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Math  /  Numbers & Operations

QuestionMercury Venus Planet Name Distance from Sun in kilometers How many times farther away from the Sun is Neptune compared to Mercury? 5.8-10' 1.1-108 Earth 1.5-10 Mars 2.3-10 Jupiter 7.8-108 Saturn 1.4-109 Uranus 2.9-109 Neptune 4.5-109 Round to the tenth's place. Mercury Venus Earth Mars Ceras Jepiter Satura Submit Uranus Neptune Pluto and Charon 2003 UB

Studdy Solution

STEP 1

1. We are given the distances of planets from the Sun in kilometers.
2. We need to find out how many times farther Neptune is from the Sun compared to Mercury.
3. The distance from the Sun to Mercury is 5.8×107 5.8 \times 10^7 km.
4. The distance from the Sun to Neptune is 4.5×109 4.5 \times 10^9 km.
5. We are asked to round the final answer to the tenth's place.

STEP 2

1. Identify the distances of Mercury and Neptune from the Sun.
2. Set up the ratio of Neptune's distance to Mercury's distance.
3. Calculate the ratio.
4. Round the result to the tenth's place.

STEP 3

Identify the distance from the Sun to Mercury and Neptune.
- Mercury: 5.8×107 5.8 \times 10^7 km - Neptune: 4.5×109 4.5 \times 10^9 km

STEP 4

Set up the ratio of Neptune's distance to Mercury's distance.
Ratio=Distance of NeptuneDistance of Mercury=4.5×1095.8×107\text{Ratio} = \frac{\text{Distance of Neptune}}{\text{Distance of Mercury}} = \frac{4.5 \times 10^9}{5.8 \times 10^7}

STEP 5

Calculate the ratio.
First, simplify the powers of ten:
4.5×1095.8×107=4.55.8×109−7=4.55.8×102\frac{4.5 \times 10^9}{5.8 \times 10^7} = \frac{4.5}{5.8} \times 10^{9-7} = \frac{4.5}{5.8} \times 10^2
Now, calculate 4.55.8 \frac{4.5}{5.8} :
4.55.8≈0.7759\frac{4.5}{5.8} \approx 0.7759
Multiply by 102 10^2 :
0.7759×100=77.590.7759 \times 100 = 77.59

STEP 6

Round the result to the tenth's place.
The result 77.59 77.59 rounded to the tenth's place is 77.6 77.6 .
Neptune is approximately 77.6 \boxed{77.6} times farther away from the Sun compared to Mercury.

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