Scientific NotationThis worksheet borrowed from: http://www.ieer.org/clssroom/scidrill.htmlScientific 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 1/10 Decimal notation 0.01 0.1 1 10 100 1,000 ____________________________________________________________________________ Scientific notation 10^{-2} 10^{-1} 10^{0} 10^{1} 10^{2} 10^{3} Practice With Scientific NotationWrite out the decimal equivalent (regular form) of the following numbers that are in scientific notation. Section A: Model: 10^{1} = 10 1) 10^{2} = _______________ 4) 10^{-2} = _________________ 2) 10^{4} = _______________ 5) 10^{-5} = _________________ 3) 10^{7} = _______________ 6) 10^{0} = __________________ Section B: Model: 2 x 10^{2} = 200 7) 3 x 10^{2} = _________________ 10) 6 x 10^{-3} = ________________ 8) 7 x 10^{4} = _________________ 11) 900 x 10^{-2} = ______________ 9) 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} 13) 10 = _____________________ 16) 0.1 = _____________________ 14) 100 = _____________________ 17) 0.0001 = __________________ 15) 100,000,000 = _______________ 18) 1 = ______________________ Section D: Model: 2,000 = 2 x 10^{3} 19) 400 = ____________________ 22) 0.005 = ____________________ 20) 60,000 = __________________ 23) 0.0034 = __________________ 21) 750,000 = _________________ 24) 0.06457 = _________________ More Practice With Scientific NotationPerform 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). 12 x 10^{5} = 1.2 x 10^{6} 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: 10^{6}). 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 10^{5}) to the second answer, which has the first part less than ten (1.2 x 10^{6}). 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 10^{3}) x (3 x 10^{1}) = ___________________ ____________________ 26) (3 x 10^{4}) x (2 x 10^{3}) = ___________________ ____________________ 27) (5 x 10^{-5}) x (11 x 10^{4}) = __________________ ____________________ 28) (2 x 10^{-4}) x (4 x 10^{3}) = ___________________ ____________________ 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 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.) 29) (8 x 10^{6}) / (4 x 10^{3}) = __________________ _____________________ 30) (3.6 x 10^{8}) / (1.2 x 10^{4}) = ________________ _____________________ 31) (4 x 10^{3}) / (8 x 10^{5}) = ___________________ _____________________ 32) (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} = 32,000First express the problem with the exponents in the same form, then solve the problem. same exponent final answer 33) (4 x 10^{3}) + (3 x 10^{2}) = ____________________ _______________________ 34) (9 x 10^{2}) + (1 x 10^{4}) = ____________________ _______________________ 35) (8 x 10^{6}) + (3.2 x 10^{7}) = ____________________ _______________________ 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 10^{4}) - (2 x 10^{3}) = (30 x 10^{3}) - (2 x 10^{3}) = 28 x 10^{3} = 2.8 x 10^{4} same exponent final answer 37) (2 x 10^{2}) - (4 x 10^{1}) = ______________________ ___________________ 38) (3 x 10^{-6}) - (5 x 10^{-7}) = ______________________ ______________________ 39) (9 x 10^{12}) - (8.1 x 10^{9}) = ____________________ ______________________ 40) (2.2 x 10^{-4}) - (3 x 10^{2}) = _____________________ ______________________ And Even MORE Practice with Scientific Notation(Boy are you going to be good at this.)
Positively positives! 42) 1.6 x 10^{3} is what? Combine this number with Pennsylvania Avenue and what famous residence do you have?
Necessarily negatives! 44) 0.000553 is what in scientific notation?
Operations without anesthesia! 46) (2 x 10^{3}) - (3 x 10^{2}) = ? 47) (32 x 10^{4}) x (2 x 10^{-3}) = ? 48) (9.0 x 10^{4}) / (3.0 x 10^{2}) = ? |