CHAPTER 17 Decimals & Percents

DECIMALS  We operate numerically within a base-ten number system.  The basic idea revolves around the idea that each place value is connected to the next with a 10 to 1 ratio.  Example: 10 ones makes 1 ten  Example: 100 ones makes 1 hundred  Example: 234 is 234 ones, 23 tens and 4 ones, and 2 hundreds and 3 tens and 4 ones.  This extends infinitely in both directions along a continuum.  As we move to the left on this continuum, we multiply by 10. To the right, we divide by 10.  This motivates the usage of a decimal point. A decimal point marks the position of the unit.  Example: represent 24 ones, 1 tenth and 2 one-hundreths. We will model this using the blocks.

PRACTICE PROBLEMS  Determine the decimal equivalents to the following fractions. Draw a model.  3/10  1/2  1/4  7/4  3/8  Determine the decimal equivalents to the following fractions. Draw a model.  1/5  1/3  1/9  4/9

TERMINATING, INFINITE REPEATING, AND INFINITE NON-REPEATING DECIMALS  Real numbers that have terminating or infinite repeating decimal expansions possess fraction equivalents.  Examples: 1/3 =.3333…  Examples: 2/5 =.4  Real numbers that have infinite non-repeating decimal expansions do not possess fraction equivalents.  Example: Pi = …  Examples: Square root of 2 = …