operations on scientific notation addition and subtraction 1. if they have the same exponent -...

Operations on Scientific Operations on Scientific NotationNotation

Addition and SubtractionAddition and Subtraction

1. If they have the same exponent1. If they have the same exponent- add/subtract the number in front- add/subtract the number in front

- keep the same exponent- keep the same exponent

2. If they don’t have the same exponent2. If they don’t have the same exponent- change the smaller to the larger exponent- change the smaller to the larger exponent

-repeat step #1-repeat step #1

AdditionAddition

Given: (2.56 X 10Given: (2.56 X 103 3 )+ (6.964 X 10)+ (6.964 X 103 3 )) Add: 2.56 + 6.964 = 9.524Add: 2.56 + 6.964 = 9.524 Answer: Answer: 9.524 X 109.524 X 1033

22

Addition/SubtractionAddition/Subtraction

If the exponents are different, you must If the exponents are different, you must move the decimal either right or left so move the decimal either right or left so that they will have the same exponent.that they will have the same exponent.

For each move of the decimal to the right For each move of the decimal to the right you have to add -1 to the exponent.you have to add -1 to the exponent.

For each move of the decimal to the left For each move of the decimal to the left you have to add +1 to the exponent.you have to add +1 to the exponent.

33

AdditionAddition(1 .5 X10(1 .5 X1033)+ (2.3 X 10)+ (2.3 X 1022)+ (2.0 X 10)+ (2.0 X 1033))

All NUMBERS MUST HAVE THE SAME All NUMBERS MUST HAVE THE SAME POWERS OF TENPOWERS OF TEN

Change 2.3 x 10Change 2.3 x 1022 by moving decimal to by moving decimal to the left, 0.23 x 10the left, 0.23 x 1033

(1.5 + 0.23 + 2.0) X 10(1.5 + 0.23 + 2.0) X 103 3 = 1.73 X 10 = 1.73 X 1033

AdditionAddition

Given: (2.46 X 10Given: (2.46 X 1066)) + (3.476 X 10+ (3.476 X 1033)) Shift decimal 3 places to the left for 10Shift decimal 3 places to the left for 1033.. Move: .003476 X 10Move: .003476 X 103+33+3

Add: 2.46 X 10Add: 2.46 X 106 6 + .003476 X 10+ .003476 X 1066

Answer: Answer: 2.463 X 102.463 X 1066

55

SubtractionSubtraction

(8.96 x 10(8.96 x 1077) – (3.41 x 10) – (3.41 x 1077)) 8.96 – 3.41 = 5.558.96 – 3.41 = 5.55 5.55 x 105.55 x 1077

66

SubtractionSubtraction

Given: (5.762 X 10Given: (5.762 X 1033)) – (2.65 X 10– (2.65 X 10-1-1)) Shift decimal 4 places to the right for 10Shift decimal 4 places to the right for 10-1-1.. Move: .000265 X 10Move: .000265 X 10(-1+4)(-1+4)

Subtract: 5.762 X 10Subtract: 5.762 X 1033-.000265 X 10-.000265 X 1033

Answer: Answer: 5.762 X 105.762 X 1033

77

Addition/SubtractionAddition/Subtraction

Add/Subtract:Add/Subtract:

A.A. ( (2.0 X 102.0 X 1044)- (3.0 X 10)- (3.0 X 1033))

B. (6.4 X 10B. (6.4 X 1022)+ (2.3 X 10)+ (2.3 X 1033) + (4.5 X 10) + (4.5 X 1044))

88


Multiplication and DivisionMultiplication and Division

1. Mult. / Divide the number in front1. Mult. / Divide the number in front

2. If Mult., add the exponents 2. If Mult., add the exponents

3. If Division, subtract the exponents.3. If Division, subtract the exponents.

MultiplyingMultiplying

MultiplicationMultiplication

(3.5 x 10(3.5 x 1022) x (2.0 x 10) x (2.0 x 1033) = ?) = ?

Multiply the coefficients, add Multiply the coefficients, add exponents.exponents.

(3.5 x 2.0) x 10(3.5 x 2.0) x 10(2 + 3)(2 + 3) = =

1010

7.0 x 107.0 x 1055


1111

MultiplicationMultiplication

(2.41 x 10(2.41 x 1044) x (3.09 x 10) x (3.09 x 1022) = ?) = ?

Multiply the coefficients, add Multiply the coefficients, add exponents.exponents.

(2.41 x 3.09) x 10(2.41 x 3.09) x 10(4 + 2)(4 + 2) = = 7.45 x 107.45 x 1066


Multiply the following:Multiply the following:

A. (2.1 x 10A. (2.1 x 1033)x (2.0 x 10)x (2.0 x 1022))

B. (3.1 x 10B. (3.1 x 10-1-1) x (3.0 x 10) x (3.0 x 10-2-2))

C. (4.0 x 10C. (4.0 x 1055) x (2.0 x 10) x (2.0 x 10-3-3))

1212

4.2 x 104.2 x 1055

9.3 x 109.3 x 10-3-3

8.0 x 108.0 x 1022

DividingDividing

DivisionDivision

4.2 x 104.2 x 104 4 / 2.0 x 10/ 2.0 x 1022 = ? = ?

Divide the coefficients, subtract the Divide the coefficients, subtract the exponentsexponents

(4.2/2.1) x 10(4.2/2.1) x 10(4-2)(4-2) = =

1313

2.1 x 102.1 x 1022

DividingDividing

DivisionDivision

4.89 x 104.89 x 1077/ 2.74 x 10/ 2.74 x 1044 = ? = ?

Divide the coefficients, subtract the Divide the coefficients, subtract the exponentsexponents

(4.89/2.74) x 10(4.89/2.74) x 10(7-4)(7-4) = =

1414

1.78 x 101.78 x 1033

DividingDividing

Divide the following:Divide the following:

A. (3.4 x 10A. (3.4 x 1055)/(1.7 x10)/(1.7 x10-2-2))

B. (6.3 x10B. (6.3 x10-3-3)/(2.1 x 10)/(2.1 x 10-3-3))

1515

2.0 x 102.0 x 1077

3.0 x 103.0 x 1000


HomeworkHomework

TextbookTextbookPg. AT4Pg. AT4#29 - 40#29 - 40

operations on scientific notation addition and subtraction 1. if they have the same exponent -...

Documents