Question

Determine the values of m and n when the following average distance from the Sun to the Earth is written in scientific notation: 150,000,000,000 m. Enter m and n, separated by commas.

Answer 1

In scientific notation, the average distance from the Sun to the Earth, 150,000,000,000 m, is written as 1.5 × 10¹¹. Values of m and n are 1.5 and 11 respectively.

Step-by-step explanation:

To express the average distance from the Sun to the Earth in scientific notation, we first identify the coefficient and the exponent that corresponds to the number 150,000,000,000 m. The coefficient (m) must be a number between 1 and 10, and the exponent (n) indicates the power of 10 that the coefficient must be multiplied by to return to the original number.

The number 150,000,000,000 m written in scientific notation is 1.5 × 10¹¹. Thus, the value of m is 1.5, and the value of n is 11. When using scientific notation in astronomy and other sciences, it simplifies the representation of very large numbers and works as a shorthand to avoid writing out many zeroes.

Answer 2

Answer: m=1.5, n=11

Step-by-step explanation:

When a number is written in scientific notation (representing the number using powers of base ten) it is expressed so that it contains a digit in the place of the units and all other digits after the decimal point, multiplied by the respective exponent. Then, the significant figures will be the digits that are before the power of ten.

In the case of the following number, which represents the average distance from the Sun to the Earth in meters:

`150,000,000,000 m`

Which expressed in scientific notation as
`m(10)^(n)` is:

`1.5(10)^(11)`

Therefore,
`m=1.5` and
`n=11`