Question

Mars is 35 million miles from the Earth. Pluto is 4.67 billion miles from the Earth.

4. Express the distance from Mars to Earth in scientific notation.


5. Express the distance from Pluto to Earth in scientific notation.


6. Calculate the ratio of the distance from Pluto to Earth to the distance from Mars to Earth. Use scientific notation to calculate the ratio and to express your answer. (round to the hundredths place)

Answer 1

we have that

Mars is
`35` million miles from the Earth.

Pluto is
`4.67` billion miles from the Earth.

we know that

`1 billion=1,000,000,000=1*10^(9)`

Part 1) Express the distance from Mars to Earth in scientific notation

`35\ million\ miles=35,000,000\ miles=3.5*10^(7)\ miles`

therefore

the answer part 1) is

`3.5*10^(7)\ miles`

Part 2) Express the distance from Pluto to Earth in scientific notation

`4.67\ billion\ miles=4,670,000,000\ miles=4.67*10^(9)\ miles`

therefore

the answer Part 2) is

`4.67*10^(9)\ miles`

Part 3) Calculate the ratio of the distance from Pluto to Earth to the distance from Mars to Earth. Use scientific notation to calculate the ratio and to express your answer

`ratio=(4.67*10^(9))/(3.5*10^(7)) \\ \\ ratio=(4.67*10^(2))/(3.5)}\\ \\ ratio=(467)/(3.5) \\ \\ ratio=133.43`

`ratio=1.3343*10^(2)`

therefore

the answer Part 3) is

`1.3343*10^(2)`

Answer 2

- Mars to Earth:
35,000,000 miles = 3.5 * 10^7 miles
- Pluto to Earth:
4,670,000,000 miles = 4.67 * 10^9 miles
- The ratio of the distances:
4.67 * 10^9 : 3.5 * 10^7 = 133.43 : 1