/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 15 \(\frac{132}{10,000}\)... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 15

\(\frac{132}{10,000}\)

Short Answer

Expert verified
0.0132

Step by step solution

01

Understand the Fraction

Recognize that \(\frac{132}{10,000}\) is a fraction where 132 is the numerator (top number) and 10,000 is the denominator (bottom number).
02

Simplify the Fraction

Look for common factors of the numerator and the denominator. Both 132 and 10,000 can be divided by 4.\(132 \div 4 = 33\) and \(10,000 \div 4 = 2,500\). So,\(\frac{132}{10,000} = \frac{33}{2,500}\).
03

Convert to Decimal Form

Divide the numerator by the denominator to convert the fraction to a decimal form.\(33 \div 2,500 = 0.0132\).

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Key Concepts

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

numerator and denominator
When dealing with fractions, it's essential to understand the terms 'numerator' and 'denominator'.
The numerator is the top number of a fraction. It tells you how many parts of a whole you have.
In the exercise \(\frac{132}{10,000}\), 132 is the numerator.
The denominator is the bottom number of a fraction. It tells you how many equal parts the whole is divided into.
In \(\frac{132}{10,000}\), 10,000 is the denominator.
Knowing these terms helps you follow the steps in fraction operations more easily.
For instance, understanding this allows us to simplify fractions correctly, and it enables efficient conversion into other forms like decimals.
common factors
To simplify a fraction, we need to find the common factors of the numerator and the denominator. Common factors are numbers that divide both the numerator and the denominator without leaving a remainder.
In our example, \(\frac{132}{10,000}\), both 132 and 10,000 can be divided by 4.
Dividing both the numerator and denominator by this common factor simplifies the fraction:
\(132 \div 4 = 33\)
\(10,000 \div 4 = 2,500\)
So, \(\frac{132}{10,000} = \frac{33}{2,500}\).
This step is significant because simplifying fractions makes them easier to understand and use in further calculations.
If there were no common factors, the fraction would already be in its simplest form.
decimal conversion
Converting a fraction to a decimal involves dividing the numerator by the denominator.
For \(\frac{33}{2,500}\), you divide 33 by 2,500:
\(33 \div 2,500 = 0.0132\)
This decimal helps in visualizing the part of the whole represented by the fraction.
Knowing how to convert fractions to decimals is very useful. It helps in various applications such as measurements, money calculations, and comparing quantities.
This gives another perspective on interpreting fractional values and enhances problem-solving versatility.

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