CHAPTER 17Decimals & 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: 24.12 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 = 3.14159265358979323846264… Examples: Square root of 2 =

1.4142135623730950488016887242096…