Scientific Notation Study Guide

Transcription

1 Scientific Notation Study Guide What is scientific notation?: Scientific notation is a shorthand method to represent VERY LARGE numbers or VERY SMALL numbers. Ex: 3,400,000,000 = = General Structure: d = Decimal This must be a number between 1 and 10. d 10 n n = Integer The number of times the decimal point is moved. THIS IS NOT THE NUMBER OF ZEROS!!! CONVERTING FROM STANDARD FORM TO SCIENTIFIC NOTATION STEP 1: Move the decimal point as many times as needed to obtain a decimal number between 1 and STEP 2: The amount of places the decimal was moved becomes the exponent on the 10 Moved the decimal 3 places 10 3 STEP 3: Put it all together: 3562 = in scientific notation. If the decimal point moves left, the exponent on the 10 is positive; if it moves right the exponent is negative.

2 CONVERTING FROM SCIENTIFIC NOTATION TO STANDARD FORM If the n in is POSITIVE Move the decimal point to RIGHT to put it back in to standard form. Ex OR If the n in is NEGATIVE Move the decimal point to LEFT to put it back in to standard form. Ex OR

3 MULTIPLYING NUMBERS IN SCIENTIFIC NOTATION ( ) ( ) STEP 1: Use the commutative property of multiplication to re-write the problem. ( ) ( ) Remember The commutative property of multiplication allows you to change the order. Therefore, you can write your decimals together and your powers of ten together. STEP 2: Use the associative property of multiplication to re-write the problem ( ) ( ) Remember The associative property of multiplication allows you to group your numbers. Therefore, you can group your decimals together and your powers of ten together.

4 STEP 3: Simplify. Multiply the decimals. Use the product law (exponent laws) to multiply the powers of ten. ( ) ( ) *Line the right most digits of the numbers up when you multiply. Multiply as if there was no decimal point * Put the decimal back in at the end. This is based on the number of decimal places in the initial problem Product Law If the bases are the same (10) then add the exponents = STEP 4: Put the final answer in scientific notation Remember d 10 n Use Product law to combine powers of ten. d = number between 1-10 FINAL ANSWER:

5 DIVIDING NUMBERS IN SCIENTIFIC NOTATION ( ) ( ) STEP 1: Re-Write the problem using a fraction bar to show division. ( ) ( ) STEP 2: Separate the problem in to two fractions. Remember This works because when we multiply fractions we multiply straight across.

6 STEP 3: Simplify. Divide the decimals. Use the quotient law (exponent laws) to divide the powers of ten. *Using the traditional long division algorithm We must turn the divisor (2.1) in to a whole number by moving the decimal point once to the right. If we do it to the divisor we must do it to the dividend (8.4). Bring the decimal point straight up and divide as you normally would without the decimal point. Quotient Law If the bases are the same (10) then subtract the exponents (numerator denominator) = STEP 4: Be sure that your final answer is in SCIENTIFIC NOTATION (if necessary)!! Remember d 10 n Use the Product law to combine powers of ten. d = number between 1-10 FINAL ANSWER:

7 ADDING/SUBTRACTING NUMBERS IN SCIENTIFIC NOTATION ( ) + ( ) STEP 1: Factor out the power of 10 with the largest ORDER OF MAGNITUDE (Exponent) using the product law (exponent laws). ( ) + ( ) The purpose of doing this is so the order of magnitudes are the same. Therefore, we would change the larger order of magnitude to match the smaller one. Using the exponent product law = = STEP 2: Use the commutative and associative properties to rearrange the problem. ( ) + ( ) ( ) COMMUTATIVE PROPERTY ASSOCIATIVE PROPERTY Use the commutative property to change the order of the powers of 10 (if necessary this depends on how you initially write it). Then use the associative property to group the decimal and the power of 10 with the smallest order of magnitude together. STEP 3: Change the new grouping (decimal power of 10 with the smallest order of magnitude) to standard form ( ) Convert to Standard Form by moving the decimal to the right two times OR = 230

8 STEP 4: Use the distributive property to re-write the problem ( ) Because ( ) STEP 5: Add* what is inside the parentheses together. ( ) * The only difference between an addition problem and a subtraction problem is at this point. If this is a subtraction problem, you must subtract what is inside the parentheses. STEP 6: Put your answer back in to scientific notation. Use the product law (exponent laws) to do this We must make sure that the decimal is between 1 and 10. Therefore, we need to move the decimal to the right (positive) two times. We must take this in to account and multiply the problem by Use the product law to simplify. Final Answer: ( ) + ( ) =