Problem 1 - 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. $$ \begin{array}{|l|l|l|l|l|} \hline & \text { Percent } & \text { Ratio } & \text { Fraction } & \text { Decimal } \\ \hline 1 . & 52 \% & & & \\ \hline \end{array} $$

Step-by-Step Solution

Answer

52% is equivalent to 13:25 as a ratio, \( \frac{13}{25} \) as a fraction, and 0.52 as a decimal.

Step 1: Convert Percent to Ratio

Percent values can be easily converted to ratios by placing the percent number over 100 and then reducing to the lowest terms. For 52\%, express this as \( \frac{52}{100} \). Simplifying by dividing both the numerator and the denominator by the greatest common divisor, which is 4, we get \( \frac{13}{25} \). Thus, the ratio is 13:25.

Step 2: Convert Percent to Fraction

To convert a percent to a fraction, write the percent value over 100. For 52\%, this is \( \frac{52}{100} \). Simplify by dividing the numerator and the denominator by their greatest common divisor, 4, resulting in \( \frac{13}{25} \). So the simplified fraction is \( \frac{13}{25} \).

Step 3: Convert Percent to Decimal

Convert a percent to a decimal by dividing the percent value by 100. For 52\%, perform the division: \( 52 \div 100 = 0.52 \). Thus, the decimal equivalent is 0.52.

Key Concepts

Percentages

Understanding percentages is crucial when dealing with mathematical conversions. A percentage is a way to express a number as a part of a whole, where the whole is divided into 100 equal parts. For example, 52% means 52 parts out of 100.

• When you see a percentage, think of it as a fraction of 100.
• To visualize, think of a pie chart where 100% represents the whole pie.
• Anything less than 100% means only a portion of that pie.

Percentages often make comparisons easier and allow us to quickly understand proportions. They are particularly useful in statistics, finance, and shopping when calculating discounts, for example.

Ratios

Ratios are used to compare two quantities, showing the relative size of one quantity to another. When converting a percentage to a ratio, you place the percentage number over 100. For instance, converting 52% to a ratio:- Write 52 over 100 to get \( \frac{52}{100} \)- Simplify the fraction by dividing by the greatest common divisor This gives the ratio 13:25 after simplifying.

• Ratios do not always need to be over 100.
• They reflect a relationship, not an absolute value.
• Examples include recipe adjustments or scaling models.

Fractions

Fractions represent a part of a whole, much like percentages, but are expressed in a different format. To convert a percentage, such as 52%, into a fraction, follow these steps:1. Write the percent as a fraction with 100 as the denominator: \( \frac{52}{100} \) 2. Reduce the fraction to its simplest form by dividing both the numerator and the denominator by the greatest common divisor (which is 4 in this case), resulting in \( \frac{13}{25} \).Fractions can show exact values where decimals and percentages might offer approximations.

• They are fundamental for understanding parts of a whole.
• Fractions can be more precise in mathematics.
• Useful in scenarios where exact division is needed.

Decimals

Decimals are another way to express parts of a whole, generally used when precision is not as critical as with fractions. Converting percentages to decimals is straightforward and involves dividing the percentage value by 100. For a percent like 52%, divide by 100 to get 0.52.

• Vastly used in measuring and finance where simple calculations are needed.
• Provide a clear and straightforward way of representing numbers.
• Unlike fractions, they are easy to use with modern calculators and computers.

Decimals are particularly useful for quick calculations and are an integral part of digital systems and scientific measurements.