Problem 47 - Prealgebra

Question

Convert the given decimal to a mixed fraction. Do not simplify your answer. 560.453

Step-by-Step Solution

Answer

560 \( \frac{453}{1000} \)

Step 1: Identify Whole Number and Decimal Part

Start by separating the whole number from the decimal. For 560.453, the whole number is 560 and the decimal part is 0.453.

Step 2: Convert Decimal to Fraction

Take the decimal part 0.453 and convert it to a fraction. Since there are three decimal places, place it over 1000 to become \( \frac{453}{1000} \).

Step 3: Form the Mixed Fraction

Combine the whole number with the fraction obtained. The mixed fraction is 560 \( \frac{453}{1000} \).

Key Concepts

mixed fractions

A mixed fraction, often called a mixed number, combines a whole number with a fractional part. This form allows us to express numbers that are not whole, in a more practical and understandable way.
For instance, when we see a number like 560.453, we can separate it into two parts:

• The 'whole number', which is 560 in this case.
• The 'fractional part', which is the decimal that comes after the whole number—0.453.

Using our understanding of mixed fractions, we write this as a combination of a whole number and a fraction. This is how 560.453 becomes 560 \( \frac{453}{1000} \). This mixed fraction represents the exact same value as the decimal, but uses a more traditional numerical format.

decimal numbers

Decimal numbers represent fractions in a linear and straightforward way. They are a crucial aspect of our daily number system, known as the base-10 system. These numbers are composed of whole numbers and a fractional part that follows the decimal point.
For example, the number 560.453 represents:

• 560, which is the whole number part.
• 0.453, the fractional part.

The digits after the decimal point each have decreasing fractional values:

• The first digit after the decimal represents tenths.
• The second digit represents hundredths.
• The third digit represents thousandths, and so on.

Understanding each position helps in converting the decimal part into a fraction easily.

fraction conversion

Fraction conversion involves changing a number from one form to another, such as from a decimal to a fraction. This process helps to provide clarity in mathematical operations. To convert a decimal to a fraction:

• Identify the place value of the last digit in the decimal. For 0.453, this is the thousandths place.
• Convert the decimal to a fraction by taking the numerator as the digits of the decimal without the point (453 in this case) and the denominator as \(10^n\), where \(n\) is the number of decimal places (1000 here).

So, 0.453 becomes \( \frac{453}{1000} \). Fraction conversion is complete without simplifying, as instructed in some problems. Mastering this conversion is essential for dealing with both exact numbers and scale-based calculations.