Scientific Notation A method for re-writing really, really big and really, really small numbers as a power of ten.

Really BIG numbers and really small numbers have too many digits to fit on a calculator.

A number that is written in scientific notation must have... 1)a decimal point after the first non- zero digit ex) )a number in the tenths position ex) 2.0 3)be written as a product of a power of 10 ex) 3.45x10 9

BIG Numbers The decimal point of any whole number is at the end of the number. To change this number to scientific notation, the decimal point has to move to the right of the first non-zero number.

BIG Numbers To get the decimal point to the new position required for scientific notation, the decimal has to travel 15 place values to reach the position immediately to the right of the first non-zero number. That means it has moved 15 multiples of 10 or...

BIG Numbers To get the decimal point to the new position required for scientific notation, the decimal has to travel 15 place values to reach the position immediately to the right of the first non-zero number. That means it has moved 15 multiples of 10 or...

BIG Numbers Disappear 1)the decimal point is after the first non-zero digit 2)a number is in the tenths position 3)it is written as a product of a power of 10

BIG Numbers Convert to scientific notation. Where is the decimal point in this number? After the last zero. Where does the decimal point need to move to? Between the 1 and the 2. How many place values will the decimal point move? 11 What is the answer? a) =

BIG Numbers Convert to scientific notation. 1)the decimal point is after the first non- zero digit 2)a number is in the tenths position 3)it is written as a product of a power of 10 a) =

BIG Numbers Convert to scientific notation. Where does the decimal place need to move to? Between the 6 and the 0. How many place values will the decimal point move? 13 What is the answer? a) =

BIG Numbers Convert to standard form. The exponent (8) tells you how many place values needs to be put back into the number. =

BIG Numbers Convert to standard form. The exponent (11) tells you how many place values needs to be put back into the number. =

SMALL Numbers Convert to scientific notation. Where does the decimal point need to move to? Between the 1 and 2. How many place values does the decimal need to move? (Notice the decimal has to move to the right) -9 What is the answer?

SMALL Numbers Convert to scientific notation. 1)the decimal point is after the first non- zero digit 2)a number is in the tenths position 3)it is written as a product of a power of 10

SMALL Numbers Convert to scientific notation. Where does the decimal point need to move to? Between the 9 and the 0. How many place values does the decimal point need to move? -5 What is the answer?

SMALL Numbers Convert to standard form. How many place values need to be put back into the number? -9 Notice that there is an extra zero for the ones place value. What is the answer?

SMALL Numbers Convert to standard form. How many place values need to be put back into the number? -7 What is the answer?

Adding Numbers in Scientific Notation Remember - Whenever you add or subtract in math, “things” must be the same. To add or subtract decimal numbers, place values must be the same. To insure this one must convert both numbers to standard form first

Multiplying Numbers in Scientific Notation Remember - When multiplying powers with the same base you can add the exponents. Reorder and regroup. Follow BODMAS. What is the answer?

Multiplying Numbers in Scientific Notation Reorder and regroup. Follow BODMAS What is the answer? But wait, is this answer in scientific notation form?

Multiplying Numbers in Scientific Notation Why is this not considered in the correct form? The decimal point is not after the first non-zero number. If the decimal point has to move one more place value to the right, what will happen to the exponent on the power? The exponent has to decrease one to move one place value to the right.

Multiplying Numbers in Scientific Notation

Dividing Numbers in Scientific Notation Remember - When dividing powers with the same base just subtract exponents on those like bases. Separate into two separate fractions. Divide.

Dividing Numbers in Scientific Notation The result is... But this in not in the correct form for scientific notation. What needs to happen? Decrease the exponent by 1 The answer is...