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Scientific Notation

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

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Scientific Notation

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

  2. 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 Pre-Algebra Review

  3. 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. Pre-Algebra Review

  4. Scientific Notation Examples Write the following numbers in scientific notation: • 27,350,000,000 • .000125 • .000003786 • 894,000,000 2.735 x 1010 1.25 x 10-4 3.786 x 10-6 8.94 x 108 Pre-Algebra Review

  5. 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 105. The E stands for exponent. Pre-Algebra Review

  6. 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 0.0000000629 20,600 0.0058 Pre-Algebra Review

  7. 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 Pre-Algebra Review

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