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.

VocabularyVocabularyScientific notation is a shorthand way to write numbers using powers of 10.

10 where 1 9na a

Examples: 8.3 x 105 4.12 x 1022 7.1 x 10-5

Standard notation is a number written with place values.

Examples: 152 9.5 0.085

Problem 1: Recognizing Scientific Problem 1: Recognizing Scientific NotationNotation

1) 0.23 x 10-3

2) 2.3 x 107

3) 9.3 x 1009

Is the number written in scientific notation? If not, explain.

Conditions:

•1st factor is between 1 and 9•2nd factor is a power of 10

Got it?Got it?

4) 53 x 104

5) 3.42 x 10-7

6) 0.35 x 100

Is the number written in scientific notation? If not, explain.

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 ______________.

Scientific Notation to Standard Form

1. Express 6.49 × 105 in standard form.

Scientific Notation to Standard Form

2. Express 1.8 × 10–2 in standard form.

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

4. Express 7.61 × 103 in standard notation.

Standard Form Scientific Form1) 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 ___________.

Standard Form to Scientific Notation

1. Express 4,062,000,000,000 in scientific notation.

Standard Form to Scientific Notation

2. Express 0.000000823 in scientific notation.

3. Express 458,000,000 in scientific notation.

4. Express 0.0000452 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.

Multiply with Scientific Notation

1. Evaluate (5 × 10–6)(2.3 × 1012). Express the result in both scientific notation and standard form.

Divide with Scientific Notation

2. Evaluate . Express the result in both

scientific notation and standard form.

3. Evaluate (8 × 105)(2.1 × 10–3). Express the result in both scientific notation and standard form.

4. Evaluate Express the result in both

scientific notation and standard form.