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Chapter 5: Problem 27

In the following exercises, convert each decimal to a fraction or mixed number. $$1.99$$

Short Answer

Expert verified
1.99 = 1 \frac{99}{100}

Step by step solution

01

Identify the Decimal

Recognize that the given decimal is 1.99.
02

Separate the Whole Number

Note that the whole number part of 1.99 is 1.
03

Convert the Decimal Part to Fraction

Take the decimal part, which is 0.99, and write it as a fraction. To do this, place 99 over 100, since 0.99 means 99 hundredths: \[ 0.99 = \frac{99}{100} \]
04

Combine the Whole Number with the Fraction

Add the whole number (1) to the fraction \( \frac{99}{100} \): \[ 1 \frac{99}{100} \]
05

Simplify the Fraction (if needed)

Check if the fraction \( \frac{99}{100} \) can be simplified further. In this case, it is already in its simplest form.
06

Write the Final Answer

Combine the whole number with the simplified fraction to get the final answer: \[ 1.99 = 1 \frac{99}{100} \]

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Key Concepts

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

Converting Decimals to Fractions
Let's dive into converting decimals to fractions. For this example, we used the decimal 1.99. We break it down into a whole number part (1) and a decimal part (0.99). Turning the decimal into a fraction involves writing it as 99 over 100, since 0.99 is the same as 99 hundredths. Combine the whole number and the fraction to form a mixed number. The result is 1 99/100. When converting, always check if the fraction can be simplified. If the fraction is already in its simplest form, you're done!
Mixed Numbers
A mixed number is a number made up of a whole number and a fraction. In our example, we have the mixed number 1 99/100. This number consists of the whole number 1 and the fraction 99/100. Mixed numbers make it easier to understand quantities that are more than a whole but not quite another whole. Converting decimals to mixed numbers is helpful in daily life, especially when dealing with measurements like inches or grams.
Simplifying Fractions
Simplifying fractions means reducing them to their simplest form. To simplify, find the greatest common divisor (GCD) of the numerator and the denominator, then divide both by this number. For example, if you have 99/100, checking the GCD would show that 99 and 100 have no common divisors other than 1, meaning the fraction is already simplified. Always look for common factors to ensure your fractions are as simple as possible.

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