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Chapter 4: Problem 31

Find decimal notation. \(\frac{7}{6}\)

Short Answer

Expert verified
The decimal notation for \(\frac{7}{6}\) is 1.16666... or 1.\bar{6}.

Step by step solution

01

- Understand the Problem

To find the decimal notation of \(\frac{7}{6}\), you need to perform the division of the numerator by the denominator.
02

- Perform the Division

Divide 7 by 6. \(\frac{7}{6}\) equals approximately 1.16667. Since 7 divided by 6 is 1 with a remainder of 1, continue dividing to get more decimal places: 1.166666...
03

- Write the Answer

The decimal notation for \(\frac{7}{6}\) is 1.16666... (repeating). This can also be written as 1.\bar{6} where the bar indicates that 6 repeats indefinitely.

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Key Concepts

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

division
Division is the process of determining how many times one number is contained within another. In the fraction \(\frac{7}{6}\), we want to find out how many 6's fit into 7. When you divide 7 by 6, you get 1 with a remainder of 1. This tells us that 6 fits into 7 once, with a bit left over.

To continue the division, you can keep dividing the remainder. In this case, you add a decimal point and a zero, making the remainder 10. By dividing 10 by 6, you get 1 again, with 4 left over. Keep adding zeros and dividing to increase the number of decimal places. This helps us find the precise decimal value.
fraction to decimal conversion
Converting a fraction to a decimal involves utilizing division. The fraction \(\frac{7}{6}\) means we are dividing 7 by 6. Think of fractions as a division problem: how many times does the denominator fit into the numerator?

To convert, perform the division step-by-step, noting how the decimal unfolds. Initially, dividing 7 by 6 gives 1. To find the decimal part, continue with the division. Since the remainder is 1, you extend the division by adding a decimal and continuing with 10 divided by 6, which gives 1.666..., showing the repeating nature of the decimal.
repeating decimal
A repeating decimal is a decimal number in which a digit or group of digits repeats infinitely. In our example of \(\frac{7}{6}\), the decimal is 1.16666... The 6 repeats indefinitely.

When you write this, you often use a bar notation to show the repeating part. Instead of writing out many 6鈥檚, write 1.1\(\bar{6}\) to indicate that 6 repeats forever. Understanding this makes it easier to work with fractions and decimals in mathematics. Repeating decimals arise frequently when converting fractions, particularly when the denominator has prime factors other than 2 or 5.

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Most popular questions from this chapter

Simplify. $$ \frac{125}{400} $$

Subtract. $$ \frac{2}{3}-\frac{5}{8} $$

Estimate by rounding as directed. $$ \begin{aligned} &12.9882+1.2115 ;\\\ &\text { nearest tenth } \end{aligned} $$

Estimate. Indicate which of the choices is an appropriate estimate. \(234.12321-200.3223\) a) 600 b) 60 c) 300 d) 30

Add. $$ \begin{array}{r} 81.008 \\ +\quad 3.409 \\ \hline \end{array} $$
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