Math Notes

EXPONENTS

 -AN EXPONENT SHOWS HOW MANY TIMES THE BASE NUMBER IS MULTIPLIED.  3^4 = 3x3x3x3=81 3 IS THE BASE AND 4 IS THE EXPONENT.  A FEW REMINDERS FOR EVALUATING EXPONENTS A BASE WITH AN EXPONENT OF 0 EQUALS 1 A BASE WITH AN EXPONENT OF 1 EQUALS THE BASE NUMBER. A POSITIVE BASE WITH A POSITIVE EXPONENT PRODUCES A POSITIVE NUMBER. A NEGATIVE BASE WITH AN EVEN EXPONENT PRODUCES A POSITIVE NUMBER. A NEGATIVE BASE WITH AN ODD EXPONENT PRODUCES A NEGATIVE NUMBER. A BASE WITH A NEGATIVE EXPONENT IS WRITTEN AS ITS RECIPROCAL(FRACTION) WITH A POSITIVE EXPONENT. RULES FOR EXPONENTS MULTIPLY EXPONENTS  ADD THE  EXPONENTS AND KEEP THE BASE THE SAME DIVIDE EXPONENTS SUBTRACT THE EXPONENTS AND KEEP THE BASE THE SAME POWER OF A POWER TO SIMPLIFY A NUMBER THAT HAS A POWER RAISED TO ANOTHER POWER, MULTIPLY THE EXPONENTS AND KEEP THE BASE THE SAME.

SCIENTIFIC NOTATION

3.4293 X 10^3

3.4293 IS THE COEFFICIENT AND 3 IS THE EXPONENT

TO CHANGE FROM SCIENTIFIC NOTATION TO STANDARD NOTATION

• IF EXPONENT POSITIVE, MOVE THE DECIMAL TO THE RIGHT THAT MANY TIMES
• IF EXPONENT NEGATIVE, MOVE THE DECIAL TO THE LEFT THAT MANY TIMES

TO CHANGE FROM STANDARD NOTATION TO SCIENTIFIC NOTATION

STEP 1:

• IDENTIFY IF THE NUMBER IS LARGER THAN ONE OR SMALLER THAN ONE.
• IF NUMBER IS LARGER THAN ONE THEN YOU KNOW THE EXPONENT IS POSITIVE AND IF THE NUMBER SMALLER THAN ONE YOU KNOW THE EXPONENT IS NEGATIVE.

STEP 2:

• FIND WHERE THE DECIMAL IS AND MOVE IT BEHIND THE FIRST NATURAL OR COUNTING NUMBER

STEP 3:

FILL IN THE EMPTY SPACES FOR THE ANSWER

______STEP 2______ X 10^_____STEP1_____

MULTIPLICATION OR DIVISION WITH SCIENTIFIC NOTATION

STEP 1:

MULTIPLY OR DIVIDE THE COEFFICIENT

STEP 2:

APPLY EXPONENT RULES FOR MULTIPLICATION OR DIVISION

• ADD IF ITS MULTIPLICATION AND SUBTRACT IF ITS DIVISION

STEP 3:

BRING IT ALL BACK TOGETHER AND MAKE SURE THE COEFFICIENT IS IN SCIENTIFIC NOTATION