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Scientific Notation Students will be able to evaluate variable expressions with negative exponents and be able to write numbers in scientific notation.

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FHSPre-Algebra Review2 Scientific Notation Scientists often deal with very large or very small numbers. To save time and space and be able to write and compute with such numbers more easily, a system of scientific notation was developed. There are two factors to each number written in scientific notation. The first factor is a number between 1 and 10. The second factor is a power of 10. Example: 523,000,000 = 5.23 x 10 8

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FHSPre-Algebra Review3 Scientific Notation For a very small number, the power of 10 is usually a negative number. Example:.00000345 = 3.45 x 10 -6 What is the method? Put a decimal point after the first non-zero digit in the number. Then count the number of digits between the original decimal point and the new decimal point. (This is the power of 10.) If you move the decimal to left, the exponent is positive; move decimal right, exponent is negative.

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FHSPre-Algebra Review4 Scientific Notation Examples Write the following numbers in scientific notation: 1.27,350,000,000 2..000125 3..000003786 4.894,000,000 2.735 x 10 10 1.25 x 10 -4 3.786 x 10 -6 8.94 x 10 8

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FHSPre-Algebra Review5 Scientific Notation with Calculator To change a number to scientific notation using your calculator, you must change the MODE to SCI. Hit MODE, then use arrow key to go over to SCI and hit ENTER. Now you just type in the number [523,000], hit ENTER and the answer will be written in scientific notation like this 5.23E5 which means 5.23 x 10 5. The E stands for exponent.

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FHSPre-Algebra Review6 Expanded Form of Scientific Notation If a number is written in scientific notation, we need to be able to translate it into expanded form. Change these numbers into expanded form: 1.3.47 x 10 7 2.6.29 x 10 -8 3.2.06 x 10 4 4.5.8 x 10 -3 34,700,000 0.0000000629 20,600 0.0058

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FHSPre-Algebra Review7 Operations with scientific notation numbers To multiply or divide two numbers written in scientific notation, just type them into the calculator and hit enter (just like any numbers you multiply or divide). Make sure you type in the parentheses. Example: (2.35 x 10 5 )*(6.83 x 10 8 ) 1.605 x 10 14

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