Space tourism is a multibillion dollar industry. For a price of $20 million, a civilian can travel on a rocket or space shuttle and visit the International Space Station for a week. a)What would $20 million look like when written out? b)What would you have to multiply $2 by to get to $20 million? c)How can you write 10,000,000 as a power of 10?

Lesson 7-2 Writing a number in scientific notation improves efficiency and accuracy of various calculations involving VERY LARGE and VERY SMALL numbers.

Vocabulary Scientific notation is a shorthand way to write numbers using powers of 10. Examples: 8.3 x x x Standard notation is a number written with place values. Examples:

Problem 1: Recognizing Scientific Notation 1) 0.23 x ) 2.3 x ) 9.3 x Is the number written in scientific notation? If not, explain. Conditions: 1 st factor is between 1 and 9 2 nd factor is a power of 10

Got it? 4) 53 x ) 3.42 x ) 0.35 x 100 Is the number written in scientific notation? If not, explain.

Concept Scientific Form  Standard Form The exponent tells you how many places to move the decimal point. If there is a positive exponent, move the decimal place to the ________. If an exponent is positive, a number gets ____________. If there is a negative exponent, move the decimal place to the _________. If an exponent is negative, a number gets ______________.

Example 2A Scientific Notation to Standard Form 1. Express 6.49 × 10 5 in standard form.

Example 2B Scientific Notation to Standard Form 2. Express 1.8 × 10 –2 in standard form.

Example 2A 3. Express 3.16 × 10 –2 in standard notation.

Example 2B 4. Express 7.61 × 10 3 in standard notation.

Concept Standard Form  Scientific Form 1) Move the decimal after the first whole number (1, 2, 3, 4, 5, 6, 7, 8, 9). 2) Add your multiplication sign and base (x 10) 3) The number of moves between the original and the new decimal place will be the exponent. If the original number is greater than one, the exponent will be ___________. If the original number is less than one, the exponent will be ___________.

Example 1A Standard Form to Scientific Notation 1. Express 4,062,000,000,000 in scientific notation.

Example 1B Standard Form to Scientific Notation 2. Express in scientific notation.

Example 1A 3. Express 458,000,000 in scientific notation.

Example 1B 4. Express in scientific notation.

Multiply and Dividing in Scientific Notation When you multiply in scientific notation, just multiply the first factor and _________ the exponents. When you divide in scientific notation, just divide the first factor and _________ the exponents.

Example 3 Multiply with Scientific Notation 1. Evaluate (5 × 10 –6 )(2.3 × ). Express the result in both scientific notation and standard form.

Example 4 Divide with Scientific Notation 2. Evaluate. Express the result in both scientific notation and standard form.

Example 3 3. Evaluate (8 × 10 5 )(2.1 × 10 –3 ). Express the result in both scientific notation and standard form.

Example 4 4. Evaluate Express the result in both scientific notation and standard form.