Question

The mass of mars is \[6.42 \times {10^{29}}\] kg and mass of the sun is \[1.99 \times {10^{30}}\] kg. What is the total mass?

Answer 1

Hint: First, we will find the sum of the mass of mars, \[6.42 \times {10^{29}}\]kilograms and the mass of earth, \[1.99 \times {10^{30}}\] kilograms to find the total mass to find the required value in kilograms.

Complete step by step answer:

We are given that the mass of mars is \[6.42 \times {10^{29}}\] kg and mass of the sun is \[1.99 \times {10^{30}}\] kg.
We will find the sum of the mass of mars and the mass of earth to find the total mass, we get
\[
   \Rightarrow {\text{Total Mass}} = 6.42 \times {10^{29}} + 1.99 \times {10^{30}} \\
   \Rightarrow {\text{Total Mass}} = 6.42 \times {10^{29}} + 1.99 \times 10 \times {10^{29}} \\
   \Rightarrow {\text{Total Mass}} = 6.42 \times {10^{29}} + 19.9 \times {10^{29}} \\
 \]
Taking \[{10^{29}}\] common from the right-hand side of the above equation, we get
\[
   \Rightarrow {\text{Total Mass}} = {10^{29}}\left( {6.42 + 19.9} \right) \\
   \Rightarrow {\text{Total Mass}} = {10^{29}}\left( {26.32} \right) \\
   \Rightarrow {\text{Total Mass}} = 26.32 \times {10^{29}} \\
 \]
Hence, the total mass is \[26.32 \times {10^{29}}\] kg.

Note: In solving these types of questions, you need to know that a mass is a measure of the amount of matter in an object. One should know to get scared with exponential powers or try to open them as that will confuse you even more. This is a simple problem, so just avoid calculation mistakes. Do not forget to write the unit in the final answer.