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Chapter 5: Problem 28

In the following exercises, convert each decimal to a fraction or mixed number. $$5.83$$

Short Answer

Expert verified
5 \( \frac{83}{100} \)

Step by step solution

01

- Understand the Number

The number to convert is 5.83. It is a decimal number with a whole part and a fractional part.
02

- Separate the Whole Number

Identify and separate the whole number part. Here, the whole number part is 5.
03

- Convert the Fractional Part

Consider the fractional part which is 0.83. This can be written as \( \frac{83}{100} \) because 83 is the numerator and the decimal place counts (hundredths) indicate the denominator.
04

- Simplify the Fraction

Simplify \( \frac{83}{100} \) if possible. Since 83 is a prime number and does not divide evenly into 100, \( \frac{83}{100} \) is already in its simplest form.
05

- Form the Mixed Number

Combine the whole number part and the fractional part. The mixed number is 5 \( \frac{83}{100} \).

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Key Concepts

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

Mixed Numbers
A mixed number is a whole number combined with a fraction. Mixed numbers make expressing quantities easier. Instead of saying 'five and eighty-three hundredths', we say 5 \(\frac{83}{100}\). Mixed numbers are practical in everyday math.
When converting a decimal like 5.83 to a mixed number:
  • Identify the whole number part (5 in this case).
  • Convert the fractional part (0.83) to a fraction.
Then, combine both parts. Here, the result is 5 \(\frac{83}{100}\). Remember to simplify fractions if possible, but more on that later!
Simplifying Fractions
Simplifying fractions means reducing them to their smallest form. This makes fractions easier to work with.
To simplify, find the greatest common divisor (GCD) of the numerator (top number) and the denominator (bottom number). Divide both by this GCD.
In our example, \(\frac{83}{100}\), 83 is a prime number. It does not share any common factors with 100 other than 1. Therefore, \(\frac{83}{100}\) is already in its simplest form. For other fractions:
  • List the factors of the numerator and denominator.
  • Identify the largest common factor.
  • Divide both the numerator and the denominator by this factor.
This process ensures that the fraction is as simple as possible.
Numerator and Denominator
Fractions are made of two parts: the numerator and the denominator.
  • The numerator is the top number, representing how many parts of the whole are taken.
  • The denominator is the bottom number, showing into how many equal parts the whole is divided.
In the fraction \(\frac{83}{100}\):
  • 83 is the numerator.
  • 100 is the denominator.
Understanding these components helps in manipulating and converting fractions easily. For instance, 0.83 can be viewed as 83 parts out of 100, translating directly to \(\frac{83}{100}\). This clarity is essential for manipulation, simplification, and conversion tasks in mathematics.

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