Problem 10 - Prealgebra

Question

Express each decimal or fraction as a percent. Round to the nearest tenth, if necessary. $$\frac{12}{9}$$

Step-by-Step Solution

Answer

133.3%

Step 1: Divide the Numerator by the Denominator

First, divide the numerator (12) by the denominator (9) to convert the fraction into a decimal. This gives you approximately 1.3333.

Step 2: Convert the Decimal to a Percentage

To express the decimal as a percentage, multiply it by 100. Hence, 1.3333 multiplied by 100 gives 133.33.

Step 3: Round to the Nearest Tenth

Round 133.33 to the nearest tenth. The digit in the tenths place is 3, and the digit in the hundredths place is 3, so you round down, keeping it 133.3.

Key Concepts

Understanding Fractions

Fractions represent parts of a whole and are made up of two parts: the numerator and the denominator. The numerator, situated above the line, indicates how many parts we have. On the other hand, the denominator, below the line, tells us how many parts make up the whole. For instance, in the fraction \(\frac{12}{9}\), 12 is the numerator and 9 is the denominator. This means we have 12 parts out of a total of 9 equal parts.
To convert a fraction into a decimal, you simply divide the numerator by the denominator. This operation helps you to understand fractions in a form that is easier for comparison or further arithmetic operations. In our example, 12 divided by 9 equals approximately 1.3333. This result means that the fraction \(\frac{12}{9}\) is equivalent in value to the decimal 1.3333. Modifying fractions into decimals is a foundational skill for many areas in math, especially when dealing with percentages.

Demystifying Decimals

Decimals are another way to represent fractions and parts of a whole. Unlike fractions, decimals express these parts using a base-10 system, which aligns with our usual counting systems.
The term 'decimal' is derived from the Latin 'decimus,' meaning tenth. For a number like 1.3333, the digits to the right of the decimal point expand the number's detail by dividing intervals into smaller segments:

• The first digit after the decimal is the tenths' place.
• The second is the hundredths' place.
• And so forth.

In our exercise, after dividing 12 by 9, we received the decimal 1.3333. This decimal makes it easy to convert to a percentage by simply shifting the decimal two places to the right, which is the same as multiplying by 100. Therefore, 1.3333 becomes 133.33%. Decimals simplify many mathematical operations and allow for precise communication in financial, scientific, and engineering contexts.

Rounding Numbers Made Simple

Rounding numbers involves changing a number to the nearest place value to make it simpler and easier to work with. This is particularly useful when dealing with long decimals or when precision to a certain decimal place is necessary.
Let's look at the concept of rounding in the context of our exercise. After converting a fraction to the decimal 1.3333 and then to the percentage 133.33, we needed to round to the nearest tenth. The digit in the tenths place is the first number after the decimal point — here it is 3, in 133.3. The next digit, in the hundredths place, determines if we round up or down. If this digit is 5 or more, we round up. If it's less than 5, we round down, which we did, bringing our percentage to 133.3%.
Rounding can make numbers easier to read and understand, especially when presenting results in a report or calculating a budget. It ensures consistency and clarity when exact figures carry less importance.