Scientific Notation Confidential

WARM UP 0.035 ÷ 0.05 = 0.7 2) Solve 0.6 ÷ 0.05 = 12 0.00132 ÷ 0.012 = 0.11 Without changing the quotient, change the problem so that the divisor is a whole number 68. 13 ÷ 0.003 It will be 68,130 ÷ 3 Confidential

Lets review what we learned in the earlier lesson To divide any two decimal numbers first move the decimal point in the divisor to the right so that it becomes a whole number Move the decimal point of the dividend the same number of places to the right as you did of the divisor Now divide as you do with whole numbers Put the decimal point for your answer directly above the one in your dividend Confidential

Let us take an example 9.09 ÷ 4.5 In the case of a remainder add zero to the dividend and divide until there is no remainder or until there are 4 decimal places in the answer 2.02 4.5 ) 9 .09 0 9 0 Confidential

Lets get started Today we are going to learn about Scientific Notation Scientific Notation is a way to express very large or very small numbers. It is most often used in “scientific” calculations where the analysis must be very precise Scientific notation has two parts A non zero number between 1 and 10 A power of 10 Confidential

What is Scientific notation ? A number in scientific notation is written as the product of a number between 1 and 10 (integer or decimal ) and an integer power of 10 A number written in scientific notation has the form N X 10r where, N is between 1 and 10 r is an integer Confidential

To Change from Standard form to Scientific notation Place the decimal point so that there is one non zero digit to the left of the decimal point Count the number of decimal places the decimal point has “ moved ” from the original number. This will be the exponent (power) of 10 Confidential

Standard form to Scientific notation Lets take some Examples The power of ten indicates how many places the decimal point has moved from the original number Confidential

If the decimal point is moved N places to the left POSITIVE EXPONENTS 100 = 1 101= 10 102 = 10 X 10 =100 10000 = 100 x 100 = 1.0000 x 104 If the decimal point is moved N places to the left The power of ten is increased by N units Confidential

If the decimal place is moved N places to the right NEGATIVE EXPONENTS 1 X 10-1 = 1 = 0.1 (one tenth) 10 1 X 10-2 = 1 = 0.01 (0ne hundredth) 100 If the decimal place is moved N places to the right then the power of 10 is decreased by N units .01 = .01 x 100 = 1 x 10-2 Confidential

If the original number is less than 1, then the exponent is negative . If the original number is greater than 1, then the exponent is positive 579,300,000 = 5.793 x 108 (Positive exponent) 0.000246 = 2.46 x 10-4 (Negative exponents) Confidential

To change Scientific notation to Standard form Move the decimal point to the right for positive exponent 10 Move the decimal point to the left for negative exponent10 Use zeros to fill in places Confidential

Lets take some examples The decimal point has moved 6 places to the right 8.951 x 10-4 = 0.0008951 The decimal point has moved 4 places to the left Confidential

You try some ! 72,500 = 7.25 x 105 27,100,000 = 2.71 x 107 5.56 x 109 = 5.56 billion 1.976 x 10-4 = 0.0001976 Confidential

BREAK TIME Confidential

Lets play a Game Click on the photo to color a picture Confidential

One light year is the distance light travels in one year. If the speed of light is 3 x 105 kilometers per second, about how many kilometers does light travel in one year ? About 9.51 x 1012 km Confidential

According to the Aluminum Association, 2,031,000,000 pounds of aluminum cans were recycled in 1993. At an average of 29.9 cans per pound, how many aluminum cans were recycled that year ? Express your answer in scientific notation. 5.95 x 1010 cans Confidential

Scientists divide Earth’s history in to small units based on the types of life-forms living on then. In the Jurassic period, which occurred about 208,000,000 years ago, dinosaurs ruled. Express the years in scientific notation. 2.08 x 108 Confidential

Assessment Write each number in scientific notation: 34,000 3.4 x 104 165,000,000,000 1.65 x 1011 310,210 3.10 x 105 Write each number in standard form: 3.05 x 102 305 2 x 1011 200,000,000,000 9.037 x 108 903,700,000 Confidential

Assessment The distance from our sun to the nearest star, Alpha Centauri, is about 42,000,000,000,000 kilometers. Write this distance in scientific notation. 4.2 x 1013 Confidential

Lets review what we have learned in this lesson Scientific notation can be expressed as the short way to write very large or very small numbers without writing all the zeros A number in scientific notation is written as the product of a number that is between 1 and 10 and an integer that is power of ten The power of ten is written with an exponent (negative or positive ) Confidential

To change from standard form to Scientific notation Place the decimal point so that there is a non zero digit to the left of the decimal point Count the number of decimal places the decimal point has “moved” from the original number If the original number was less than 1, then the exponent is negative. If the original number is greater than 1,then the exponent is positive Confidential

Lets take a few examples (Standard form to Scientific notation) 7.8 x 106 = 7,80,0000 ( Scientific notation to standard form) Confidential

You had a Great Lesson Today Be sure to practice what you have learned today Confidential