Scientific Notation and Significant Figures

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 0.0000048 = 4.8 x 10-6

Try These 60,800,000,000 6.08 x 1010 245,000,000 2.45 x 108 0.0000000068 6.8 x 10-9 602,000,000,000,000,000,000,000 6.02 x 1023 0.000000467 4.67 x 10-7 -0.0000712 -7.12 x 10-5

On your calculator Get out your calculator!!! How to enter the following number in your calculator… 6.02 x 1023 6.02 EE 23 or 6.02 EXP 23 Enter the following in your calculator: 6.02 x 1023/2.5 x 10-12 2.408 x 1035

Significant Figures Not all digits in a number are significant We use significant figures to show how precisely something in measured.

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.

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 0.0000489

You Try 6088 12000 01500 1200.00 12.003 0.000650 00450060.0 4 2 6 5 3 7

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.

Adding Example 89.8943 + 123.0 + 34.321 247.2153 = 247.2

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

Defined Numbers Defined numbers have infinite significant figures. 1 dozen = 12 1 gross = 144 1 mile = 5280 ft Counted numbers have infinite sig figs.