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Published byVictor Reeves Modified over 9 years ago
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Large Numbers 1,000 X 1 thousand = 1 million (106) 1,000 X 1 million = 1 billion (109) 1,000 X 1 billion = 1 trillion (1012) 1,000 X 1 trillion = 1 quadrillion (1015) 1,000 X 1 quadrillion =1 quintillion(1018) 1,000 X 1 quintillion = 1 sextillion (1021)
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Large Numbers 1,000 X 1 sextillion =1 septillion (1024) 1,000 X 1 septillion =1 octillion (1027) 1,000 X 1 octillion = 1 nonillion (1030) 1,000 X 1 nonillion = 1 decillion (1033) 1,000 X 1 decillion = 1 undecillion (1036) 1,000 X 1 undecillion =1 duodecillion (1039)
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One googol = 10100 One googolplex = 10googol One googolplexian = 10googolplex
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EXIT Ticket People in the US eat approximately 1,120,000,000 pounds of popcorn a year. Write this number in Scientific Notation.
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Scientific Notation
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VOCABULARY scientific notation exponential notation standard form base
Factor power Exponent decimal place value positive number negative number
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rational numbers= whole numbers and decimal numbers
OBJECTIVE The students will be able to represent rational numbers by using scientific notation. rational numbers= whole numbers and decimal numbers
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Powers of 10 105 = 104 = 103 = 102 = 101 = 100 =
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Powers of 10 10-5 = 10-4 = 10-3 = 10-2 = 10-1 =
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-used to represent large and small numbers
Scientific Notation -used to represent large and small numbers -it is made up of two factors: the first is greater than or equal to 1 and less than 10; and the second is a power of ten. .
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The Distance From the Sun to the Earth
93,000,000
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Step 1 93,000,000 = 9.3000000 Move decimal left
Leave only one number in front of decimal 93,000,000 =
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Step 2 Write number without zeros 93,000,000 = 9.3
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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
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The power of ten is 7 because the decimal moved 7 places. 7
93,000,000 = 9.3 x 10 7
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93,000, Standard Form 9.3 x Scientific Notation
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Practice Problem -----> -----> -----> ----->
Write in scientific notation. Decide the power of ten. 98,500,000 = 9.85 x 10? 64,100,000,000 = 6.41 x 10? 279,000,000 = 2.79 x 10? 4,200,000 = 4.2 x 10? 9.85 x 107 -----> 6.41 x 1010 -----> 2.79 x 108 -----> -----> 4.2 x 106
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Scientific Notation in Word Problems
1. There are over 300,000,000,000 stars in the Andromeda Galaxy. Write the number of stars in scientific notation.
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Scientific Notation in Word Problems
2. There are approximately 306,000,000 people in United States of America. Write the population in the US in scientific notation.
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Scientific Notation in Word Problems
3. The current population in the world is about 6.9 billion. Write the population in scientific notation.
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Scientific Notation in Word Problems
4. The thickness of a soap bubble is about meter. What is the thickness of the soap bubble written in scientific notation?
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More Practice Problems
On these, decide where the decimal will be moved. 734,000,000 = ______ x 108 870,000,000,000 = ______x 1011 90,000,000,000 = _____ x 1010 Answers 3) 9 x 1010 7.34 x 108 2) 8.7 x 1011
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Answers Practice Problems Write in scientific notation. 50,000
7,200,000 802,000,000,000 Answers 1) 5 x 104 2) 7.2 x 106 3) 8.02 x 1011
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Scientific Notation to Standard Form
Move the decimal to the right 3.4 x 105 in scientific notation move the decimal ---> 340,000 in standard form
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Move the decimal to the right.
Write in Standard Form Move the decimal to the right. 6.27 x 106 9.01 x 104 =6,270,000 =90,100
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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
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With a positive exponent, move the decimal to the right:
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!
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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 = Don’t forget to fill in your zeroes!
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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.
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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.
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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.
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Try changing these numbers from Scientific Notation to Standard Notation:
9.678 x 104 x 10-3 x 107 x 10-5 96780
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When changing from Standard Notation to Scientific Notation:
1) First, move the decimal after the first whole number: 2) Second, add your multiplication sign and your base (10). x 10 3) Count how many spaces the decimal moved and this is the exponent. x 10 3 3 2 1
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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. = x 105 If the number is less than one, the exponent will be negative. = 6.72 x 10-8
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Try changing these numbers from Standard Notation to Scientific Notation:
.08376 5673 x 106 3.45 x 10-5 8.376 x 102 5.673 x 103
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