Scientific Notation and Order of Magnitude

Order of magnitude is a method for describing the size of measures in terms of powers of _____.

• a.1
• b.5
• c.10
• d.100

Which of the following equations is written in the form of scientific notation?

• a.(5 x 1000) + (3 x 100) + (1 x 10) + (7 x 1)
• b.(5 x 10³) + (3 x 10²) + (1 x 10¹) + (7 x 10⁰)
• c.(5 x 612) + (3 x 111) + (1 x 14) + (7 x 9)
• d.(5 x 6¹²) + (3 x 11¹) + (1 x 1⁴) + (7 x 9¹)

Researchers use scientific notation to write very large and very small numbers.

• a.true
• b.false

If you were to convert the number 52,468 to scientific notation, you would write it in this manner:

• a.(5 x 10000) + (2 x 1000) + (4 x 100) + (6 x 10) + (8 x 1)
• b.(50 x 1000) + (20 x 100) + (40 x 10) + (60 x 1) + 8
• c.5.2468 x 10⁴
• d.5.2468 x 10000

The mass of one water molecule is 2.992 x 10^-23 grams in scientific notation. What would be the decimal notation of this number? (Note: spaces added to make the numbers more legible.)

• a.0.000 000 000 000 000 000 000 029 92
• b.000 000 000 000 000 000 000 02.992
• c.000 000 000 000 000 000 000 002 992
• d.29,920,000,000,000,000,000,000.0

While visiting the Redwood National Forest in California, an informational sign says that one of the trees weighs 3.6287 x 10⁹ grams. What is that number in decimal notation? (Note: spaces added to make the numbers more legible.)

• a.0.000 000 003 628 7
• b.36,287.0
• c.3,628,700,000.0
• d.36,287,000,000,000.0

There are approximately 100,000,000 people living in the Philippines. This means the population has an order of magnitude of nine.

• a.false
• b.true

While working in the chemistry lab, your instructor tells you that a prepared solution contains 10g of sodium per 1,000 grams (g) of water. How many orders of magnitude less is the amount of sodium compared to the amount of water?

• a.One
• b.Two
• c.Three
• d.Four