Problem 84 - Prealgebra

Question

Compute the quotient 3/75, and round your answer to the nearest hundredth.

Step-by-Step Solution

Answer

The quotient is 0.04.

Step 1: Divide the Numerator by the Denominator

To find the quotient of \(\frac{3}{75}\), we need to divide the numerator (3) by the denominator (75). Using long division or a calculator, we divide 3 by 75 and get 0.04.

Step 2: Round the Quotient to the Nearest Hundredth

The result from division, 0.04, is already at two decimal places, which corresponds to the hundredth place. Therefore, rounding 0.04 to the nearest hundredth means that the answer remains 0.04.

Key Concepts

Fractions

Fractions represent parts of a whole. They are composed of two essential parts: the numerator, which is the top number indicating how many parts we have, and the denominator, which is the bottom number showing how many equal parts the whole is divided into.
This way, fractions are expressed as \( \frac{numerator}{denominator} \). For example, if we have \( 3/4 \), it means we have 3 parts out of a total of 4 parts.

• When you divide the numerator by the denominator, you can find the decimal equivalent.
• This can be done using long division or a calculator.

In the exercise example \( \frac{3}{75} \), you get the decimal 0.04 by dividing 3 by 75.

Rounding Numbers

Rounding is a useful mathematical technique that makes numbers simpler to work with by keeping them close to their original value. It's especially useful when you want to present data more concisely or need to work with estimates.
The exercise required rounding the number to the nearest hundredth. Here's how you can do that:

• Identify the digit in the place value you are rounding to. For the hundredths place, this is the second digit to the right of the decimal point.
• Look at the digit immediately after it, on its right.
• If that digit is 5 or greater, you increase the hundredth's place by 1.
• If it's less than 5, you leave the hundredth's place as is.

In the exercise example, 0.04 rounds to 0.04 because the digit in the thousandths place is 0, which is less than 5.

Numerator and Denominator

Understanding the roles of the numerator and the denominator is crucial for working with fractions. The numerator is the top number. It tells us how many parts of the whole we have. The denominator is the bottom number. It tells us into how many parts the whole is divided.
In a fraction like \( \frac{3}{75} \), 3 is the numerator, indicating that we have 3 parts. The denominator, 75, indicates that these 3 parts are out of a total of 75 equal parts.

• The larger the denominator, the smaller each part is, assuming the numerator stays the same.
• If the numerator is equal to the denominator, the fraction equals 1, representing a whole.

Dividing the numerator by the denominator converts the fraction into a decimal, as shown in the exercise where \( \frac{3}{75} \) equals 0.04.