MATH SOLVE

4 months ago

Q:
# The following table lists the masses, in grams, of the nine planets (including dwarf planet Pluto). Use the data to choose the correct answers in the item below.Planet Mass (in grams)Jupiter 1.989 ∙ 1030Saturn 5.685 ∙ 1029Neptune 1.024 ∙ 1029Uranus 8.681 ∙ 1028Earth 5.974 ∙ 1027Venus 4.869 ∙ 1027Mars 6.419 ∙ 1026Mercury 3.302 ∙ 1026Pluto 1.31 ∙ 1025Jupiter has a mass that is approximately times greater than Venus's.

Accepted Solution

A:

The ratio between the masses of Jupiter and Venus is[tex]\dfrac{1.989\cdot 10^{30}}{4.869\cdot 10^{27}}[/tex]We can separate the coefficient and the powers of ten:[tex]\dfrac{1.989\cdot 10^{30}}{4.869\cdot 10^{27}}=\dfrac{1.989}{4.869}\cdot \dfrac{10^{30}}{10^{27}}[/tex]Use the exponent rule[tex]\dfrac{a^b}{a^c}=a^{b-c}[/tex]to simplify the powers of 10:[tex]\dfrac{10^{30}}{10^{27}}=10^3[/tex]So, the ratio is[tex]\dfrac{1.989}{4.869}\cdot 10^3\approx 0.4\cdot 10^3=400[/tex]So, Jupiter has a mass that is approximately 400 times greater than Venus's.