Question

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The length of Rectangle 1 is 3.2 x 10^5 m. The width of Rectangle 1 is 1.6 x 10^4 m. What is the area of Rectangle 1? Write the answer in Scientific Notation.


Find the area of Rectangle 2 if its length is 1.28 x 10^7 m and its width is 8 x 10^3 m. Write the answer in Scientific Notation.


How many times larger is the area of Rectangle 2 than the area of Rectangle 1? Write the answer in Scientific Notation.


How many times larger is the area of Rectangle 2 than the area of Rectangle 1? Write the answer in Standard Form: __________ times larger

Answer 1

2.0 x
`10^(1)`

Explanation:

1. length = 3.2 x
`10^(5)` m

width = 1.6 x
`10^(4)` m

Area of a rectangle = length x width

= (3.2 x
`10^(5)`) x (1.6 x
`10^(4)`)

= 5.12 x
`10^(9)`
`m^(2)`

2. length = 1.28 x
`10^(7)` m

width = 8 x
`10^(3)` m

Area of a rectangle = length x width

= (1.28 x
`10^(7)`) x (8 x
`10^(3)`)

= 1.024 x
`10^(11)`
`m^(2)`

`(Area of rectangle 2)/(Area of rectangle 1)` =
`(1.024*10^(11) )/(5.12*10^(9) )`

= 20

= 2.0 x
`10^(1)`

Thus,

The area of rectangle 2 is 2.0 x
`10^(1)` times greater than the area of rectangle 1.