8.EE.4 - Operations in Scientific Notation

EXPRESS THE FOLLOWING AS WHOLE NUMBERS OR AS DECIMALS PROBLEMSANSWERS 1) 4.9 X ) 3.75 X ) 5.95 X ) 9.46 X ) 3.87 X ) 7.10 X ) 8.2 X )490 2) ) )9460 5)38.7 6)7.10 7)

Multiplication When multiplying numbers written in scientific notation…..multiply the coefficients and add the exponents. Sample Problem: Multiply (3.2 x ) (2.1 x 10 5 ) Solution: Multiply (3.2 x 2.1). Add the exponents (10 -3 x 10 5 ) = Answer: 6.7 x 10 2

Foldable Example (2.6 x 10 5 ) x (3 x 10 2 )

Foldable Example 2 (3.2 x ) (4.3 x 10 5 ) LARS Alert!

Let’s Practice… (4 x 10 3 ) x (2 x 10 2 )(3.22 x ) x (8 x 10 5 ) LARS Alert!

Scientific Notation Word Problems Apple’s iPhone 6 has a thickness of 2.7 x inches. What would be the thickness (in inches) of 20 iPhone 6’s stacked on top of one another? What operation will be used to solve this problem?

Scientific Notation Word Problems For the 2014 season, the cast of The Big Bang Theory each earned $1.0 x 10 6 per episode. If the cast filmed 15 episodes, how much total salary did they earn? What operation will be used to solve this problem?

Practice Problems 1)(8x10 5 )(7x10 9 ) 1)(2x10 -5 )(4x10 -3 ) 1)(9x10 -3 )(5x10 4 ) 4) (2x10 8 )(6x10 -3 ) 5) (3.12 x 10 2 )(6.501 x 10 5 ) 6) ( x 10 1 )(7.1 x 10 4 ) LARS Alert! LARS Alert! LARS Alert! LARS Alert! LARS Alert!

Division Divide the coefficients. Subtract the exponent in the denominator from the exponent in the numerator. Sample Problem: Divide (6.4 x 10 6 ) by (1.7 x 10 2 ) Solution: Divide 6.4 ÷ 1.7 Subtract the exponents Answer: 3.8 x 10 4

Foldable Example (5.4 x 10 6 ) (1.2 x 10 3 )

Foldable Example 2 (6 x 10 7 ) (8 x 10 4 ) LARS Alert!

Scientific Notation Word Problems Tennessee covers an area of x 10 4 square miles. The largest state, Alaska, covers x 10 5 square miles. About how many times greater is the area covered by Alaska than by Tennessee? What operation will be used to solve this problem?

The area of the Pacific Ocean is 6.0 x 10 7 square miles. The area of the Atlantic Ocean is 2.96 x 10 7 square miles. About how many times greater is the area of the Pacific Ocean than the Atlantic Ocean?

Practice with Quotients (8 x 10 3 ) (4 x 10 2 ) (7 x 10 8 ) (4 x 10 5 ) 3) (9.64 x ) / (2.5 x 10 7 ) (4 x 10 6 ) ÷ (5 x 10 3 ) (6 x ) / (2 x 10 3 ) LARS Alert!

Addition and Subtraction To add or subtract numbers written in scientific notation, you must….express them with the same power of ten. Sample Problem: Add (5.8 x 10 3 ) and (2.16 x 10 4 ) Solution: Since the two numbers are not expressed as the same power of ten, one of the numbers will have to be rewritten in the same power of ten as the other. 5.8 x 10 3 =.58 x 10 4 so (.58 x 10 4 ) + (2.16 x 10 4 ) =? Answer: 2.74 x 10 4 LARS

Foldable Example 1 (4.5 x 10 7 ) + (2.5 x 10 7 )

Foldable Example 2 (4.5 x 10 7 ) + (2.5 x 10 8 ) LARS

Foldable Example 3 (8.7 x 10 5 ) – (4 x 10 5 )

Foldable Example 4 (8.7 x 10 5 ) – (4 x 10 3 ) LARS

Adding and Subtracting 1)(6.2 x 10 3 ) + (1.3 x 10 3 ) 2)(3.4 x ) + (4.6 x ) 3)(7.2 x 10 8 ) + (2.3 x 10 7 ) 4) (6.2 x 10 3 ) - (1.3 x 10 3 ) 5) (5.8 x ) - (4.6 x ) 6) (7.2 x 10 8 ) - (2.3 x 10 7 ) LARS