1 - Sig Figs/Scientific Notation

Significant Figures

Pacific (Decimal is Present)

NUMBER

Atlantic (Decimal is Absent)

Significant figures (Sig Figs) are used to take the tool of measurement into account. The last digit in a measurement is an approximation.

Example:

Rules for Sig Figs

1. If a decimal is Absent, count from the right side (ignore trailing zeros) 2. If a decimal is Present, count from the left side (ignore leading zeros) 3. Count total number of sig figs once you hit a nonzero number 4. Only worry about sig figs at the end of the problem when you are calculating a final answer 5. Use the LOWEST number of sig figs for your answer

Examples:

8.346

# Sig Figs __________

9.87 + 0.0045

Calculator LOWEST Answer # Sig Figs

Actual Answer

9.8745

________ ____________

91345 0.0004056 12000 806402 12000.00

__________ __________ __________ __________ __________

10.54 - 3 24.32 - 18.0 0.034 x 4.2 400 x 2.567 400.0 / 3.5000 1000 / 2

7.54

________ ____________

6.32

________ ____________

0.1428

________ ____________

1026.8

________ ____________

114.285714 ________ ____________

500

________ ____________

Scientific Notation

Scientific notation helps us write really big or really small numbers. Instead of writing out 0.00000000000000067, we use scientific notation to write it as 6.7 x 10-16. Alternatively, instead of writing out 98628000000, we use scientific notation to write is as 9.8628 x 1010

The general form is N x 10x where N is a number with only one digit to left of the decimal

For really small numbers (0.000000000034)

1. Take the decimal and move it to the right until there is one digit to the left of the decimal 2. However many places you moved the decimal becomes your exponent 3. Small numbers have negative exponents. If you moved the decimal to the right, you

should have a negative exponent

For really big numbers (3,400,000,000)

1. If there is no decimal, place one at the end of the number 2. Take the decimal and move it to the left until there is one digit to the left of the decimal 3. However many places you moved the decimal becomes your exponent 4. Big numbers have positive exponents. If you moved the decimal to the left, you should

have a positive exponent

**Answers in scientific notation should have the same number of sig figs as the original** Examples:

1,200,000,000,000 0.000000000034 1,000,000 0.0000000400003 543,000,900 0.03006 3,560 0.01 100

# Sig Figs Moved Decimal # Times Decimal

L or R

Moved

Scientific Notation

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