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Significant Figures. Indicate precision of a measured value 1100 vs. 1100.0 Which is more precise? How can you tell? How precise is each number? Determining significant figures can be tricky. There are some very basic rules you need to know. Most importantly, you need to practice!.

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Significant figures
Significant Figures

Indicate precision of a measured value

1100 vs. 1100.0

Which is more precise? How can you tell?

How precise is each number?

Determining significant figures can be tricky.

There are some very basic rules you need to know. Most importantly, you need to practice!




Scientific notation
Scientific Notation

Number expressed as:

Product of a number between 1 and 10 AND a power of 10

5.63 x 104, meaning

5.63 x 10 x 10 x 10 x 10

or 5.63 x 10,000

ALWAYS has only ONE nonzero digit to the left of the decimal point

ONLY significant numbers are used in the first number

First number can be positive or negative

Power of 10 can be positive or negative


When to use scientific notation
When to Use Scientific Notation

Astronomically Large Numbers

mass of planets, distance between stars

Infinitesimally Small Numbers

size of atoms, protons, electrons

A number with “ambiguous” zeros

59,000

HOW PRECISE IS IT?


Powers of 10
Powers of 10

Positive Exponents

Exponent of Zero Means “1” 100 = 1


Powers of 101
Powers of 10

Negative Exponents

Exponent of Zero Means “1” 100 = 1


Converting from standard to scientific notation
Converting From Standard to Scientific Notation

Move decimal until it is behind the first sig fig

Power of 10 is the # of spaces the decimal moved

Decimal moves to the left, the exponent is positive

Decimal moves to the right, the exponent is negative

428.5  4.285 x 102(decimal moves 2 spots left)

0.0004285  4.285 x 10-4(decimal moves 4 spots right)


Converting from scientific to standard notation
Converting From Scientific to Standard Notation

Move decimal point

# of spaces the decimal moves is the power of 10

If exponent is positive, move decimal to the right

If exponent is negative, move decimal to the left

4.285 x 102  428.5(move decimal 2 spots right)

4.285 x 10-4  0.0004285(decimal moves 4 spots left)


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