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Chapter 5: Problem 49

In the following exercises, convert each decimal to a fraction or mixed number. $$14.125$$

Short Answer

Expert verified
14\frac{1}{8}

Step by step solution

01

Identify the Whole Number

The given decimal is 14.125. Identify the whole number part, which is 14.
02

Identify the Fractional Part

The decimal part is 0.125. This is the fractional part we need to convert to a fraction.
03

Convert the Fractional Part to a Fraction

Rewrite 0.125 as a fraction. Since 0.125 is equivalent to 125/1000, simplify it by dividing both the numerator and the denominator by their greatest common divisor, which is 125: \[\frac{125}{1000} = \frac{125 \div 125}{1000 \div 125} = \frac{1}{8}\]
04

Form the Mixed Number

Combine the whole number part with the fractional part to form the mixed number: \[14 + \frac{1}{8} = 14\frac{1}{8}\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Converting Decimals to Fractions
Decimals and fractions are two sides of the same coin. Converting a decimal to a fraction helps you better understand the value of the number in different mathematical contexts.
To convert a decimal to a fraction, follow these simple steps:
  • Identify the decimal part of the number.
  • Count the number of decimal places. This tells you the denominator.
  • Write the decimal as a fraction by placing it over the appropriate power of 10.
  • Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
For example, converting 0.125 to a fraction involves writing 0.125 as 125/1000, then simplifying it to 1/8 by dividing by the common factor 125.
Mixed Numbers
A mixed number is a combination of a whole number and a fraction. When you convert a decimal that includes a whole number and a fractional part, the result is often a mixed number.
Here's how to form a mixed number:
  • Identify the whole number part of the decimal.
  • Convert the decimal part to a fraction.
  • Combine the whole number with the simplified fraction.
For instance, to convert 14.125 to a mixed number, first recognize the whole number 14. Then, convert the decimal part 0.125 to a fraction, which is 1/8. Thus, 14.125 becomes the mixed number 14_1/8.
Simplifying Fractions
Simplifying fractions means reducing them to their smallest form. This is important for making fractions easier to understand and work with.
To simplify a fraction, follow these steps:
  • Identify the numerator (top number) and the denominator (bottom number) of the fraction.
  • Find the greatest common divisor (GCD) of the numerator and the denominator.
  • Divide both the numerator and the denominator by the GCD.
For example, to simplify 125/1000, find the GCD of 125 and 1000, which is 125. Divide both the numerator and the denominator by 125 to get 1/8. Now, the fraction is in its simplest form.

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