debt was
about 10.6 trillion dollars, and there were about 305 million people in the United States.
Determine how much debt is owed per person.
Example 4 (Estimating costs): You’re going on a 1,211 mile trip, and your car gets about 29
miles per gallon. Gas prices along your route average $1.99. Estimate the cost of gasoline for
this trip rounding the distance to 1200 miles, the mileage to 30 miles per gallon, and the cost of
gas to $2.00 per gallon.
Calculate the cost without using estimation. Compare.
Example 5 (Areas): Carpet is priced in both square feet and square yards. There are 3 feet in a
yard. How many square feet are in a square yard?
Example 6 (Distance): A lightyear is the distance light travels in a year. Light travels 186,000
miles in a second. How many trillion miles long is a lightyear?
Practice Problems from Exercise Set 1.5: 1, 3, 5, 13, 19, 21