Question

If the mass of Jupiter is \[1.9 \times {10^{27}}Kg\] and the mass of the sun is \[1.99 \times {10^{30}}Kg\] Find their total combined mass.

Answer 1

Hint: Just like in any normal question of finding total, we will also add the quantities here the only thing to be conscious of is the power raised to 10, overlooking that will create an enormous gap with the correct answer.

Complete step by step answer:
So we are given that the mass of sun is \[1.99 \times {10^{30}}Kg\] and the mass of Jupiter is \[1.9 \times {10^{27}}Kg\]
Clearly the mass of the sun is greater than the mass of Jupiter because the power raised to 10 in the sun is higher than Jupiter, just like our basic understanding of the solar system.
Now as for adding them we will get
\[\begin{array}{l}
 = 1.9 \times {10^{27}}Kg + 1.99 \times {10^{30}}Kg\\
 = {10^{27}}(1.9 + 1.99 \times {10^{30 - 27}})Kg\\
 = {10^{27}}(1.9 + 1.99 \times {10^3})Kg\\
 = {10^{27}}(1.9 + 1.99 \times 10 \times 10 \times 10)Kg\\
 = {10^{27}}(1.9 + 1.99 \times 1000)Kg\\
 = {10^{27}}(1.9 + 1990)Kg\\
 = 1991.9 \times {10^{27}}Kg\\
 = 1.9919 \times 1000 \times {10^{27}}Kg\\
 = 1.9919 \times {10^{27 + 3}}Kg\\
 = 1.9919 \times {10^{30}}Kg
\end{array}\]

Which means that \[1.9919 \times {10^{30}}Kg\] is the correct answer.

Note: The only thing to be conscious about in this question is power which is raised to 10 also note some important properties of exponents are \[{x^a} \times {x^b} = {x^{a + b}}\& \dfrac{{{x^a}}}{{{x^b}}} = {x^{a - b}}\] .