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Answer :
Sure! Let's go through the steps to convert 113.4 gallons to deciliters. Here's how we can do it:
1. Understand the Conversion Factors:
- 1 gallon equals 3.7854 liters.
- 1 liter equals 10 deciliters.
2. Convert Gallons to Liters:
- We are given 113.4 gallons.
- To convert gallons to liters, we multiply the number of gallons by the conversion factor from gallons to liters:
[tex]\[
113.4 \text{ gallons} \times 3.7854 \text{ liters/gallon}
\][/tex]
3. Calculate the Number of Liters:
- By multiplying, we get:
[tex]\[
113.4 \times 3.7854 = 429.26436 \text{ liters}
\][/tex]
4. Convert Liters to Deciliters:
- Next, we need to convert the liters to deciliters.
- Since 1 liter equals 10 deciliters, we multiply the number of liters by 10:
[tex]\[
429.26436 \text{ liters} \times 10 \text{ deciliters/liter}
\][/tex]
5. Calculate the Number of Deciliters:
- By multiplying, we get:
[tex]\[
429.26436 \times 10 = 4292.6436 \text{ deciliters}
\][/tex]
So, 113.4 gallons is equal to approximately 4292.6436 deciliters.
Now, looking at the given options:
- A) [tex]\(3.000 \times 10^2 \text{ dL}\)[/tex]
- B) [tex]\(4.293 \times 10^2 \text{ dL}\)[/tex]
- C) [tex]\(1.134 \times 10^3 \text{ dL}\)[/tex]
- D) [tex]\(4.293 \times 10^3 \text{ dL}\)[/tex]
The correct answer is:
[tex]\[ \boxed{4.293 \times 10^3 \text{ dL}} \][/tex]
1. Understand the Conversion Factors:
- 1 gallon equals 3.7854 liters.
- 1 liter equals 10 deciliters.
2. Convert Gallons to Liters:
- We are given 113.4 gallons.
- To convert gallons to liters, we multiply the number of gallons by the conversion factor from gallons to liters:
[tex]\[
113.4 \text{ gallons} \times 3.7854 \text{ liters/gallon}
\][/tex]
3. Calculate the Number of Liters:
- By multiplying, we get:
[tex]\[
113.4 \times 3.7854 = 429.26436 \text{ liters}
\][/tex]
4. Convert Liters to Deciliters:
- Next, we need to convert the liters to deciliters.
- Since 1 liter equals 10 deciliters, we multiply the number of liters by 10:
[tex]\[
429.26436 \text{ liters} \times 10 \text{ deciliters/liter}
\][/tex]
5. Calculate the Number of Deciliters:
- By multiplying, we get:
[tex]\[
429.26436 \times 10 = 4292.6436 \text{ deciliters}
\][/tex]
So, 113.4 gallons is equal to approximately 4292.6436 deciliters.
Now, looking at the given options:
- A) [tex]\(3.000 \times 10^2 \text{ dL}\)[/tex]
- B) [tex]\(4.293 \times 10^2 \text{ dL}\)[/tex]
- C) [tex]\(1.134 \times 10^3 \text{ dL}\)[/tex]
- D) [tex]\(4.293 \times 10^3 \text{ dL}\)[/tex]
The correct answer is:
[tex]\[ \boxed{4.293 \times 10^3 \text{ dL}} \][/tex]
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