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Chapter 6: Problem 50

Convert each fraction to a decimal. Round to five decimal places. \(\frac{6}{11}\)

Short Answer

Expert verified
The decimal form of \( \frac{6}{11} \) rounded to five decimal places is 0.54545.

Step by step solution

01

Understanding the Fraction

The fraction \( \frac{6}{11} \) is a division problem, where 6 is the numerator (the number being divided) and 11 is the denominator (the number by which you divide). To find its decimal equivalent, you need to divide 6 by 11.
02

Performing the Division

Carry out the division 6 divided by 11. You can use long division or a calculator. Doing this division yields approximately 0.5454545454... As you want to round to five decimal places, keep in mind the digits up to the sixth decimal place.
03

Rounding the Result

To round 0.5454545454... to five decimal places, look at the sixth decimal place, which is 4. Since it is less than 5, you do not need to round up the fifth decimal place. Hence, the decimal rounded to five decimal places is 0.54545.

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Key Concepts

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

Rounded Decimal
Rounding decimals is an essential skill in mathematics to simplify numbers and make them more readable. It helps in approximating a number to a desired degree of precision.
When converting a fraction to a decimal, you sometimes get a long string of repeating digits. For example, when you convert \( \frac{6}{11} \), the decimal is approximately 0.5454545454... To make this number easier to work with, you'll often round it.
  • Identify the place value you are rounding to. Here, it's the fifth decimal place.
  • Check the digit immediately after your rounding position, which is the sixth decimal place.
  • If this digit is 5 or higher, round the specified digit up. If it is less, leave it as it is.
  • In this instance, the sixth decimal place is 4, so the rounded decimal becomes 0.54545.
Rounding makes numbers easier to communicate and use, especially in calculations and when comparing different values.
Long Division
Long division is a mathematical method used to divide large numbers, providing a convenient means to determine decimals when you divide numbers that don't evenly split. To convert a fraction like \( \frac{6}{11} \) to a decimal, you can use long division.
  • Set up the division by placing the numerator (6) inside the division bracket and the denominator (11) outside.
  • Since 6 is smaller than 11, you start by multiplying 6 by 10 to make 60.
  • Determine how many times 11 fits into 60, which is 5 times, and write 5 as your first decimal digit.
  • Subtract \( 5 \times 11 = 55 \) from 60 to get 5.
  • Bring down another 0, making it 50, and repeat the process.
Continue this process to find that the decimal repeats itself as 0.54545454... This repetitive cycle is why knowing how to round is helpful.
Numerator and Denominator
Numerators and denominators are fundamental when dealing with fractions. Understanding their roles helps in converting fractions like \( \frac{6}{11} \) into decimals.
  • The **numerator** is the top number in a fraction, indicating how many parts of a whole are being considered. In \( \frac{6}{11} \), the numerator is 6.
  • The **denominator** is the bottom number, showing the total number of equal parts the whole is divided into. Here, it's 11.
By dividing the numerator by the denominator, you determine how much of the whole the fraction represents. This division process yields a decimal form of the fraction. The concepts of the numerator and denominator are essential in evaluating fractions, performing operations, and transitioning between fractional to decimal notation.

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Most popular questions from this chapter

Perform the following operations. Exercise 6.10 .26\((0.6)^{2} \cdot\left(\frac{1}{20}-\frac{1}{25}\right)\)

Perform each operation. $$ \text { Convert } 0.5 \frac{9}{16} \text { to a decimal. } $$

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Convert each fraction to a decimal. $$ 1.3 \frac{1}{3} $$

Perform the following operations. \(5.198-0.26 \cdot\left(\frac{14}{250}+0.119\right)\)
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