Problem 26 - Elementary and Intermediate Algebra

Question

Write decimal notation for each number. $$ -\frac{1}{8} $$

Step-by-Step Solution

Answer

-0.125

Step 1: Understand the Fraction

The fraction \(-\frac{1}{8}\) represents a negative value where 1 is divided by 8.

Step 2: Divide the Numerator by the Denominator

Perform the division \(\frac{1}{8}\). This can be done using a calculator or by long division. \(\frac{1}{8} = 0.125\).

Step 3: Apply the Negative Sign

Add the negative sign to the result from step 2, so \(\-\frac{1}{8} = -0.125\).

Key Concepts

Understanding Fractions

Fractions represent a part of a whole. They are written as \(\frac{a}{b}\), where \(\frac{a}{b}\) means 'a' parts out of 'b' equal parts. For example, \(\frac{1}{8}\) means 1 part out of 8. The number above the line is the numerator, and the one below is the denominator. To grasp fractions better, remember these points:

• The numerator tells how many parts we have.
• The denominator tells into how many parts the whole is divided.

So, \(\frac{1}{8}\) means 1 part of something that is divided into 8 parts.
Once we understand this, converting it into decimal becomes much easier.

Steps for Division

Division is the process of splitting a number into equal parts. When we say \(\frac{1}{8}\), it means dividing 1 by 8. To solve \(\frac{1}{8}\), we can use a calculator or long division method. Here’s how long division works for \(\frac{1}{8}\):

• Divide 1 by 8, noting that 8 goes into 1, 0 times.
• Place a decimal point to the right of 1 and add a zero to make it 10.
• Now 8 goes into 10 once, so write 1 after the decimal point making it 0.1.
• Subtract 8 from 10 to get 2. Add another zero making it 20.
• 8 goes into 20, 2 times. Subtract 16 from 20 to get 4. Add a zero making it 40.
• 8 goes into 40, 5 times. Subtract 40 from 40 to get 0. So, the division process ends here.

This gives us \(\frac{1}{8} = 0.125\).
Practice this a few times to get the hang of it!

Working with Negative Numbers

Negative numbers are values less than zero, often representing a loss or a deficit. When working with negative fractions, like \(-\frac{1}{8}\), follow the same arithmetic rules but remember the negative sign.
Here’s what to keep in mind:

• A negative sign before a fraction means the overall value is less than zero.
• Perform the division as usual (ignoring the negative sign initially).
• Once you get the result of the division, apply the negative sign to your answer.

Using our example, we already found \(\frac{1}{8} = 0.125\). Now, just add the negative sign: \(-\frac{1}{8} = -0.125\).
Negative numbers can be tricky, but always ensure to place the sign where it belongs.