Question

Write each given percent as a decimal and a fraction in lowest terms Write each given fraction as a decimal and a percent. In \(1820,\) almost \(72 \%\) of U.S. workers were employed in farm occupations. By \(1994,\) only \(\frac{1}{40}\) of U.S. workers were employed in farming.

Short answer

72% = 0.72 = 18/25; 1/40 = 0.025 = 2.5%

Step-by-step solution

- Convert Percent to Decimal

To convert a percent to a decimal, divide by 100. So for 72%, we perform the operation: 72% ÷ 100 = 0.72

- Convert Percent to Fraction

To convert a percent to a fraction, place the percent value over 100 and simplify. For 72%, the fraction is: 72/100 = 18/25

- Convert Fraction to Decimal

To convert a fraction to a decimal, divide the numerator by the denominator. In this case: 1 ÷ 40 = 0.025

- Convert Fraction to Percent

To convert a fraction to a percent, first convert it to a decimal (already done: 0.025), and then multiply by 100. So: 0.025 × 100 = 2.5%

Key concepts

Fraction Simplification

Simplifying fractions is an essential skill in math. It makes calculations easier and helps in understanding values better. The process involves reducing the fraction to its smallest possible form. For example, the fraction \(\frac{72}{100}\) can be simplified by finding the greatest common divisor (GCD) of 72 and 100, which is 4. Dividing both the numerator and the denominator by this number, we get \(\frac{18}{25}\).
Another example from the exercise is converting \(\frac{1}{40}\). This fraction is already in its simplest form because the numerator (1) and the denominator (40) do not have any common divisors other than 1. Simplifying fractions helps in making the numbers easier to work with, especially when performing further calculations.

Decimal Conversion

Decimal conversion involves changing fractions and percentages into decimal form. This process is straightforward. To convert a fraction to a decimal, you simply divide the numerator by the denominator.
For example, converting \(\frac{1}{40}\) involves the calculation \(\frac{1}{40} = 0.025\).
Similarly, converting a percentage to a decimal involves dividing the percentage by 100. For instance, with 72%, you perform the operation \(\frac{72}{100} = 0.72\). Converting values to decimals makes them easier to add, subtract, multiply, or divide in further calculations.

Percentage Calculation

Calculating percentages is a common math task, often related to real-world situations. To convert a fraction to a percentage or calculate a percentage from a decimal, specific methods are used.
For example, to convert a fraction like \(\frac{1}{40}\) to a percentage, first convert it to a decimal, which results in 0.025. Then multiply by 100 to find the percentage: \0.025 \times 100 = 2.5\%.
Similarly, turning a decimal like 0.72 into a percentage involves multiplying by 100: \0.72 \times 100 = 72\%.
These conversions are useful in various fields such as statistics, business, and everyday life to express proportions and comparisons more clearly.