Problem 33 - Prealgebra

Question

Express each decimal or fraction as a percent. Round to the nearest tenth,if necessary. $$\frac{14}{8}$$

Step-by-Step Solution

Answer

The fraction \( \frac{14}{8} \) is 175%.

Step 1: Convert the Fraction to Decimal

First, divide the numerator by the denominator to convert the fraction to a decimal. So, divide 14 by 8: \[ 14 \div 8 = 1.75 \]

Step 2: Convert the Decimal to a Percent

To convert a decimal to a percent, multiply it by 100. So, multiply 1.75 by 100: \[ 1.75 \times 100 = 175 \text{%} \]

Key Concepts

Understanding Fractions

A fraction is a way of expressing a number that is not whole. It consists of two parts: the numerator and the denominator. The numerator, which is the top number, represents the number of parts we have, while the denominator, the bottom number, signifies the total number of equal parts that make up a whole.
For example, in the fraction \( \frac{14}{8} \), 14 is the numerator, and 8 is the denominator. This fraction tells us that we have 14 parts out of 8 equal parts.
Every fraction can be converted into a decimal. By dividing the numerator by the denominator, you can determine the decimal equivalent. Fractions and decimals are two different ways of expressing the same concept and are often interchangeable.

Decimals Simplified

Decimals are a fundamental part of mathematics. A decimal number consists of a whole number part and a fractional part separated by a decimal point.
For instance, when you divide 14 by 8, you arrive at the decimal 1.75. The number 1.75 has a whole number (1), a decimal point, and a fractional part (.75).
Decimals are crucial because they provide an easy way to represent fractions in a different form. They make it easier to perform operations like addition, subtraction, multiplication, or division. In mathematics, converting fractions into decimals is a common task that helps in making calculations straightforward.

Mathematics Education

Mathematics education focuses on developing skills and understanding in the various topics of mathematics. One such aspect is learning the conversion between fractions, decimals, and percentages.
It is essential to understand these conversions to tackle problems effectively. Educational resources, such as textbooks and online platforms, often emphasize these conversions as they form a critical foundation in mathematics.
Students can benefit from practicing these conversions, as it enhances numerical fluency and confidence in handling mathematical problems. A robust grasp of these concepts often leads to a deeper understanding and ability to solve more complex mathematical equations.

Rounding Numbers with Ease

Rounding numbers is a mathematical process that simplifies numbers to make them easier to work with. In rounding, you replace a number with another number that is approximately equal but simpler or shorter.
In the context of percentages, rounding to the nearest tenth might be necessary when the decimal equivalent does not end in a whole number.

• If the digit in the tenths place is 5 or more, round up.
• If it is less than 5, round down.

For example, if you have a percentage of 175 from a decimal, and you need to round it to the nearest tenth, since it is already a whole number, no further rounding is needed.
Rounding helps to make numbers more manageable in calculations and provides answers that are easier to interpret.