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Practice with Scientific Notation!

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Review of Scientific Notation

Scientific notation provides a place to hold the zeroes that come after a whole number or before a fraction. The number 100,000,000 for example, takes up a lot of room and takes time to write out, while 108 is much more efficient.

Though we think of zero as having no value, zeroes can make a number much bigger or smaller. Think about the difference between 10 dollars and 100 dollars. Even one zero can make a big difference in the value of the number. In the same way, 0.1 (one-tenth) of the US military budget is much more than 0.01 (one-hundredth) of the budget.

The small number to the right of the 10 in scientific notation is called the exponent. Note that a negative exponent indicates that the number is a fraction (less than one).

The line below shows the equivalent values of decimal notation (the way we write numbers usually, like "1,000 dollars") and scientific notation (103 dollars). For numbers smaller than one, the fraction is given as well.

	                smaller			bigger

Fraction		1/100	1/10

Decimal notation         0.01	0.1	1	10	100	1,000
 ____________________________________________________________________________
Scientific notation	 10-2	 10-1	 100	 101	 102	  103 
    

Practice With Scientific Notation

Write out the decimal equivalent (regular form) of the following numbers that are in scientific notation.

Section  A:    Model:   101  =     10  

1)  102  =  _______________		4)  10-2  =  _________________

2)  104  =  _______________		5)  10-5  =  _________________

3)   107 =  _______________ 		6)  100  =  __________________

Section B:    Model:   2 x 102  =      200  

7)  3 x 102  =  _________________	10)  6 x 10-3  =  ________________

8)  7 x 104  =  _________________	11)  900 x 10-2  =  ______________

9)  2.4 x 103   =  _______________ 	12)  4 x 10-6    =  _________________

Section C:  Now convert from decimal form into scientific notation.
    Model:    1,000  =  103

13)  10   =  _____________________	16)  0.1  =  _____________________

14)   100 =  _____________________	17)  0.0001  =  __________________

15)   100,000,000 = _______________	18)  1  =  _______________________

Section D:   Model:   2,000  =  2 x 103

19)  400  =  ____________________	22)  0.005 =  ____________________

20)  60,000  =  __________________	23)  0.0034  =  __________________

21)  750,000  =  _________________	24)  0.06457  =  _________________


More Practice With Scientific Notation

Perform the following operations in scientific notation. Refer to the introduction if you need help.

Section E: Multiplication (the "easy" operation - remember that you just need to multiply the main numbers and add the exponents).

Model: (2 x 102) x (6 x 103) =
12 x 105 =
1.2 x 106

Remember that your answer should be expressed in two parts, as in the model above. The first part should be a number less than 10 (eg: 1.2) and the second part should be a power of 10 (eg: 106). If the first part is a number greater than ten, you will have to convert the first part. In the above example, you would convert your first answer (12 x 105) to the second answer, which has the first part less than ten (1.2 x 106). For extra practice, convert your answer to decimal notation. In the above example, the decimal answer would be 1,200,000

                            scientific notation		decimal notation

25)  (1 x 103) x (3 x 101) =  ___________________	____________________




26)  (3 x 104) x (2 x 103) = ___________________	____________________




27)  (5 x 10-5) x (11 x 104) = __________________	____________________




28) (2 x 10-4) x (4 x 103) = ___________________	____________________


Section F: Division (a little harder - we basically solve the problem as we did above, using multiplication. But we need to "move" the bottom (denomenator) to the top of the fraction. We do this by writing the negative value of the exponent. Next divide the first part of each number. Finally, add the exponents).

   
             (12 x 103)   
Model:      ----------- =   2 x (103 x 10-2) = 2 x 101 = 20
             (6 x 102)

Write your answer as in the model; first convert to a multiplication problem, then solve the problem.

                           multiplication problem	  final answer 
                                                        (in sci. not.)

29)   (8 x 106) / (4 x 103)  =  __________________	_____________________




30)  (3.6 x 108) / (1.2 x 104) = ________________	_____________________




31)  (4 x 103) / (8 x 105) =  ___________________	_____________________




32)  (9 x 1021) / (3 x 1019) = __________________	_____________________

Section G: Addition The first step is to make sure the exponents are the same. We do this by changing the main number (making it bigger or smaller) so that the exponent can change (get bigger or smaller). Then we can add the main numbers and keep the exponents the same.

Model:  (3 x 104) + (2 x 103)   =  (3 x 104) + (0.2 x 104) 
                               =  3.2 x 104 
                               =  32,000

First express the problem with the exponents in the same form, then solve the problem.

			      same exponent		final answer

33)   (4 x 103) + (3 x 102)  =  ____________________	_______________________





34)   (9 x 102) + (1 x 104)  =  ____________________	_______________________







35)   (8 x 106) + (3.2 x 107) = ____________________	_______________________





36)   (1.32 x 10-3) + (3.44 x 10-4) = __________________	_______________________

Section H: Subtraction Just like addition, the first step is to make the exponents the same. Instead of adding the main numbers, they are subtracted. Try to convert so that you will not get a negative answer.

Model:  (3 x 104) - (2 x 103)  =  (30 x 103) - (2 x 103)  
                               =  28 x 103  
                               =  2.8 x 104  
				same exponent	      final answer

37)  (2 x 102) - (4 x 101) =  ______________________	___________________





38)  (3 x 10-6) - (5 x 10-7) = ______________________	______________________





39)  (9 x 1012) - (8.1 x 109)  = ____________________	______________________




 
40)   (2.2 x 10-4) - (3 x 102) = _____________________	______________________

And Even MORE Practice with Scientific Notation

(Boy are you going to be good at this.)

Positively positives!
41) What is the number of your street address in scientific notation?

42) 1.6 x 103 is what? Combine this number with Pennsylvania Avenue and what famous residence do you have?

Necessarily negatives!
43) What is 1.25 x 10-1? Is this the same as 125 thousandths?

44) 0.000553 is what in scientific notation?

Operations without anesthesia!
45) (2 x 103) + (3 x 102) = ?

46) (2 x 103) - (3 x 102) = ?

47) (32 x 104) x (2 x 10-3) = ?

48) (9.0 x 104) / (3.0 x 102) = ?

Food for thought........and some BIG numbers

49) The cumulative national debt is on the order of $4 trillion. The cumulative amount of high-level waste at the Savannah River Site, Idaho Chemical Processing Plant, Hanford Nuclear Reservation, and the West Valley Demonstration Project is about 25 billion curies. If the entire amount of money associated with the national debt was applied to cleanup of those curies, how many dollars per curie would be spent?


Back to Scientific Notation Page

Answers:

A) 1) 100	2) 10,000	3) 10,000,000		4) 0.01	
5) 0.00001 6) 1 B) 7) 300 8) 7,000 9) 2,400 10) 0.006
11) 9 12) 0.000004 C) 13) 101 14) 102 15) 108 16) 10-1
17) 10-4 18) 100 D) 19) 4x102 20) 6X104 21) 7.5X105 22) 5x10-3
23) 3.4x10-3 24) 6.457x10-2 E) 25a) 3x104 25b ) 30,000 26a) 6x107 26b) 60,000,000
27a) 5.5x100 27b) 5.5 28a) 8x10-1 28b) 0.8 F) 29) 2x103 30) 3x104 31) 5x10-3 32) 3x102 G) 33) 4.3x103 34) 1.09x104 35) 4x107 36) 1.664x10-3 H) 37) 1.6x102 38) 2.5x10-6 39) 8.9919x1012 40) -2.9999978x102 I) 41) Depends 42) 1600 43)0.125, Yes 44) 5.53x104
45) 2.3x103 46) 1.7x103 47) 6.4x102 48) 3x102
49) 160 dollars/curie

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