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Mat 391 Decimals Qz

NAME                                             

Evaluate the following as appropriate.  Show ALL your work.  Explain your answer(s) thoroughly, particu­larly if the work shown on your test paper does not fully justify your answer.  Answer(s) without neat and logical sup­porting work will not receive credit. The intent is to explain the algorithms involved in the decimal arithmetic used to obtain the answers, so                              NO CALCULATORS!

1.  Use fractional notation to explain why/how the following rational numbers are defined as a decimal.

      a.   

      b. 

      c. 

2.  Find the sum of  3.26 + 14.7  using fractional notation to fully exhibit and explain the algorithm of addition for terminating decimals.

3.  State the definition of the operation of subtraction for decimal numbers.  Use the definition to find the difference between 14.7  and  3.26.

4.  Find the product of  (4.62)(2.4)  using fractional notation to fully exhibit and explain the algorithm of multiplication for terminating decimals.

5.  Find the quotient of ( 1.2032 ) ( 0.32 ) using both decimal and fractional notation to fully exhibit and explain the algorithm of division for terminating decimals.  Use arrows to show where each method uses and/or explains the process often stated as "move the decimal point  'so many'  places to the right and divide as whole numbers."  Be sure to equate the fractional representation of the "so many" places to the decimal notation.

6.  a.  Can     be written as a terminating decimal?                         .  Fully explain your answer.

     b.  Can     be written as a terminating decimal?                      .  Fully explain your answer.

7.  Show all you work and discuss your steps as necessary to prove the following answers.

      a.  Use the "powers of ten method" to express the fraction    as a decimal.

      b.  Use the "divide the denominator into the numerator" to express fraction    as a decimal.

c.  Which method (and why) would you recommend to a capable 5th grader to solve this problem who has only pencil and paper available?

8.  Complete the following table.  DO NOT round-off any of your answers.

FRACTION	DECIMAL	PERCENT (%)
3
		0.33%
	30.3
		%

9.  a.  What percent of 28 is 21?                      .

      b.  What is  7  percent of  (   )?                      .

      c.  Thirty-three and one-third percent of 15 is                     ?

      d.  33 = 11%  of                     ?

10.  It takes    cups of water to make  2  packages of putty dough.   How many packages of putty dough can be made with 9 cups of water?                      .                  

11.  Find N       |                       |                       |                       |                       |                 |                       |

                  -5 + √2                                                                                       N                  5 + √2

                                                                                                                                    N=                                       .

12.  Use the number line below to construct and plot  1 + √2

                        |                       |                       |                       |                       |                 |                       |

                  -2               -1               0                1                2            3                4

Bonus:  (5 pts, no partial credit).  Using expanded notation, completely write out the first three steps that verify the algorithm which says that    =