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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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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 108 FHS Pre-Algebra Review

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Scientific Notation For a very small number, the power of 10 is usually a negative number. Example: = 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. FHS Pre-Algebra Review

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**Scientific Notation Examples**

Write the following numbers in scientific notation: 27,350,000,000 894,000,000 2.735 x 1010 1.25 x 10-4 3.786 x 10-6 8.94 x 108 FHS Pre-Algebra Review

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**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 x The E stands for exponent. FHS Pre-Algebra Review

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**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: 3.47 x 107 6.29 x 10-8 2.06 x 104 5.8 x 10-3 34,700,000 20,600 0.0058 FHS Pre-Algebra Review

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**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 FHS Pre-Algebra Review

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Holt Algebra 2 1-5 Properties of Exponents In an expression of the form a n, a is the base, n is the exponent, and the quantity a n is called a power.

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