Question

Express the following using numerals and abbreviations: one-third ounce

Short answer

\( \frac{1}{3} \text{ oz} \)

Step-by-step solution

Understand the phrase

The phrase "one-third ounce" indicates a measurement of quantity. "One-third" refers to the fraction 1/3, and "ounce" is a unit of mass or weight. Our task is to express this information using numerals and abbreviations.

Convert the fraction to numeral

The term "one-third" is mathematically represented as the fraction \( \frac{1}{3} \). This is the numeric part of our expression.

Abbreviate the unit

The unit "ounce" is commonly abbreviated as "oz" in measurements. This is the abbreviation for the unit of mass or weight.

Combine numeral and abbreviation

Now, combine the numeral from Step 2 with the abbreviation from Step 3. Therefore, "one-third ounce" is expressed numerically and abbreviated as \( \frac{1}{3} \text{ oz} \).

Key concepts

Fractions

Fractions are an essential concept in mathematics that help us express parts of a whole. They come in handy when dealing with quantities that are not whole numbers. A fraction consists of a numerator and a denominator. The numerator is the top number, indicating how many parts we have, and the denominator is the bottom number, showing the total parts the whole is divided into. For example, in the fraction \( \frac{1}{3} \), the "1" is the numerator, and "3" is the denominator. This particular fraction tells us that we have one part out of a total of three parts. Understanding fractions is crucial because they allow us to precisely describe amounts that are less than one. In many cases, like dividing a pizza among friends or measuring ingredients, fractions provide a clear and concise way to communicate these partial quantities.

Units of Measurement

Units of measurement are standardized quantities that allow us to express mass, length, volume, or other attributes in a way that everyone understands. They ensure that we all speak the same 'language' when it comes to dimensions or quantities. Common units of mass include "pounds," "ounces," and "grams." Each of these units has an abbreviation that makes it easier to write or say. For example, "ounce" is abbreviated as "oz." This shorter form is used in recipes, instructions, and labels to save space while still providing accurate information. Using units of measurement with their correct abbreviations is important in fields ranging from science to everyday cooking. Knowing these abbreviations helps you read and understand a wide range of materials. When you see "1 oz" on a label or in a recipe, this instantly communicates a quantity without needing extra words.

Numerical Expressions

Numerical expressions are mathematical expressions that use numbers and symbols to represent quantities or operations. These expressions are a fundamental part of mathematics as they provide a clear and standardized way to communicate mathematical ideas. Take the example from our data: the expression \( \frac{1}{3} \text{ oz} \). This integrates both numerals and units to express an idea concisely. Numerical expressions can range from simple to complex. They might include whole numbers, fractions like \( \frac{1}{3} \), percentages, or operations involving these numbers. They play a vital role when converting verbal descriptions into mathematical language, allowing for accurate calculations and analytics. The key is understanding how to manipulate these numbers and when to use specific expressions to accurately represent real-world quantities.