Scientific Notation to Standard Notation Positive Exponents

Let’s look at some science stuff … Science?! I LOVE science!!

Mercury The closest planet to the Sun 36,000,000 miles from the Sun 3.6 x 107 miles from the Sun

Venus The second planet from the Sun Considered to be Earth’s twin 67,000,000 miles from the Sun 6.7 x 107 miles from the Sun

Earth The third planet from the Sun 93,000,000 miles from the Sun 9.3 x 107 miles from the Sun

Mars The fourth planet from the Sun 142,000,000 miles from the Sun 1.42 x 108 miles from the Sun

Jupiter The fifth planet from the Sun 484,000,000 miles from the Sun 4.84 x 108 miles from the Sun

Saturn The sixth planet from the Sun 888,000,000 miles from the Sun 8.88 x 108 miles from the Sun

Uranus The seventh planet from the Sun 1,784,000,000 miles from the Sun 1.784 x 109 miles from the Sun

Neptune The eighth planet from the Sun 2,799,000,000 miles from the Sun 2.799 x 109 miles from the Sun

Pluto? The ninth planet(?) from the Sun 3,674,000,000 miles from the Sun 3.674 x 109 miles from the Sun

Lightspeed! That’s even faster than me! Travel at Light Speed! 300,000,000 miles per second 3 x 108 miles per second Lightspeed! That’s even faster than me!

Yo Yo Yo … in West Philadelphia, we never done use the long numbers with all those. Seriously, take the short cut.

1 Listen, High School Musical 3 is out and I have to travel the world promoting it. I don’t have time to write all these 0s. Isn’t there an easier way?

1 Of course Troy! It’s called scientific notation. That number looks like this: 1.0 x 1013

Standard Notation Expanded form of a number It includes ALL the zeros

Scientific Notation Used to represent a very large or a very small number Also known as exponent notation

Scientific Notation Consists of three parts (in this order): 1.) A number between 1 and 10 2.) A multiplication x 3.) A power of 10

Wait … What do you mean a number between 1 and 10? In scientific notation, the first number must be at least 1.0 and no more than 9.9

10-7 1011 Wait … what’s a power of 10? A power of 10 is the number 10 and an exponent. It looks like: 10-7 1011

3.87 x 105 1.0 x 10-8 9.9999 x 1023 So what does this mean? These are examples of scientific notation: 3.87 x 105 1.0 x 10-8 9.9999 x 1023

38.7 x 105 10.0 x 10-8 99.999 x 1023 So what does this mean? These are NOT examples of scientific notation: 38.7 x 105 10.0 x 10-8 99.999 x 1023

3.87 x 1004 1.0 x 0.1-7 9.999 x 100021 So what does this mean? These are NOT examples of scientific notation: 3.87 x 1004 1.0 x 0.1-7 9.999 x 100021

To write a number in scientific notation 1.) Put a decimal after the first digit that is NOT a zero . 1 23,000,000,000

To write a number in scientific notation 2.) For a number that is greater than 1, count the amount of numbers behind the decimal point 1.23000000000 1 2 3 4 5 6 7 8 9 10 11

To write a number in scientific notation 3.) Take the amount of numbers behind the decimal point and make that the exponent that goes with the 10 There were 11 digits behind the decimal. Therefore, it will say 1011

To write a number in scientific notation 4.) Write all the digits that are not 0 (with the decimal point), a multiplication x, and the power of 10 1.23 x 1011 Don’t forget to box your answer!

Let’s try a few! Convert the following number from standard notation to scientific notation 469700000000

Let’s try a few! . 4 69700000000  Start with the decimal point

Let’s try a few! 4.69700000000  Count the numbers behind the decimal point.  There are 11 numbers behind the decimal point

Let’s try a few! 4.697 x 1011

Let’s try a few! Convert the following number from standard notation to scientific notation 736000000

Let’s try a few! . 7 36000000  Start with the decimal point

Let’s try a few! 7.36000000  Count the numbers behind the decimal point.  There are 8 numbers behind the decimal point

7.36 x 108 Let’s try a few!

Let’s try a few! 0.00000000782  Start with the decimal point

Let’s try a few! 0.000000000012  Start with the decimal point

Now it’s your turn!  39400 0.003 3.94 x 104 3 x 10-3 7253740 7.25374 x 106

Now it’s your turn!  0.000234 540 2.34 x 10-4 5.4 x 102 30000000000 3.0 x 1010

Now it’s your turn!  76345 873234 7.6345 x 104 8.73234 x 105 0.00023 2.3 x 10-4