Question

one estimate for the number of protons in betelgeuse is 2.16×10^58. the mass of one proton is about 1.67×10^(-27) kg. what is the total mass of all the protons in betelgeuse? which scientist do you agree with?

Explanation:

Step1: Recall product rule of exponents

When multiplying numbers in scientific - notation \(a\times10^{m}\) and \(b\times10^{n}\), the result is \((a\times b)\times10^{m + n}\). Here, \(a = 2.16\), \(m = 58\), \(b=1.67\), and \(n=-27\).

Step2: Multiply the coefficients

Multiply the non - exponential parts: \(2.16\times1.67 = 3.6072\).

Step3: Add the exponents

Add the exponents of 10: \(58+( - 27)=58 - 27 = 31\).

Step4: Write the result in scientific notation

The total mass is \(3.6072\times10^{31}\text{ kg}\).

Answer:

\(3.6072\times10^{31}\text{ kg}\)