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Numbers and Their Application to Math and Science

Homework for Numbers Lesson 8

  1. Compare in magnitude the decimal representations for: 22/7, 355/113, and .

     

  2. Put in order from least to greatest:
                           
    .1958, .1958, .1958,  .1958, .1958,

     

  3. Convert 468.468468... into the ratio of two integers.

     

  4. Find a rational number between 2/7 and 1/3.

     

  5. Simplify: 3 × 15 + 2 × 6.

     

  6. Simplify: 2 × 6 + 32 ÷ 42 + 5.

     

  7. Simplify: 4 × [2 - 3(x + 1)2] × (2 - 10 ÷ 5).

     

  8. Solve for x and graph on a number line: 14 - 3x < 13.

     

     

  9. Solve for x and graph on a number line: 2x - 4 > -11(x - 2).

     

     

  10. Expand and simplify: (2x - 3y)(2x + 3y)

     

  11. Factor completely: x2 + 8x - 20     and     x2 + 9x + 20.

     

     

  12. Calculate the decimal representation of the unit fractions with denominators 2 through 21. Clearly indicate the repeat length or whether it terminates (rep.len.=0). Can you find any pattern to the repeat lengths? (Note: this one problem is over half the homework points.)

     

    FractionDecimal ValueTerminates? non-rep. Length Repeat Length
    1/20.5 yes 1 0
    1/30.33333... no 0 1
    1/4     
    1/5     
    1/60.16666... no11
    1/7     
    1/8     
    1/9     
    1/10     
    1/11     
    1/12     
    1/13     
    1/14     
    1/15     
    1/16     
    1/17     
    1/18     
    1/19     
    1/20     
    1/21     

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