Question

the approximate diameters of uranus and mars are listed below:

uranus: $5.11 \times 10^4$ kilometers
mars: $6.79 \times 10^3$ kilometers

how many times larger is the diameter of uranus than mars?
write your answer in standard notation, rounding to the nearest tenth.

answer
attempt 1 out of 3
standard notation
answer:

Explanation:

Step1: Divide Uranus' diameter by Mars' diameter

To find how many times larger Uranus' diameter is than Mars', we divide the diameter of Uranus by the diameter of Mars. So we have the expression $\frac{5.11 \times 10^{4}}{6.79 \times 10^{3}}$.

Step2: Simplify the exponents and the coefficients

Using the rule of exponents $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$, we can simplify the expression. First, simplify the exponents: $10^{4-3}=10^{1} = 10$. Then simplify the coefficients: $\frac{5.11}{6.79}\approx0.7526$.

Step3: Multiply the results from Step2

Now we multiply the two results: $0.7526\times10 = 7.526$. Rounding to the nearest tenth, we get $7.5$.

Answer:

7.5