Question

On average, Mercury is about 57 , 000 , 000 km from the sun, whereas Neptune is about 4.5 x 10^9 from the sun. What is the difference between Mercury's and Neptune's distance from the sun?

Answer 1

On average, Mercury is about 57,000 ,000 km from the sun, whereas Neptune is about 4.5 x 10^9 km from the sun. What is the difference between Mercury's and Neptune's distance from the sun?

Answer:

Difference between Mercury's and Neptune's distance from the sun is
`4.443 * 10^9 \text{ km }`

Solution:

Given that,

Distance of mercury from sun = 57, 000, 000 km

Distance of Neptune from sun =
`4.5 * 10^9 \text{ km }`

To find: Difference between Mercury's and Neptune's distance from the sun

Let us convert distance of mercury from sun to scientific notation

Scientific notation is used to represent a decimal number between 1 and 10 multiplied by ten, so you can write large numbers using less digits

Steps to remember:

Move the decimal point in your number until there is only one non-zero digit to the left of the decimal point. The resulting decimal number is a.

Count how many places you moved the decimal point. This number is b.

If you moved the decimal to the left b is positive.

If you moved the decimal to the right b is negative.

If you did not need to move the decimal b = 0.

Write your scientific notation number as a x 10^b

`57, 000, 000 = 5.7 * 10^7`

Therefore,

Distance of mercury from sun =
`5.7 * 10^7 \text{ km }`

Calculating difference between Mercury's and Neptune's distance from the sun:

difference = Distance of Neptune from sun - Distance of mercury from sun

`\text{ difference } = (4.5 * 10^9) - (5.7 * 10^7)`

Let us make both powers same

`\text{ difference } = (4.5 * 10^9) - (0.057 * 10^9)`

Taking 10 power 9 common we get,

`\text{ difference } = 10^9(4.5-0.057)\\\\\text{ difference } = 10^9 * (4.443)\\\\\text{ difference } = 4.443 * 10^9`

Thus difference between Mercury's and Neptune's distance from the sun is
`4.443 * 10^9 \text{ km }`