Scientific Notation

Scientific Notation 과학적 기수법 A short-hand way of writing large numbers without writing all of the zeros.

The Distance From the Sun to the Earth in miles 93,000,000

Step 1 93,000,000 = 9.3000000 Move decimal left Leave only one number in front of decimal (one number to the left of the decimal). 93,000,000 = 9.3000000

Step 2 Write number without zeros 93,000,000 = 9.3

Step 3 7 93,000,000 = 9.3 x 10 Count how many places you moved decimal Make that your power of ten 93,000,000 = 9.3 x 10 7

The power of ten is 7 because the decimal moved 7 places. 7 93,000,000 = 9.3 x 10 7

93,000,000 --- Standard Form (Decimal form) 9.3 x 107 --- Scientific Notation

Scientific notation Decimal notation Scientific notation 127   (정수) Decimal notation Scientific notation 127 1.27 x 102 0.0907 9.07 x 10 – 2 0.000506 5.06 x 10 – 4 2 300 000 000 000 2.3 x 1012

Place Value Decimal System 1 2 3 . 4 5 6 7 Millions Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones Tenths Hundredths Thousandths Ten thousandths Hundred Thousandths Millionths Ten Millionths 106 105 104 103 102 101 100 10-1 10-2 10-3 10-4 10-5 10-6 10-7 20 0.4 0.05 0.006 0.0007 `

When using Scientific Notation, there are two kinds of exponents: positive and negative Positive Exponent: 2.35 x 108 Negative Exponent: 3.97 x 10-7

When changing scientific notation to standard notation, the exponent tells you if you should move the decimal: With a positive exponent, move the decimal to the right: 4.08 x 103 = 4 0 8 Don’t forget to fill in your zeroes!

When changing scientific notation to standard notation, the exponent tells you if you should move the decimal: With a negative exponent, move the decimal to the left: 4.08 x 10-3 = 4 0 8 Don’t forget to fill in your zeroes!

An easy way to remember this is: If an exponent is positive, the number gets larger, so move the decimal to the right. If an exponent is negative, the number gets smaller, so move the decimal to the left.

The exponent also tells how many spaces to move the decimal: In this problem, the exponent is +3, so the decimal moves 3 spaces to the right.

The exponent also tells how many spaces to move the decimal: In this problem, the exponent is -3, so the decimal moves 3 spaces to the left.

When changing from Standard Notation to Scientific Notation: 1) First, move the decimal after the first whole number: 3 2 5 8 2) Second, add your multiplication sign and your base (10). 3 . 2 5 8 x 10 3) Count how many spaces the decimal moved and this is the exponent. 3 . 2 5 8 x 10 3 3 2 1

When changing from Standard Notation to Scientific Notation: 4) See if the original number is greater than or less than one. If the number is greater than one, the exponent will be positive. 348943 = 3.48943 x 105 If the number is less than one, the exponent will be negative. .0000000672 = 6.72 x 10-8

Page 82 Try changing these numbers to proper Scientific Notation: 430 3,400,000 0.0000045 11.2 x 104 0.01 x 10-2 4.3 x 102 3.4 x 106 4.5 x 10-6 1.12 x 105 1 x 10-4

Rewrite these in decimal form Page 82    

Multiplying with Scientific Notation (5. X 102)(3.3 X 103) Multiply the Coefficients 5 X 3.3 = 16.5 Add the Exponents 102 X 103 = 105 16.5 X 105 BUT 16.5 is not greater than or equal to 1 and less than 10. so we must move the decimal place, 1.65 X 106  

Practice Page 83 #1,2 Multiplying with Scientific Notation (2.2 X 10-2) X (3 X 105) = (-3.2 X 105) X (2.1 X 102) = 6.6x103 -6.72x107

Dividing with Scientific Notation (3.3 X 104)/ (6.6 X 102) 3.3/ 6.6 = 0.5 Subtract the Exponents 104 / 102 = 102 0.5 X 102 BUT 0.5 is not greater than or equal to 1 and less than 10. 5 X 101 (3.3 X 104)/ (2.3 X 102) 33000 / 230 = 143.4783 Divide the Coefficients 3.3/ 2.3 = 1.434783 Subtract the Exponents 104 / 102 = 102 1.4347823 X 102 143.4783

Dividing with Scientific Notation (2.1 X 104) / (8.4 X 103) = (3.1 X 103) / (6.2 X 105) = 2.5 x 100 5 x 10-3

Scientific Notation page 84 Addition/Subtraction  

Homework page 83 # 3-6 page 84 all