Question

perform the following calculations and report your answers with the correct number of significant figures: $\frac{(6.531\times10^{13})(6.02\times10^{23})}{(435)(2.000)} = square\times10^{square}$ $\frac{4.476+(3.44)(5.6223)+5.666}{(4.3)(7\times10^{4})}=square\times10^{square}$ etextbook and media save for later attempts: 4 of 5 used

Explanation:

Step1: Calculate numerator of first - fraction

First, multiply the numbers in scientific - notation in the numerator: $(6.531\times10^{13})(6.02\times10^{23})=(6.531\times6.02)\times10^{13 + 23}=39.31662\times10^{36}=3.931662\times10^{37}$.

Step2: Calculate denominator of first - fraction

Multiply the non - scientific numbers in the denominator: $(435)(2.000)=870$.

Step3: Calculate first - fraction result

$\frac{3.931662\times10^{37}}{870}=\frac{3.931662}{870}\times10^{37}\approx0.00452\times10^{37}=4.52\times10^{34}$.

Step4: Calculate numerator of second - fraction

First, multiply $(3.44)(5.6223)=19.340712$. Then, $4.476+(3.44)(5.6223)+5.666=4.476 + 19.340712+5.666=29.482712$.

Step5: Calculate denominator of second - fraction

Multiply $(4.3)(7\times10^{4})=(4.3\times7)\times10^{4}=30.1\times10^{4}=3.01\times10^{5}$.

Step6: Calculate second - fraction result

$\frac{29.482712}{3.01\times10^{5}}=\frac{29.482712}{3.01}\times10^{-5}\approx9.8\times10^{-5}$.

Answer:

The first result is $4.52\times10^{34}$, and the second result is $9.8\times10^{-5}$.