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Chapter 5: Problem 37

In the following exercises, convert each decimal to a fraction or mixed number. $$-0.00007$$

Short Answer

Expert verified
-\(\frac{7}{100000}\)

Step by step solution

01

Identify the decimal

Consider the given decimal, which is $$-0.00007.$$ Make sure to take note of the negative sign.
02

Write the decimal as a fraction

To write $$-0.00007$$ as a fraction, first recognize the place value of the last digit. The last digit '7' is in the fifth decimal place, so the fraction is $$\frac{7}{100000}.$$ Hence, $$-0.00007 = -\frac{7}{100000}.$$
03

Simplify the fraction if possible

Check if the fraction $$\frac{7}{100000}$$ can be simplified. Since 7 is a prime number and does not divide $$100000$$ evenly, the fraction is already in its simplest form. Thus, the final answer is $$-\frac{7}{100000}.$$

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Key Concepts

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

Negative Decimal Fractions
When we talk about negative decimal fractions, we're dealing with decimals that have a negative sign in front of them, just like in our example with $$-0.00007$$.

It's important to remember that the negative sign simply means the value is less than zero. Always keep track of the negative sign during your conversion process.

For instance, if you start with a positive decimal and convert it to a fraction, you will need to place the negative sign in front of your final answer to correctly represent the negative value.

Let's break down the steps:
  • Identify the decimal number.
  • Write the number as a fraction without considering the negative sign initially.
  • After finding and simplifying the fraction, reapply the negative sign to your final answer.
This ensures the accuracy of your solution.
Place Value in Decimals
Understanding the place value in decimals is crucial for converting them to fractions. In our example, the decimal is $$-0.00007$$. Each digit in the decimal has a specific place value, starting from the tenths, hundredths, thousandths, and so forth.

Here's how it works for our example:
  • The digit '7' is in the fifth place, which is the ten-thousandths place.
  • To convert this to a fraction, we put '7' over the place value, which is '100000', resulting in $$\frac{7}{100000}$$.
Therefore, our original decimal $$-0.00007$$ converts to $$-\frac{7}{100000}$$ as a fraction.

Carefully noting the place value ensures that you correctly convert every decimal to its equivalent fraction.
Simplifying Fractions
Simplifying fractions is the process of reducing a fraction to its lowest terms. A fraction is in its simplest form when both the numerator and the denominator cannot be divided by any common number other than 1.

For instance, in the solution, we have the fraction $$\frac{7}{100000}$$.

First, we check if either number can be divided by a common factor:
  • The number 7 is a prime number, meaning it can only be divided by 1 and 7.
  • 100000, however, cannot be evenly divided by 7.
Hence, $$\frac{7}{100000}$$ cannot be simplified further. Our fraction is already in its simplest form.

Always attempt to simplify fractions to make calculations easier and your final answer clearer.

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Most popular questions from this chapter

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