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Answer :
To solve the problem of expressing [tex]\(\frac{12.0}{7.11}\)[/tex] to the correct number of decimal places, let's go through the options one by one and see which matches the true value.
The division [tex]\(\frac{12.0}{7.11}\)[/tex] gives us approximately 1.6877637.
Now, let's match this with the given answer choices:
- Option A: 1.688
This option involves rounding the result to three decimal places. If we round 1.6877637 to three decimal places, it indeed becomes 1.688.
- Option B: 1.69
This involves rounding the result to two decimal places. The number 1.6877637 becomes 1.69 when rounded to two decimal places because the third decimal (7) rounds up the second decimal (8) to 9.
- Option C: 1.7
This rounds the number to one decimal place. When we round 1.6877637 to one decimal place, we get 1.7 as 6 at the second place pushes 8 to 7 rounding up.
- Option D: 1.70
This also presents an answer to two decimal places. When 1.6877637 is rounded to two decimal places, it becomes 1.69, not 1.70.
So, based on the above steps, the closest true value of [tex]\(\frac{12.0}{7.11}\)[/tex] when rounded to a specified number of decimal places can be matched with:
- Option A: 1.688 if rounded to three decimal places,
- Option B: 1.69 if rounded to two decimal places,
- Option C: 1.7 if rounded to one decimal place.
Therefore, both Options A and C represent valid rounding of the result, with different decimal precision requirements. In context of this question, Option C, 1.7, is typically the simplest and most universally accepted when no exact precision is specified, but each option corresponds to different rounding rules.
The division [tex]\(\frac{12.0}{7.11}\)[/tex] gives us approximately 1.6877637.
Now, let's match this with the given answer choices:
- Option A: 1.688
This option involves rounding the result to three decimal places. If we round 1.6877637 to three decimal places, it indeed becomes 1.688.
- Option B: 1.69
This involves rounding the result to two decimal places. The number 1.6877637 becomes 1.69 when rounded to two decimal places because the third decimal (7) rounds up the second decimal (8) to 9.
- Option C: 1.7
This rounds the number to one decimal place. When we round 1.6877637 to one decimal place, we get 1.7 as 6 at the second place pushes 8 to 7 rounding up.
- Option D: 1.70
This also presents an answer to two decimal places. When 1.6877637 is rounded to two decimal places, it becomes 1.69, not 1.70.
So, based on the above steps, the closest true value of [tex]\(\frac{12.0}{7.11}\)[/tex] when rounded to a specified number of decimal places can be matched with:
- Option A: 1.688 if rounded to three decimal places,
- Option B: 1.69 if rounded to two decimal places,
- Option C: 1.7 if rounded to one decimal place.
Therefore, both Options A and C represent valid rounding of the result, with different decimal precision requirements. In context of this question, Option C, 1.7, is typically the simplest and most universally accepted when no exact precision is specified, but each option corresponds to different rounding rules.
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