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## What Fun! It's: Practice with Scientific Notation!

### 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

```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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