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Chapter 6: Problem 48

Convert each fraction to a decimal. $$ \frac{82}{1000} $$

Short Answer

Expert verified
The decimal form of \( \frac{82}{1000} \) is 0.082.

Step by step solution

01

Understanding the fraction

The given fraction is \( \frac{82}{1000} \), which means 82 divided by 1000.
02

Dividing the numerator by the denominator

To convert the fraction to a decimal, divide the numerator (82) by the denominator (1000). This can be done by performing the division: \( 82 \div 1000 = 0.082 \).
03

Writing the final decimal form

The decimal form of \( \frac{82}{1000} \) is \( 0.082 \).

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Key Concepts

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

Understanding the Numerator
The numerator is a key component of any fraction. It sits above the fraction line. In our exercise, the numerator is 82. This number represents how many parts of the whole are being considered. For example, if a cake is cut into 1000 equal slices, and you take 82, the numerator shows these 82 parts you have.
To easily distinguish, remember that the numerator is the top number in the fraction. When converting fractions to decimals, the numerator is the number you will "give away" or divide by the denominator. It's like counting how many portions of the whole you have, before deciding on their size in relation to the whole.
The Role of the Denominator
The denominator is the number below the fraction line. In this exercise, it's 1000. The denominator shows the total number of equal parts the whole is divided into.
Think about the denominator as a way to measure collectively how many individual segments the whole is broken into. Multiply this by the size of each part (represented by the numerator), and you'll understand how the fraction works. Because the denominator is 1000 in our example, it signifies that our "whole" is divided into 1000 parts.
  • The greater the denominator, the smaller each part becomes.
  • The denominator never tells you about quantity; it talks about size and divisibility.
Understanding the denominator helps when converting to decimals, since it provides the framework against which you will measure the numerator.
Expressing Fractions as Decimal Form
Decimal form is a way to express fractions in a linear format that's easier to read and understand鈥攅specially when performing calculations. In this exercise, the fraction \( \frac{82}{1000} \) converts to the decimal form \( 0.082 \).
Once the division is performed (82 divided by 1000), you achieve the decimal form.
Decimals are used extensively in daily mathematics, allowing for quick arithmetic and comparisons. To convert any fraction to a decimal, simply divide the numerator by the denominator.
  • Decimals show the same value as fractions but in a different format.
  • They are especially useful for precision and ease of use in adding, subtracting, multiplying, or dividing numbers.
Overall, transforming fractions to decimal form streamlines complex fractions into an easier-to-understand number format.

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Most popular questions from this chapter

Perform the following operations. \(\frac{\frac{0.32}{12}}{\frac{12}{0.35}}\)

Convert each fraction to a decimal. $$ 9 \frac{4}{7} $$

Perform each operation and simplify. $$ 0.014 \div 47.6 . \text { Round to three decimal places. } $$

Read each decimal by writing it in words. 7.2

Perform each operation and simplify. $$ 10.000 \cdot 0.14 $$
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