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Chapter 1: Problem 65

Decimals and Percents. Write as a mixed number: 5.32.

Short Answer

Expert verified
5.32 as a mixed number is \( 5 \frac{8}{25} \).

Step by step solution

01

Understand the Components

A mixed number consists of a whole number and a fractional part. In this case, write 5.32 as a whole number (5) and a decimal (0.32).
02

Convert Decimal to Fraction

Take the decimal part 0.32 and express it as a fraction. Since there are two decimal places, 0.32 is the same as \( \frac{32}{100} \).
03

Simplify the Fraction

Simplify the fraction \( \frac{32}{100} \) by finding the greatest common divisor (GCD) of 32 and 100, which is 4. Divide the numerator and the denominator by 4 to get \( \frac{8}{25} \).
04

Combine Whole Number and Fraction

Combine the whole number 5 with the simplified fraction \( \frac{8}{25} \) to form the mixed number. Therefore, 5.32 as a mixed number is \( 5 \frac{8}{25} \).

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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 way to express numbers that have both a whole part and a fraction part. Imagine having 5 full cakes and another part of a cake that isn't complete. Here, the number '5' represents the whole cakes, and the fractional part represents the slice that makes up the rest. For the number 5.32, we break it down into 5 as the whole number, and the decimal 0.32, which we will later convert into a fraction. This breakdown helps readers visualize a clearer image of mixed numbers, showcasing both parts distinctly.
Simplifying Fractions
Simplifying fractions means reducing them to their simplest form, where no number other than 1 can divide both the numerator and the denominator. Let's put it into perspective using our example where we have the fraction \( \frac{32}{100} \).
  • Firstly, find a common factor for the numerator and denominator, which is the largest number that can evenly divide both. In this case, our greatest common divisor (GCD) is 4.
  • Now, divide both the numerator and the denominator by 4. So, \( \frac{32}{4} = 8 \) and \( \frac{100}{4} = 25 \).
This gives us the simplified fraction \( \frac{8}{25} \). Simplifying fractions helps in making the numbers easier to understand and use in calculations, because smaller numbers are typically easier to work with.
Converting Decimals to Fractions
When you convert a decimal to a fraction, you're essentially expressing a part of a whole as a fraction. Starting with a decimal like 0.32 involves knowing the place value of each digit. The number 0.32 has its last digit in the hundredths place.
  • This means it can initially be written as \( \frac{32}{100} \), since 32 is in the place of hundredths.
  • Once converted to a fraction, the next step is simplification, as we discussed in the previous section.
By converting decimals to fractions, it aligns the numerical reading in a different format, often one that is needed for specific types of mathematical operations or applications. It also introduces a simpler way to understand and utilize the numbers we commonly see in decimal forms, especially when dealing with parts of a whole or percentages.

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Most popular questions from this chapter

Simplify. $$ 52-40 \div 5(-2) 2-(-4) $$

Convert to a percent. 0.055

Perform the operations. $$ 9.246 \div 4.02 $$

Simplify. $$ 34+23-112 $$

Simplify. $$ -4+2\|22-32\| $$
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