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james y.

What is the best strategy to adding and subtracting scientific notation?

1. Make the exponents match

Ex. 2.76 x 10^{4} + 6.91 x 10^{5 }

Matching = 2.76 x 10^{4} + 69.1 x 10^{4}

Answer = 71.76 x 10^{4} = 7.2 x 10^{5}

What does LARS stand for? And how is it significant for scientific notation?

Left

Add

Right

Subtract

When dealing with scientific notation, if the decimal is moved to the left than add 1 power to your exponent. If the decimal is moved to the right subtract 1 power from the exponent.

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Multiplying exponents with similar bases

Add the exponents

Dividing with similar bases

Subtract the bases

Multiplying and Dividing scientific notation.

1. Separate the mantissa (the variable that is not held to the power) from the exponential term.

2. Round accordingly.

3. Deal with the mantissa and the exponential term separately.

Scientific notation to a square root or power.

1. Separate the terms

2. Multiply the exponent by the power

3. Put back into scientific notation

How can you take the square root of scientific notation?

1. Make the exponential term even (10^{5}->10^{4})

2. Separate the mantissa and the exponential term and the the square root of each.

Ex. √(8.1 x 10^{5)} -> √(81 x 10^{4})

√81 x √10^{4} = 9 x 10^{2}

Significant Figures

*Convey accuracy - "that table is 13 ft. long" vs. "that table is 13.725 ft. long"**Rule 1** - Any zero BETWEEN two significant numbers is *also *a significant number (ex. 70.004 = 5 significant figures)

**Rule 2** - Any zero IN FRONT of a significant number is NOT significant**Rule 3 **- Any zero TO THE RIGHT of a significant number IS significant

- The number of numbers in your measurement = level of accuracy

(ex. 0.000819 = 3 significant figures - because 8.19 x 10^-4 is also true)

(ex. 0.2000 = 4 sf)

What are the answers for...

√2√3

1.4

1.7

30-60-90 Triangle

θ=30°=1

θ=60°=sqrt(3)

θ=90°=2

Or

θ=30°=a

θ=60°= a[(sqrt)(3)]

θ=90°=2a

The main idea is re recognize the ratios here. The large leg to the small leg is a 1.7:1 ratio.

45-45-90 proportions

θ=45°=1

θ=45°=1

θ=90°=sqrt(2) ~ 1.4

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