Question

A baseball player has 36 hits in a season where he was at bat 110 times. What percent of his times at bat did he get a hit?

Short answer

Answer: 32.73%

Step-by-step solution

Identify the given numbers

The number of hits is 36, and the number of times at bat is 110. We will use these numbers to calculate the ratio of hits to at-bats.

Calculate the ratio of hits to at-bats

To calculate the ratio, we will divide the number of hits by the number of times at bat. This will give us a fraction representing the proportion of hits to at-bats. In this case, the ratio is: \[\frac{36}{110}\]

Convert the ratio to a percentage

To convert the ratio to a percentage, we will multiply the fraction by 100. This will change the fraction to a decimal, which can then be represented as a percentage. The calculation is as follows: \[\frac{36}{110} \times 100\%\]

Calculate the percentage

Now, we can calculate the percentage by performing the division and multiplication in the above expression: \[(\frac{36}{110}) \times 100\% = 32.73\%\]

Interpret the result

The baseball player got a hit in 32.73% of his times at bat. This means that out of every 100 at-bats, he got a hit approximately 33 times.

Key concepts

Ratios and Proportions

Ratios and proportions are mathematical concepts used to express relationships between numbers. In this context, the ratio of hits to at-bats is important to understand the baseball player's performance. A ratio is essentially a fraction that shows how many times one number contains another. In this problem, the number of hits (36) is compared to the number of at-bats (110).
The process begins by creating a fraction:

• Numerator: The part - in this case, the number of hits - goes on top, which is 36.
• Denominator: The whole - the total number of at-bats - goes on the bottom, which is 110.

Thus, the ratio of hits to at-bats is expressed as \(\frac{36}{110}\). Ratios like this help us compare the part (hits) to the whole (at-bats) and can further be used to calculate percentages to better convey the player's performance in a more understandable way.

Fraction to Decimal Conversion

Fraction to decimal conversion is a useful skill, especially when dealing with percentages. This conversion helps in moving between various forms of numerical expression. Once we have the ratio \(\frac{36}{110}\), the next step is to convert it into a decimal to simplify understanding or make further calculations.
This is done by performing the division \(36 \div 110\). When you divide these numbers, you get a decimal result of approximately 0.3273. Decimal numbers offer a way to easily interpret ratios in day-to-day scenarios.

• Step 1: Divide the numerator (36) by the denominator (110).
• Step 2: The result is a decimal - here, it is 0.3273.

The decimal conversion is particularly significant when multiplying by 100 to get the percentage, smoothing transition from fractions to percentages.

Interpreting Results in Context

Interpreting results helps to understand the practical meaning of numerical outcomes. Here, we validate the calculation result, where dividing \(\frac{36}{110}\) gave us 0.3273 as a decimal. By multiplying this by 100, we convert it to 32.73%.
To put these figures into a familiar context, we interpret this percentage as a general batting performance metric, indicating that the baseball player hits successfully 32.73 times out of every 100 at-bats. Simplifying further, it means:

• If he bats 100 times, he's likely to hit successfully around 33 times.
• This evaluation is crucial for coaches or statisticians who are analyzing player performance.

Understanding percentages through this kind of contextual interpretation is essential, as it translates raw numerical data into real-world insights and helps in making informed decisions regarding players' effectiveness.