Scientific Notation Practice: Understanding Exponents and Efficient Number Representation, Lecture notes of Mathematics

A comprehensive review of scientific notation, its importance, and how to convert between decimal notation and scientific notation. It includes numerous examples and practice problems to help students master the concept.

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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
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Download Scientific Notation Practice: Understanding Exponents and Efficient Number Representation and more Lecture notes Mathematics in PDF only on Docsity!

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 10^8 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 (10^3

dollars). For numbers smaller than one, the fraction is given as well.

smaller bigger Fraction 1/100 1/ Decimal notation 0.01 0.1 1 10 100 1,


Scientific notation 10 -^2 10 -^1 100 101 102

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. 10^2 = _______________ 4) 10-^2 = _________________
  2. 10^4 = _______________ 5) 10-^5 = _________________
  3. 107 = _______________ 6) 10^0 = __________________ Section B: Model: 2 x 10^2 = 200
  4. 3 x 10^2 = _________________ 10) 6 x 10-^3 = ________________
  5. 7 x 10^4 = _________________ 11) 900 x 10-^2 = ______________
  6. 2.4 x 10^3 = _______________ 12) 4 x 10-^6 = _________________ Section C: Now convert from decimal form into scientific notation. Model: 1,000 = 10^3
  7. 10 = _____________________ 16) 0.1 = _____________________ 14 ) 100 = _____________________ 17) 0.0001 = __________________
  8. 100,000,000 = _______________ 18) 1 = _______________________ Section D: Model: 2,000 = 2 x 10^3
  9. 400 = ____________________ 22) 0.005 = ____________________
  10. 60,000 = __________________ 23) 0.0034 = __________________
  11. 750,000 = _________________ 24) 0.06457 = _________________

Section F: Division (a little harder - we basically solve the problem as we did

above, using multiplication. But we need to "move" the bottom

(denominator) 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 10^3 ) Model: ----------- = 2 x (10^3 x 10-^2 ) = 2 x 10^1 = 20 (6 x 10^2 )

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

then solve the problem.

multiplication problem final answer (in sci. not.)

  1. (8 x 10^6 ) / (4 x 10^3 ) = __________________ ____________________
  2. (3.6 x 10^8 ) / (1.2 x 10^4 ) = ________________ _____________________
  3. (4 x 10^3 ) / (8 x 10^5 ) = ___________________ _____________________
  4. (9 x 10^21 ) / (3 x 10^19 ) = __________________ _____________________

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 10^4 ) + (2 x 10^3 ) = (3 x 10^4 ) + (0.2 x 10^4 ) = 3.2 x 10 4 ( same exponent ) = 32,000 ( final answer )

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

the problem.

same exponent final answer

  1. (4 x 10^3 ) + (3 x 10^2 ) = ___________________________________________
  2. (9 x 10^2 ) + (1 x 104 ) = ___________________________________________
  3. (8 x 10 6 ) + (3.2 x 10 7 ) = ___________________________________________
  4. (1.32 x 10-^3 ) + (3.44 x 10-^4 ) = _______________________________________

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 10^3 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 10

3

) + (3 x 10

2

46) (2 x 10^3 ) - (3 x 10^2 ) =

47) (32 x 10^4 ) x (2 x 10-^3 ) =

48) (9.0 x 1 0

4

) / (3.0 x 10

2

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?

Answers:

2 2

    1. 10,
    1. 10,000,
    1. 70,
    1. 2,
    1. 10-
    1. 4x10
    1. 6X
    1. 7.5X10
    1. 5x10-
    1. 3.4x
    1. 6.457x10-
  • 25a) 3x
  • 25b) 30,
  • 26a) 6x10
  • 26b) 60,000,
  • 27a) 5.5x
  • 27b) 5.
  • 28a) 8x - -
  • 28b) 0.
    1. 2x10
    1. 3x
    1. 5x10-
    1. 3x10
    1. 4.3x
    1. 1.09x10
    1. 4x10
    1. 1.664x - -
    1. 1.6x10 - 38) 2.5x10- - 39) 8.9919x10 - 40) -2.9999978x - 42) 41) Depends - 44) 5.53x10- 43)0.125, Yes - 45) 2.3x - 46) 1.7x - 47) 6.4x10 - 48) 3x