Problem 2 - Calculate With Confidence

Question

Complete the table below. Express each of the following measures in their equivalents where indicated. Reduce fractions and ratios to lowest terms; round decimals to hundreths. $$ \begin{array}{|l|l|l|l|l|} \hline & \text { Percent } & \text { Ratio } & \text { Fraction } & \text { Decimal } \\ \hline 2 . & 71 \% & & & \\ \hline \end{array} $$

Step-by-Step Solution

Answer

71% is 71:100 as a ratio, \( \frac{71}{100} \) as a fraction, and 0.71 as a decimal.

Step 1: Convert Percent to Ratio

The percentage given is 71%. To convert a percentage to a ratio, express the percentage as a fraction over 100 and reduce it to its lowest terms. 71% as a fraction is \( \frac{71}{100} \). The ratio equivalent of 71% is 71:100, already in simplest form since 71 and 100 have no common factors other than 1.

Step 2: Convert Percent to Fraction

Convert 71% to a fraction. Percent means per hundred, so 71% is \( \frac{71}{100} \). The fraction is already in its simplest form because 71 and 100 do not have any common factors other than 1.

Step 3: Convert Percent to Decimal

To convert 71% to a decimal, divide the percentage by 100. Thus, \( 71\% = \frac{71}{100} = 0.71 \). The decimal equivalent of 71% is 0.71.

Key Concepts

Percent to Ratio Conversion

Understanding how to convert percentages to ratios is a useful skill in many real-life situations. When we say a number is a certain percent, it tells us that the number is that many parts out of 100. For example, consider 71%. This means 71 parts out of 100. To convert this percentage into a ratio, we simply express it in the form of "parts to whole."

• A percentage like 71% becomes the ratio 71:100.

Since ratios are already presented in their simplest terms when there are no common factors between the numbers, the ratio form of 71%, 71:100, does not require any further simplification. This conversion helps us to easily compare different quantities or portions directly, as ratios are an intuitive way to see the relationship between parts and the whole.

Percent to Fraction Conversion

Turning a percent into a fraction is straightforward once you understand the meaning of percent, which stems from the Latin phrase "per centum," meaning per hundred. So, when you have 71%, it essentially means 71 out of every 100 units. To express this as a fraction, you write it like this:\[\frac{71}{100}\]

• The numerator (the top part of the fraction) is the percent number itself, 71 in this case.
• The denominator (the bottom part of the fraction) is always 100 because percent means per hundred.

This fraction \( \frac{71}{100} \) is already in its simplest form because 71 is a prime number, which means it doesn’t share any factors with 100 other than the number 1. When converting percentages to fractions, always check to see if the fraction can be reduced by finding any greatest common factors.

Percent to Decimal Conversion

Converting a percentage to a decimal is a straightforward process that involves simple division. A percentage represents a number as parts per hundred, so to ditch the percent sign and find the decimal equivalent, you divide by 100. This turns the percent into its decimal form, making it easier to use in different types of mathematical calculations.Here's how to do it for 71%:

• Take the number 71 (the percent without the percent sign).
• Divide it by 100 because percent means per 100: \( \frac{71}{100} = 0.71 \).

So, 71% becomes 0.71. When converting, make sure to align the decimal point correctly, especially if dealing with more complex or large numbers. This method applies universally, and knowing it simplifies the process, allowing for quick conversions between different numerical formats.