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

Concepts and reason

The problem deals with the concept of significant figures and scientific notations. Convert the given value into scientific notation and then determine the value of significant figure and scientific notation.

Fundamentals

Significant figures: The significant figures are the non-zero digits. These are counted from the non-zero digit. It gives the required degree of accuracy. The significant figures is represented by \(m\). Scientific notation: The scientific notation is a way of writing a very large or very small number. Generally, it is written by writing the digit one place left to the decimal. The scientific notation is represented by \(n\).

 

The average distance from the sun to the earth \(150,000,000,000 \mathrm{~m}\) contains 10 zero. Therefore in scientific notation the average distance can be written as \(1.5 \times 10^{11} \mathrm{~m}\), the decimal is placed before the unit's digit.

The average distance from the sun to the earth is represented in the scientific notation as \(1.5 \times 10^{11} \mathrm{~m}\) in which the number of zeros in the value are placed in the power of 10 which include one extra zero as the decimal is placed before the unit's digit.

 

since the average distance from the sun to the earth is \(1.5 \times 10^{11} \mathrm{~m}\). Therefore the values of \(m\) and \(n\) are 1.5 and 11 respectively.

The value of \(m\) and \(n\) are \((m, n)=(1.5,11)\)

The decimal is placed after one digit and there is one digit after the decimal. It is the general rule of writing a value in significant figures. The value of \(m\) and \(n\) are \((m, n)=(1.5,11)\).