Problem 46 - Prealgebra

Question

Convert the given decimal to a mixed fraction. Do not simplify your answer. 676.037

Step-by-Step Solution

Answer

676.037 as a mixed fraction is \( 676 \frac{37}{1000} \).

Step 1: Identify the Whole Number Part

The given decimal is 676.037. The whole number part is the number before the decimal point. In this case, it is 676.

Step 2: Determine the Decimal Part

The decimal part is the number after the decimal point: 0.037.

Step 3: Convert the Decimal Part to a Fraction

To convert 0.037 to a fraction, recognize that 0.037 can be written as \( \frac{37}{1000} \) because 37 is the numerator and there are three decimal places, making the denominator 1000.

Step 4: Combine Whole Number and Fraction Parts

Combine the whole number part and the fractional part to form the mixed fraction. Therefore, 676.037 can be written as \( 676 \frac{37}{1000} \).

Key Concepts

Mixed Fractions

A mixed fraction is a mathematical expression that combines a whole number with a fraction. When you have a decimal like 676.037, you can express it as a mixed fraction to include both parts of the number. The mixed fraction would show the whole number "676" alongside the fractional component "\( \frac{37}{1000} \)." This way, a mixed fraction helps represent numbers that are not whole. These numbers have both an integer and a fractional component.

Here are some key points about mixed fractions:

• They consist of a whole number and a proper fraction.
• The fraction's numerator is smaller than the denominator.
• They provide a way to explicitly show both integer and fractional parts.

Understanding mixed fractions can make calculations, especially those involving everyday measurements, easier by clearly representing each part of the number.

Decimal to Fraction Conversion

Converting a decimal to a fraction involves a straightforward process, which can transform any decimal number into a fraction. For example, the decimal 0.037 can be converted to a fraction. This is achieved by identifying the digits after the decimal point and placing them over a denominator based on the decimal's place value.

To convert 0.037 to a fraction, you:

• Note that there are three digits after the decimal point: "037."
• Our denominator will be 1000 because the last digit is in the thousandths position.
• This gives us the fraction \( \frac{37}{1000} \).

These steps show how to evaluate decimal values and turn them into fractions, making it easier to perform arithmetic operations involving decimals.

Numerator and Denominator Identification

Identifying the numerator and denominator is crucial in the process of converting a decimal to a fraction. These are the two components of a fraction, each playing a distinctive role.

Nominator- The numerator is the top part of the fraction, representing how many parts we have. For instance, in the fraction \( \frac{37}{1000} \), "37" is the numerator.Denominator- The denominator is the bottom part, symbolizing the total number of equal parts. In \( \frac{37}{1000} \), the denominator is "1000," denoting the total divisions in a whole.

• The numerator tells you what portion of the whole is being represented.
• The denominator indicates into how many parts the whole is divided.

By correctly identifying the numerator and the denominator, you can better understand fractions and their relevance to both decimals and whole numbers.