Scientific Notation in the Real World

Scientific Notation in the Real World

8-E2

Precalculus

8-E2

Precalculus

Scientific notation in the real world: Exercises 1-4

Exercise 1:

Earth has a diameter of approximately d ? 1.27 ¡Á 10 4 km.

Use the formula for the volume of a sphere to calculate

the volume of the Earth (the formula is given at the end

of the page).

Exercise 2:

Planet Jupiter has an approximate volume V ? 1.53 ¡Á 10 15 km3 .

Determine its diameter.

Exercise 3:

Determine the ratio of diameters and the ratio of volumes of

Jupiter and Earth.

Exercise 4:

The Sun is approximately 150 millions kilometers away from

the Earth. How long does it take for the light to reach us?

The speed of light is approximately 300.000.000 m/s.

The formula of the volume of a sphere : V =

8-P1

4

¦Ð r3 .

3

Precalculus

Scientific notation in the real world: Exercises 5, 6

Exercise 5:

Knowing the surface s and the average depth d of the

Atlantic Ocean calculate its volume

s ? 106.400.000 km 2 ,

d ? 3293 m .

Exercise 6:

Taking the mass of a grain of fine sand to be

m s ? 4? 10?9 kg

,

determine the mass of 1.000.000 grains.

8-P2

Precalculus

Scientific notation in the real world: Solution 1

d ? 1.27 ¡Á 10 4 km



The Earth

d

r= ,

2

8-1

( )

4

4

d

V = ¦Ðr3 = ¦Ð

3

3

2

? 1.07?10 12 km3

3

=

4¦Ð

3

¦Ð d 3 ? 3.14 ( 1.27?10 4 ) 3 ?

d

=

6

6

3?2 3

Precalculus

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