Question

Write each given percent as a decimal and a fraction in lowest terms Write each given fraction as a decimal and a percent. About \(\frac{2}{3}\) of U.S. households with televisions subscribe to a cabletelevision service.

Short answer

Fraction: \(\frac{2}{3}\); Decimal: 0.6667; Percent: 66.67%.

Step-by-step solution

Convert the Fraction to a Decimal

To convert the fraction \(\frac{2}{3}\) to a decimal, perform the division of the numerator by the denominator. So, divide 2 by 3 which gives approximately 0.6667.

Convert the Decimal to a Percent

To convert the decimal 0.6667 to a percent, multiply by 100. So, 0.6667 \( \times \) 100 equals approximately 66.67%.

Write the Percent as a Fraction

To convert 66.67% to a fraction, start with \(\frac{66.67}{100}\). This can be simplified by recognizing that 66.67 is approximately two-thirds, hence \(\frac{66.67}{100} \approx \frac{2}{3} \).

Key concepts

Fraction to Decimal Conversion

To convert a fraction to its decimal form, you need to divide the numerator (the top number) by the denominator (the bottom number). This process gives you a decimal number representing the fraction.
For example, consider the fraction \(\frac{2}{3} \). You divide 2 by 3. Perform the division and you get 0.6667. This is the decimal equivalent of \(\frac{2}{3} \).

If you have a calculator, use it for precise division. If not, practice long division.

• Step 1: Set up the division problem as 2 divided by 3.
• Step 2: Perform the division, bringing down zeros as necessary.
• Step 3: After getting the repeating decimal 0.6667, you can round it based on your required precision. Here, we rounded to four decimal places.

Understanding how to convert fractions to decimals is crucial since it allows more versatile use in calculations and real-life applications.

Decimal to Percent Conversion

To change a decimal into a percent, simply multiply the decimal by 100.
This process shifts the decimal point two places to the right.

For example, if you have the decimal 0.6667, multiply it by 100 to get 66.67%.

• Step 1: Take the decimal number, which is 0.6667.
• Step 2: Multiply 0.6667 by 100 (0.6667 x 100 = 66.67).

Thus, 0.6667 becomes 66.67%.

It’s helpful to remember that converting decimals to percents is just a matter of moving the decimal point two digits to the right.
This conversion is useful in many fields, like banking, shopping, and statistics, helping compare different quantities quickly and easily.

Simplifying Fractions

Simplifying fractions means reducing them to their smallest form, where the numerator and denominator are as small as possible but still retain the same value.
To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator and then divide both by this number.

For instance, to simplify the fraction \(\frac{66.67}{100} \):

• Step 1: Recognize that the fraction resembles \(\frac{2}{3} \). This is because 66.67 is close to two-thirds of 100.
• Step 2: Directly relate it to \(\frac{2}{3} \), acknowledging they approximate each other.
• Step 3: The fraction \(\frac{2}{3} \) is already in its simplest form, where 2 and 3 share no common divisors other than 1.

It’s essential to get comfortable with recognizing patterns and simplifying fractions because it makes calculations and understanding numbers easier.

Practicing more examples will make this process quicker and intuitive.