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Chapter 1: Problem 26

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

Short Answer

Expert verified
-0.125

Step by step solution

01

Understand the Fraction

The fraction \(-\frac{1}{8}\) represents a negative value where 1 is divided by 8.
02

Divide the Numerator by the Denominator

Perform the division \(\frac{1}{8}\). This can be done using a calculator or by long division. \(\frac{1}{8} = 0.125\).
03

Apply the Negative Sign

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

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Key Concepts

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

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鈥檚 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鈥檚 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.

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