Problem 29 - Elementary and Intermediate Algebra

Question

Write decimal notation for each number. $$ -\frac{7}{6} $$

Step-by-Step Solution

Answer

-1.1667

Step 1: Understand Fraction to Decimal Conversion

To convert a fraction to decimal notation, divide the numerator (top number) by the denominator (bottom number). Here, the numerator is -7 and the denominator is 6.

Step 2: Perform the Division

Divide -7 by 6. This can be done by long division or using a calculator. Performing the division gives us approximately -1.1667.

Step 3: Write the Decimal Notation

After performing the division, write the result in decimal form. So, -7/6 is approximately -1.1667.

Key Concepts

Understanding Numerator and Denominator

In any fraction, the top number is known as the numerator, and the bottom number is called the denominator. For example, in the fraction \(-\frac{7}{6}\), the numerator is -7 and the denominator is 6. The numerator represents the number of parts we are considering, while the denominator shows the total number of equal parts the whole is divided into. So, in \(-\frac{7}{6}\), we are taking 7 parts out of a whole that is divided into 6 equal parts. This setup is crucial to understand when converting a fraction to a decimal.

Using Long Division for Fraction to Decimal Conversion

Long division is a method used to divide larger numbers that cannot be easily divided mentally or with a simple equation. To turn a fraction into a decimal using long division, we divide the numerator by the denominator. With our example \(-\frac{7}{6}\), we need to divide -7 by 6. Start by seeing how many times 6 fits into 7, which is once. Subtract 6 from 7 to get 1. Then, bring down a 0 to make it 10 and see how many times 6 fits into 10, which is again once, and repeat this process. This gives us the decimal -1.1667. Understanding long division helps make sense of how fractions are turned into decimals step-by-step.

Decimal Notation Explained

Once you have divided the numerator by the denominator, you will get a decimal number. Decimal notation represents numbers in base-10 format, which is the standard system for denoting integer and non-integer numbers. In our example, dividing -7 by 6 gives us -1.1667. In decimal notation, -1.1667 means we have 1 whole part and a little over 0.16 of another part. By using decimals, we can express fractions and parts of whole numbers clearly and accurately. Decimals make it easier to perform arithmetic operations and compare values in different contexts.