Problem 211 Convert each fraction to a decim... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 5: Problem 211

Convert each fraction to a decimal. $\frac{5}{9}$

Short Answer

Expert verified

0.\overline{5}

Step by step solution

- Understand the Problem

The goal is to convert the fraction \[ \frac{5}{9} \] into a decimal form.

- Set Up the Division

To convert the fraction to a decimal, divide the numerator (5) by the denominator (9).

- Perform the Division

Perform the long division \[ 5 \div 9 \]. Place the decimal point immediately after the 5 inside the division bracket and add zeros as needed.

- Carry Out the Division

Divide 5 by 9 to get approximately 0.555... (repeating). Each step of the division will keep giving 5 as a remainder, repeating the process.

- Write the Decimal as a Repeating Decimal

Since the division repeats, the decimal is 0.555... This can be written as \[ 0.\overline{5} \].

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Key Concepts

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

long division

Long division is the method we use here to convert the fraction $\frac{5}{9}$ into a decimal. It involves dividing the numerator (5) by the denominator (9). This method lets us break down the division process step-by-step, even when it doesn't divide evenly. To start, place the decimal point right after 5 and append zeros to continue dividing. As you go through each step, bring down zero from the appended list to keep working on the division. If you find the same digit reappearing as a remainder, you鈥檝e likely encountered a repeating decimal. This incremental approach makes it easier to see each part of the process in action.

repeating decimal

A repeating decimal happens when a digit or a sequence of digits keeps coming up in the quotient. When we convert $\frac{5}{9}$ using long division, we find that the decimal is 0.555... Since 5 keeps repeating, this is known as a repeating decimal. To notate this, we can write it as $\text{0.}\bar{5}$ to show the digit '5' repeats indefinitely. Repeating decimals are common when the denominator has prime factors other than 2 and 5.

numerator and denominator

Understanding the terms numerator and denominator is crucial when dealing with fractions. The numerator is the top part of the fraction, which in our example is 5. It represents how many parts we have. The denominator is the bottom part, which is 9 in our case. It indicates into how many parts the whole is divided. When converting $\frac{5}{9}$ to a decimal, we are essentially dividing the numerator by the denominator. This fundamental concept of fractions helps us convert them to decimals with methods like long division.

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91影视

Convert each fraction to a decimal. \(\frac{5}{9}\)

Short Answer

Step by step solution

- Understand the Problem

- Set Up the Division

- Perform the Division

- Carry Out the Division

- Write the Decimal as a Repeating Decimal

Key Concepts

long division

repeating decimal

numerator and denominator

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