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Scientific Notation and Significant Figures
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Scientific Notation In science we often use very large or very small numbers, scientific notation make them easier to calculate. Multiply a number by a power of 10x It takes the form N.NN x 10N If the number is larger than 1, move the decimal to the left and multiply by 10x 836,000,000,000 = 8.36 x 1011 If the number is less than 1, move the decimal to the right and multiply by 10-x = 4.8 x 10-6
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Try These 60,800,000,000 6.08 x 1010 245,000,000 2.45 x 108 6.8 x 10-9 602,000,000,000,000,000,000,000 6.02 x 1023 4.67 x 10-7 -7.12 x 10-5
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On your calculator Get out your calculator!!!
How to enter the following number in your calculator… 6.02 x 1023 6.02 EE or EXP 23 Enter the following in your calculator: 6.02 x 1023/2.5 x 10-12 2.408 x 1035
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Significant Figures Not all digits in a number are significant
We use significant figures to show how precisely something in measured.
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What digits are significant? THINK Right Right Rule
All digits 1-9 are significant. Zeros between digits 1-9 are significant. Zeros to the right of digits after a decimal are significant. Zeros at the end of a number with no decimal are never significant. Zeros at the beginning of a number are never significant.
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For example 1001 4 0015.0 3 3.42 x 105 2.00 x 10-8 100.00 5 865035 6 842000 3 348.00 5 04892 4
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You Try 6088 12000 01500 12.003 4 2 6 5 3 7
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Adding and subtracting
When adding or subtracting the answer can only have as many decimal places as the least amount from numbers being added in the problem.
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Adding Example =
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Multiplying and dividing
Take the least amount of sig figs of the numbers that are being multiplied or divided. 4.25 x 3.2 = 13.6 or 14 3 2
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Defined Numbers Defined numbers have infinite significant figures.
1 dozen = 12 1 gross = 144 1 mile = 5280 ft Counted numbers have infinite sig figs.
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