Numbers and Their Application to Math and Science

Odd Solutions for Numbers Lesson 4

1. Write out the definition of googol from the dictionary.
   Answer: 1 followed by 100 zeroes (10¹⁰⁰)

2.  

3. Compare the American, French, British, and German number systems for the term billion and milliard.
   Answer: American and French number systems are the same; British and German number systems are the same. American billion and British milliard are the same (10⁹), billion in British number system is/was? 10¹².
4. Try here!

5. Solve for x: 2²•2³ = 2^x and (2²)³ = 2^z.

   A. x = 5, z = 6

6.  

7. Write a huge number using ONLY three 9's (and nothing else).
   Answer: 999 < 99⁹ < 9⁹⁹ << 9⁹⁹

8.  

9. Calculate 2²⁰ and 2³⁰. Compare with 10⁶ and 10⁹, respectively.
   Answer: 2²⁰= 1,048,576 and 10⁶=1,000,000, 5% bigger
          2³⁰=1,073,741,824 and 10⁹=1,000,000,000, 7% bigger.
10.  

11. Madam I'm Adam. Name no one man. Some numbers are palindromes. (look it up in dictionary). Write some prime 3 digit palindrome.
    Answer: 101, 131, etc. (was 1 bonus pt each extra).

12. Convert 1101₂ into base 10.

    A.1101₂ = 2³ + 2² + 2⁰ = 8 + 4 + 1 = 13

13. Convert 27 into base 2.

    A. 27 = 16 + 8 + 2 + 1 = 2⁴ + 2³ + 2¹ + 2⁰ = 11011₂

14.  

15. Convert 34₅ into base 10.

    A. 34₅ = 3 × 5¹ + 4 × 5⁰ = 19

16.  

17. Change 210 hours into days and hours.

    A. 210 hours = 8 days and 18 hours

18.  

19. 10•16³+3•16²+11•16¹+5•16⁰=41909.

20.  

21. Simplify:
    

    1. 15x4y5	=	315x41y53	=	3xy3
       5x3y2		15x3y2		1

    2. 7x - 28	=	7(x - 4)	=	7(x - 4)	=	7
       3x - 12		3(x - 4)		3(x - 4)		3

    3. -28yx5	=	4-28yx5	=	-4
       35x6y2		535x61y21		5xy

    4. Multiply: (4d + 7)(4d - 7) = 16d² - 49

    5. Expand: (4x + 5)² = 16x² + 40x + 25

    6. Expand: (4c - 5d)(2x + 3y) = 8cx + 12cy - 10dx - 15dy