What Fun!It's Practice with Scientific Notation!Review of Scientific NotationScientific notation provides a place to hold the zeroes that come after awhole 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 moreefficient.Though we think of zero as having no value, zeroes can make a number muchbigger or smaller. Think about the difference between 10 dollars and 100dollars. 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 than0.01 (one-hundredth) of the budget.The small number to the right of the 10 in scientific notation is called theexponent. Note that a negative exponent indicates that the number is afraction (less than one).The line below shows the equivalent values of decimal notation (the way wewrite numbers usually, like "1,000 dollars") and scientific notation (103dollars). For numbers smaller than one, the fraction is given as well.smallerbiggerFraction1/1001/10Decimal notation0.010.11101001,000-2-10123Scientific notation101010101010
Practice With Scientific NotationWrite out the decimal equivalent (regular form) of the following numbersthat are in scientific notation.1Section A: Model: 10 1024) 10 -245) 10 1) 10 -52) 10 703) 10 2Section B: Model: 2 x 10 6) 10 200210) 6 x 10 -3411) 900 x 107) 3 x 10 8) 7 x 10 39) 2.4 x 10-6 12) 4 x 10-2 Section C: Now convert from decimal form into scientific notation.Model: 1,000 10313) 10 16) 0.1 14) 100 17) 0.0001 15) 100,000,000 18) 1 Section D: Model: 2,000 2 x 10319) 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 theintroduction if you need help.Section E: Multiplication (the "easy" operation - remember that you justneed to multiply the main numbers and add the exponents).Model: (2 x 102) x (6 x 103) 12 x 105 1.2 x 106Remember that your answer should be expressed in two parts, as in themodel above. The first part should be a number less than 10 (eg: 1.2) and thesecond part should be a power of 10 (eg: 106). If the first part is a numbergreater than ten, you will have to convert the first part. In the aboveexample, you would convert your first answer (12 x 105) to the secondanswer, 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 decimalanswer would be 1,200,000scientific notationdecimal notation314325) (1 x 10 ) x (3 x 10 ) 26) (3 x 10 ) x (2 x 10 ) -5427) (5 x 10 ) x (11 x 10 ) -4328) (2 x 10 ) x (4 x 10 )
Section F: Division (a little harder - we basically solve the problem as we didabove, using multiplication. But we need to "move" the bottom(denominator) to the top of the fraction. We do this by writing the negativevalue of the exponent. Next divide the first part of each number. Finally, addthe exponents).3(12 x 10 )3-21Model: ----------- 2 x (10 x 10 ) 2 x 10 202(6 x 10 )Write your answer as in the model; first convert to a multiplication problem,then solve the problem.multiplication problem6329) (8 x 10 ) / (4 x 10 ) 8430) (3.6 x 10 ) / (1.2 x 10 ) 3531) (4 x 10 ) / (8 x 10 ) 211932) (9 x 10 ) / (3 x 10 ) final answer(in sci. not.)
Section G: Addition The first step is to make sure the exponents are thesame. 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 themain numbers and keep the exponents the same.4344Model: (3 x 10 ) (2 x 10 ) (3 x 10 ) (0.2 x 10 )4 3.2 x 10 (same exponent) 32,000 (final answer)First express the problem with the exponents in the same form, then solvethe problem.same exponent3224final answer33) (4 x 10 ) (3 x 10 ) 34) (9 x 10 ) (1 x 10 ) 6735) (8 x 10 ) (3.2 x 10 ) -3-436) (1.32 x 10 ) (3.44 x 10 )
Section H: Subtraction Just like addition, the first step is to make theexponents the same. Instead of adding the main numbers, they aresubtracted. Try to convert so that you will not get a negative answer.4333Model: (3 x 10 ) - (2 x 10 ) (30 x 10 ) - (2 x 10 )3 28 x 10 (same exponent)4 2.8 x 10 (final answer)same exponentfinal answer21-6-737) (2 x 10 ) - (4 x 10 ) 38) (3 x 10 ) - (5 x 10 ) 129239) (9 x 10 ) - (8.1 x 10 ) -440) (2.2 x 10 ) - (3 x 10 )
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 andwhat 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 numbers49) The cumulative national debt is on the order of 4 trillion. The cumulativeamount of high-level waste at the Savannah River Site, Idaho ChemicalProcessing Plant, Hanford Nuclear Reservation, and the West ValleyDemonstration Project is about 25 billion curies. If the entire amount ofmoney associated with the national debt was applied to cleanup of thosecuries, how many dollars per curie would be spent?
Answers:1) 1002) 10,0003) 10,000,0004) 0.015) 0.000016) 17) 3008) 70,0009) 2,40010) 0.00611) 912) 0.00000413) 10114) 10215) 10816) 10-117) 10-418) 10019) 4x10220) 6X10421) 7.5X10522) 5x10-323) 3.4x10-324) 6.457x10-225a) 3x10425b) 30,00026a) 6x10726b) 60,000,00027a) 5.5x10027b) 5.528a) 8x10-128b) 0.829) 2x10330) 3x10431) 5x10-332) 3x10233) 4.3x10334) 1.09x10435) 4x10736) 1.664x10-337) 1.6x10238) 2.5x10-639) 8.9919x101240) -2.9999978x10241) Depends42) 160043)0.125, Yes44) 5.53x10-445) 2.3x10346) 1.7x10347) 6.4x10248) 3x10249) 160 dollars/curie
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.File Size: 290KBPage Count: 8People also search forscientific notation worksheet answersscientific notation worksheet keyscientific notation worksheet pdf answersscientific notation worksheet with answersscientific notation worksheetscientific notation worksheet with answer key
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