Scientific Notation to Standard Notation Positive and Negative Exponents

But first … A review! x x x 10 11

But first … A review! x x x 10 10

But first … A review! x x x 10 -6

But first … A review! x x

And now, what I tried to show you yesterday … Convert the following number from standard notation to scientific notation Convert the following number from standard notation to scientific notation

The first step is the same: The first step is the same: Put the decimal point after the first number. Put the decimal point after the first number

Now count how many spaces are between the original decimal point and the new decimal point Now count how many spaces are between the original decimal point and the new decimal point There are 5 spaces between the 2 decimal points

Therefore … in scientific notation is … in scientific notation is … x 10 5 I will ALWAYS be a positive exponent!

Now it’s your turn! Now it’s your turn! x x x 10 6

And now going the other way! Yes! Let’s go from scientific to standard notation! That sounds fun!

Going from Scientific Notation Positive Exponents How do you go from 9.12 x 10 4 to 91,200? How do you go from 9.12 x 10 4 to 91,200?

Going from Scientific Notation Positive Exponents To go from scientific notation to standard notation, you must move the decimal to the RIGHT To go from scientific notation to standard notation, you must move the decimal to the RIGHT The number of spaces you move is equal to the number in the exponent. The number of spaces you move is equal to the number in the exponent.

Going from Scientific Notation Positive Exponents Ze positive numbers are ze numbers to the right. As a result, ze positive exponents move the decimal to the right.

Going from Scientific Notation Positive Exponents Write x 10 7 in standard notation Write x 10 7 in standard notation

Going from Scientific Notation Positive Exponents So let’s move the decimal 7 spaces to the right. So let’s move the decimal 7 spaces to the right

Going from Scientific Notation Positive Exponents Now, for all the empty spaces, put a zero in them. Now, for all the empty spaces, put a zero in them

Going from Scientific Notation Positive Exponents Drop the decimal and add the commas. Drop the decimal and add the commas ,,

Going from Scientific Notation Positive Exponents So … So … x 10 7 = 82,740,000

Going from Scientific Notation Positive Exponents Write x 10 6 in standard notation Write x 10 6 in standard notation

Going from Scientific Notation Positive Exponents So let’s move the decimal 6 spaces to the right. So let’s move the decimal 6 spaces to the right

Going from Scientific Notation Positive Exponents Now, for all the empty spaces, put a zero in them. Now, for all the empty spaces, put a zero in them

Going from Scientific Notation Positive Exponents Drop the decimal and add the commas. Drop the decimal and add the commas ,,

Going from Scientific Notation Positive Exponents So … So … x 10 6 = 5,003,000

Let’s try a few Let’s try a few x x x , ,402,100,000

Going from Scientific Notation Negative Exponents How do you go from 9.12 x to ? How do you go from 9.12 x to ?

Going from Scientific Notation Negative Exponents To go from scientific notation to standard notation, you must move the decimal to the LEFT To go from scientific notation to standard notation, you must move the decimal to the LEFT The number of spaces you move is equal to the number in the exponent. The number of spaces you move is equal to the number in the exponent.

Going from Scientific Notation Negative Exponents Remember what I told you – the negative numbers go in the box to the left to the left!

Going from Scientific Notation Negative Exponents Write x in standard notation Write x in standard notation

Going from Scientific Notation Negative Exponents So let’s move the decimal 7 spaces to the left. So let’s move the decimal 7 spaces to the left

Going from Scientific Notation Negative Exponents Now, for all the empty spaces, put a zero in them. Now, for all the empty spaces, put a zero in them

Going from Scientific Notation Negative Exponents Drop the decimal point, put a new decimal in the very front, and put a zero in front of that decimal. Drop the decimal point, put a new decimal in the very front, and put a zero in front of that decimal

Going from Scientific Notation Negative Exponents So … So … x =

Going from Scientific Notation Negative Exponents Write x in standard notation Write x in standard notation

Going from Scientific Notation Negative Exponents So let’s move the decimal 6 spaces to the left. So let’s move the decimal 6 spaces to the left

Going from Scientific Notation Negative Exponents Now, for all the empty spaces, put a zero in them. Now, for all the empty spaces, put a zero in them

Going from Scientific Notation Negative Exponents Drop the decimal point, put a new decimal in the very front, and put a zero in front of that decimal. Drop the decimal point, put a new decimal in the very front, and put a zero in front of that decimal

Going from Scientific Notation Negative Exponents So … So … x =

Let’s try a few Let’s try a few x x x

Wait, I think I see a pattern with negative exponents. I can just write 0s for the number of the exponent and put a decimal point after the first zero. Is that true?

Very clever young singing basketball boy. For NEGATIVE exponents only, you can just add the number of 0s as the exponent and then put the decimal point after the first zero.

Independent Practice Convert the following numbers from scientific to standard notation. Convert the following numbers from scientific to standard notation x x x x ,000,00083,

Independent Practice Convert the following numbers from scientific to standard notation. Convert the following numbers from scientific to standard notation x x x x , ,345,