Question

Express the following using numerals and abbreviations: three and one-half quarts

Short answer

3.5 qt

Step-by-step solution

Identify the Quantity and its Fractional Part

The phrase "three and one-half quarts" consists of two parts. First, "three" means 3 quarts. Second, "one-half" refers to the fractional part of 1/2 quart.

Convert the Fraction to Decimal

The fractional part "one-half" can be converted to a decimal by dividing 1 by 2. This results in 0.5. Hence, "one-half" is equivalent to 0.5.

Combine Whole and Fractional Parts

Now, let's combine the whole number with its fractional part. The whole number is 3, and the fractional part as a decimal is 0.5. Adding these two gives 3.5 quarts.

Write the Unit Abbreviation

The unit given is quarts, which can be abbreviated as 'qt'. Therefore, 3.5 quarts can be represented in numerals and abbreviation as 3.5 qt.

Key concepts

Fraction to Decimal Conversion

Converting fractions into decimals is a fundamental concept in mathematics. It can help us in various calculations and ensure precision. To convert a fraction to a decimal, divide the numerator by the denominator. For example, the fraction \( \frac{1}{2} \) can be converted to the decimal 0.5 by dividing 1 by 2. This method is reliable for any fraction:

• Divide the top number (numerator) by the bottom number (denominator).
• The result will be a decimal.

Remember that in some cases, you might get a repeating decimal. Examples are \( \frac{1}{3} \) which is 0.333... and \( \frac{2}{3} \) which is 0.666... Knowing how to convert fractions to decimals is useful especially in tasks requiring quick numeric assessments.

Measurement Units

Measurement units serve as standard quantities to express physical properties. In everyday life, they help make sense of various dimensions such as weight, volume, and length. For instance, when referring to liquid measurements in the United States, 'quarts' is a common unit. It's important to know how to abbreviate measurement units to simplify communication and calculations:

• Quart can be abbreviated as 'qt'.
• Other volume units include 'gallon' (gal), 'pint' (pt), and 'cup' (c).

Understanding measurement units allows smoother conversions and accuracy in expressing quantities. Always pay attention to both the full names and the standard abbreviations to prevent misunderstandings.

Step-by-Step Problem Solving

Problem-solving in mathematics often requires a structured method to ensure success. By taking a step-by-step approach, complex problems become manageable. Here’s how to apply this method effectively:

• Understand the Problem: Break down the given information. In this case, identify that 'three and one-half quarts' involves both a whole number and a fraction.
• Solve in Steps: Convert the fraction part to a decimal, then combine it with the whole number.
• Represent the Answer: Use numeral and unit abbreviations efficiently, like transforming quarts to qt as in "3.5 qt".

A structured approach by using sequential steps ensures no part of a problem is overlooked. Developing this habit builds a solid foundation for tackling more complex problems.

Numeral Representation

Expressing numbers correctly is vital in mathematics and everyday communication. Numeral representation helps in conveying exact quantities clearly and concisely. When converting words into numbers, as in 'three and one-half', follow these tips:

• Identify whole numbers and fractional parts separately.
• Convert the fractional part to its decimal equivalent.
• Combine them to form a complete decimal number, like turning 'three and one-half' into 3.5.

Finally, always ensure that the unit of measurement is clearly stated, either in full or abbreviated form, such as '3.5 quarts' becoming '3.5 qt'. Numerals make numerical information easier to read and reduce the potential for misinterpretation.