Scientific Notation to Standard Notation
Positive Exponents Lets 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 Earths 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! Thats even faster than me!
Travel at Light Speed! 300,000,000 miles per second 3 x 108 miles per second Lightspeed!Thats 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 dont have time to write all these 0s.Isnt there an easier way? 1 Of course Troy!Its 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 whats 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 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 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 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 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 Dont forget to box your answer! Lets try a few! Convert the following number from standard notation to scientific notation Lets try a few! . Start with the decimal point Lets try a few! Count the numbers behind the decimal point. There are 11 numbers behind the decimal point Lets try a few! 4.697 x 1011 Lets try a few! Convert the following number from standard notation to scientific notation Lets try a few! . Start with the decimal point Lets try a few! Count the numbers behind the decimal point. There are 8 numbers behind the decimal point 7.36 x 108 Lets try a few! Lets try a few! Start with the decimal point Lets try a few! Start with the decimal point Now its your turn! 39400 0.003 3.94 x 104 3 x 10-3 x 106 Now its your turn! 540 2.34 x 10-4 5.4 x 102 3.0 x 1010 Now its your turn! 76345 873234 x 104 x 105 2.3 x 10-4