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Chapter 10: Problem 15

Convert to decimal notation. $$ -\frac{7}{6} $$

Short Answer

Expert verified
-1.1667

Step by step solution

01

Understand the fraction

The given fraction is \(-\frac{7}{6}\). This means that 7 is divided by 6, and the result is negative.
02

Perform the division

Divide 7 by 6. To do this, calculate \(7 \div 6 \) which equals approximately \(1.1667\).
03

Apply the negative sign

Since the original fraction is negative, the decimal result should also be negative. Thus, \(-1.1667\).

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Key Concepts

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

negative fractions
When working with fractions, it's important to know how to handle negative signs. A negative fraction means that the value is less than zero. To identify a negative fraction, look for the negative sign either before the fraction or in front of the numerator or denominator.
For example, in the fraction \(-\frac{7}{6}\), the negative sign indicates that the overall value is negative.
There are various ways a fraction can be negative:
  • - Before the fraction: \(-\frac{7}{6}\)
  • - Before the numerator: \(\frac{-7}{6}\)
  • - Before the denominator: \(\frac{7}{-6}\)
Each of these representations means the same thing: the value of the fraction is negative. Converting these to a decimal involves performing the division as usual, and then applying the negative sign to the result.
division
Division is a key concept in converting fractions to decimal notation. To convert a fraction to a decimal, you simply need to divide the numerator (the top number) by the denominator (the bottom number). In our example of \(-\frac{7}{6}\), we will divide 7 by 6. This can be expressed mathematically as \(7 \div 6\).
This division results in approximately 1.1667, which is a repeating decimal. Performing the division step-by-step helps in understanding the process better:
  • Calculate how many times 6 fits into 7. The answer is 1 time.
  • Subtract 6 from 7 to get a remainder of 1.
  • Bring down a 0 to make it 10.
  • See how many times 6 fits into 10. This goes 1 time with a remainder of 4.
  • Repeat the process until a repeating pattern or desired precision is achieved.
Each of these steps helps in getting a clearer idea of the decimal representation of the fraction.
decimal notation
Decimal notation is a way of expressing fractions or real numbers in a base-10 numeral system. Once you perform the division, you convert the fraction to its decimal form. In this case, when you divide 7 by 6, you get approximately 1.1667. Since our original fraction \(-\frac{7}{6}\) was negative, our decimal will also be negative, \(-1.1667\).
This helps in showing the result in a way that is easier to read and compare. It's much simpler for most people to understand decimal form rather than fractions in everyday use.
Let鈥檚 summarize the transformation:
  • Start with the fraction \(-\frac{7}{6}\)
  • Perform the division: \(7 \div 6 = 1.1667\)
  • Apply the negative sign: \(-1.1667\)
Remember, the negative sign remains throughout the entire conversion process.

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