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Chapter 5: Problem 38

In the following exercises, convert each decimal to a fraction or mixed number. $$-0.00003$$

Short Answer

Expert verified
-\frac{3}{100000}

Step by step solution

01

- Understand the Decimal Number

The given decimal number is \(-0.00003\). It is essential to note the number of decimal places.
02

- Express as a Fraction

Count the number of decimal places. \(-0.00003\) has five decimal places, so it can be written as \(-\frac{3}{100000}\).
03

- Simplify the Fraction (if possible)

Check if the fraction \(-\frac{3}{100000}\) can be simplified. In this case, it is already in its simplest form.

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Key Concepts

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

Fraction Simplification
Fraction simplification is a process of reducing fractions to their simplest form.
To simplify a fraction means to make the numerator and the denominator as small as possible.
You do this by finding the greatest common divisor (GCD) of both numbers and dividing them by it.
Simplifying fractions makes them easier to work with, especially in further calculations.
Here are some steps to follow:
  • Find the GCD of the numerator and the denominator.
  • Divide both the numerator and the denominator by this GCD.
  • The result is a simplified fraction where the numerator and denominator have no common factors other than 1.
Decimal Places
Decimal places are the positions of digits to the right of the decimal point in a decimal number.
Each position represents a power of 10. For example, in the number 0.123, the 1 is in the tenths place, 2 is in the hundredths place, and 3 is in the thousandths place.
Knowing how many decimal places a number has helps in accurately converting it to a fraction.
  • Count how many digits are to the right of the decimal point.
  • Use that number to define the denominator of the fraction. For each digit, you'll need an extra zero in the denominator (e.g., 0.001 = 1/1000).
Understanding decimal places is crucial because it lays the foundation for translating between decimals and fractions accurately.
Mixed Numbers
Mixed numbers are numbers consisting of an integer and a fraction. They are useful for representing values greater than one but not whole numbers.
To convert a decimal to a mixed number:
  • First, identify the whole number part of the decimal.
  • Then, convert the fractional part of the decimal to a fraction.
Let's look at an example. The decimal 2.75 can be split into 2 (the whole number) and 0.75 (the decimal part). Convert 0.75 to the fraction 3/4, so 2.75 as a mixed number is 2 3/4.
Mixed numbers are especially helpful in practical applications, such as measurements and everyday calculations.

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