# Scientific Notation and Significant Figures Scientific Notation n

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Scientific Notation and Significant Figures

Scientific Notation n n 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 10 x It takes the form N. NN x 10 N If the number is larger than 1, move the decimal to the left and multiply by 10 x n n 836, 000, 000 = 8. 36 x 1011 If the number is less than 1, move the decimal to the right and multiply by 10 -x n 0. 0000048 = 4. 8 x 10 -6

Try These n 60, 800, 000 n n 245, 000 n n 6. 02 x 1023 0. 000000467 n n 6. 8 x 10 -9 602, 000, 000, 000 n n 2. 45 x 108 0. 000068 n n 6. 08 x 1010 4. 67 x 10 -7 -0. 0000712 n -7. 12 x 10 -5

On your calculator n n Get out your calculator!!! How to enter the following number in your calculatorâ€¦ 6. 02 x 1023 n 6. 02 EE 23 n n or 6. 02 EXP 23 Enter the following in your calculator: 6. 02 x 1023/2. 5 x 10 -12 n 2. 408 x 1035 n

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

What digits are significant? THINK Right Rule n n n 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 n 865035 n n n 04892 n n 5 4 0. 0000489 n 3 1001 n n 3 348. 00 n n 6 842000 n n 0015. 0 n n 3 2. 00 x 10 -8 n n 3 3. 42 x 105 n n 4 3 100. 00 n 5

You Try n n n n 6088 12000 01500 1200. 00 12. 003 0. 000650 00450060. 0 n n n n 4 2 2 6 5 3 7

Adding and subtracting n 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 n n 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 n Defined numbers have infinite significant figures. 1 dozen = 12 n 1 gross = 144 n 1 mile = 5280 ft n n Counted numbers have infinite sig figs.