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

We recommend printing out this page for use as a worksheet.

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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.

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 (e.g.: 1.2) and the second part should be a power of 10 (e.g.: 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 (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 10³)
----------- = 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.

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.

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

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?

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Answers:

A) 1) 100 2) 10,000 3) 10,000,000 4) 0.01 5)0.00001 6) 1

B) 7) 300 8) 70,000 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) -2.9999978x10^-2

I) 41) Depends 42) 1600 43)0.125, Yes 44) 5.53x10^-4 45) 2.3x10³ 46) 1.7x10³ 47) 6.4x10² 48) 3x10² 49) 160 dollars/curie

Note: This page is not copyrighted by Paul J. Marquard. Permission to use this page and creation was by the Institute for Energy and Environmental Research

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Comments to Outreach Coordinator, Pat Ortmeyer: ieer@ieer.org
Takoma Park, Maryland, USA

This page was last updated on 06/06/01.