Scientific Notation

Scientific Notation When would someone think of using scientific notation?

You guessed right! • Scientific Notation is used when the actual numbers are too LARGE or too small. • Mostly in science • Small numbers from items impossible to see with the human eye • Large numbers too big to fit on the page • Makes calculations easier.

How to write in Scientific Notation • Get your number to be between 1 and 9 by moving the decimal to the left or right. • 1,624,000,000,000,000 changes to 1.624000000000000

How Many Spaces? • Count the number of spaces from the beginning decimal point to the new point. • Ex. 1.624,000,000,000,000 (15 spaces)

Moving the Decimal Point • Copy all the whole numbers with the new decimal point : 1.624

Power of Ten • Multiply the remaining number by 10 raised to the number of places the decimal point moved. • 1.624 x 1015

Positive Exponent • Use a positive exponent if the decimal point moved to the left. • 392,000. • 3.92 x 100,000 • 3.92 x 105 • A large number to a smaller number - positive exponent

Negative Exponent • Use a negative exponent if the decimal point moved to the right. • .00000432 • 4.32 x 10 -6 • A small number to a larger number is a negative exponent.

Your Turn • 1.) 29,900 5.) 222.6 • 2.) 0.0000000033 6.) 2,230,000 • 3.) 883 7.) 0.0000002 • 4.) 0.0199 8.) 17,250

Answers 1.) 29,900 5.) 222.6 2.99 x 104 2.226 x 102 2.) 0.0000000033 6.) 8,230,000 3.3 x 10-9 8.23 x 106 3.) 983 7.) 0.0000002 9.83 x 102 2 x 10-7 4.) 0.0199 8.) 17,250 1.99 x 10-2 1.725 x 104

If given the information in SCIENTIFIC NOTATION how do you write out the number? EX. 1.25 x 104 = ? STEP 1- Write the whole numbers with the decimal. 1.25 STEP 2- If there is a POSITIVE exponent, count the number of spaces to the RIGHT of the decimal point to match the exponent. 1.2500 = 12500

6.4 x 10-3 • STEP 3- If there is a NEGATIVE exponent, count the number of spaces going to the LEFT of the decimal point to match the exponent. 006.4 = .0064

TRY THESE!Rewrite these numbers so they are no longer in scientific notation. • 1.) 2.27 x 10-2 5.) 1.33586(105) • 2.) 3.772 x 104 6.) 1.33586(10-5) • 3.) 5.6 X 10-1 7.) 4.22 x 102 • 4.) 9.7 x 107 8.) 8.96 x 103

ANSWERS • 1.) 2.27 x 10-2 5.) 1.33586(105) 0.0227 133,586. • 2.) 3.772 x 104 6.) 1.33586(10-5) 37,720 0.0000133586 • 3.) 5.6 X 10-1 7.) 4.22 x 102 0.56 422 • 4.) 9.7 x 107 8.) 8.96 x 103 97,000,000 8,960

Computing in Scientific Notation • Example: 0.0000006 x 32,000,000 x 0.0043 • Step 1- Write the numbers in Scientific Notation. 6 x 10-7 x 3.2 x 107 x 4.3 x 10-3 • Step 2- Use the commutative property to change the order of the factors. 6 x 3.2 x 4.3 x 10-7 x107 x10-3.

6 x 3.2 x 4.3 x 10-7 x107 x10-3. • Step 3- Complete the multiplication, using the rule for multiplying with exponents. 6 x 3.2 x 4.3 = 82.56 10-7 x107 x10-3 = 10(-7 + 7 + -3) =10-3 Answer: 82.56 x 10-3 • Step 4- Write the product in scientific notation. 82.56 x 10-3= 8.256 x 10(-3+1)= Answer: 8.256 x 10-2

YOUR TURN 1.) 0.00645 x 0.00004302 x 0.000000035 2.) (11,000,000)2

TO FIND THE QUOTIENT:9,250,000 divided by 25,000 • Step 1- Write each number in scientific notation. • 9.25 x 106 2.5 x 104 • Step 2- Rewrite the division as a fraction. 9.25 x 106 2.5 x 104

9,250,000 / 25,000 • Step 3- Complete the division, using the rule for dividing with exponents. 9.25 x 106 = 9.25 x 106 = 3.7 x 102 2.5 x 104 2.5 104 • Step 4- Check that the product is written in scientific notation. 3.7 x 102

YOUR TURN • 1.) 350,000 divided by 1,400,000

Answer 350,000 / 1,400,000 1.) 3.5 x 105 / 1.4 x 106 2.) 3.5 x 105 1.4 x 106 3.) 3.5 x 105 = 3.5 x 105 = 2.5 x 10-1 1.4 x 106 1.4 106 4.) 2.5 x 10-1

Using your calculator to solve Scientific Notation Problems • Push MODE • Scroll to SCI (scientific notation) • 2nd MODE (Quit) • Put number into calculator ENTER • E means “time 10 to the power of” • Ex. 40,000,000 = 4E7 = 4 x 107

Scientific Notation Open Ended Question • Consider this multiplication expression. (3.2 x 104) (3 x 103) • Set your calculator in scientific notation mode and evaluate this expression. • Explain how you could do the multiplication above without using a calculator. • Find the product (2.1 x 106) (4 x 105) and write it in scientific notation.

Scientific Notation