/*! 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 23 Convert to decimal notation. $$... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 23

Convert to decimal notation. $$ 125 \% $$

Short Answer

Expert verified
1.25

Step by step solution

01

Understand the percent notation

Percent means 'per hundred'. So, 125% means 125 per 100.
02

Convert percent to fraction

To convert percent to a fraction, divide by 100. Hence, 125% becomes \(\frac{125}{100}\).
03

Simplify the fraction

Simplify the fraction \( \frac{125}{100} \). This fraction simplifies to \( \frac{5}{4} \) because both 125 and 100 can be divided by 25.
04

Convert the fraction to decimal

Convert \( \frac{5}{4} \) to a decimal by performing the division \( 5 \div 4 = 1.25 \).

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Key Concepts

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

Percent Notation
Percent notation is a way to express numbers as parts of 100. When we see a percentage, it means how many parts out of 100. For example, 50% means 50 out of 100. This can help in comparing different quantities easily.

To convert a percentage into a more workable form, we often change it into other types like fractions or decimals. Let's look at how you can do this.
Fraction Simplification
After understanding percent notation, the next step is to convert it into a fraction. This involves dividing the given percentage by 100. For example, 125% becomes \( \frac{125}{100} \).

Simplifying fractions means reducing them to their simplest form. You do this by dividing both the numerator (top number) and denominator (bottom number) by their greatest common divisor (GCD). In our example, 125 and 100 can both be divided by 25:
\[\frac{125 \/ 25}{100 \/ 25} = \frac{5}{4} \]
Now, the fraction is simplified and easier to work with.
Decimal Conversion
Once you have a simplified fraction, converting it to decimal form is straightforward. You simply perform the division of the numerator by the denominator. For the fraction \(\frac{5}{4}\):
\[5 \div 4 = 1.25\]
Therefore, 125% is equivalent to 1.25 in decimal notation.

Understanding how to convert between these forms can make working with percentages much easier and more intuitive. Remember, practice helps in solidifying these concepts!

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Most popular questions from this chapter

Use an inequality and the five-step process to solve each problem. Most insurance companies will replace a vehicle if an estimated repair exceeds \(80 \%\) of the "blue-book" value of the vehicle. Michelle's insurance company paid \(\$ 8500\) for repairs to her Subaru after an accident. What can be concluded about the blue-book value of the car?

Translate to an inequality. The temperature is at most \(-3^{\circ} \mathrm{C}\)

Use an inequality and the five-step process to solve each problem. Abriana rented a compact car for a business trip. At the time of the rental, she was given the option of prepaying for an entire tank of gasoline at \(\$ 3.099\) per gallon, or waiting until her return and paying \(\$ 6.34\) per gallon for enough gasoline to fill the tank. If the tank holds 14 gal, how many gallons can she use and still save money by choosing the second option?

Translate to an inequality. The age of the Mayan altar exceeds 1200 yr.

Use an inequality and the five-step process to solve each problem. Rick's Automotive charges \(\$ 50\) plus \(\$ 15\) for each \((15-\text { min })\) unit of time when making a road call. Twin City Repair charges \(\$ 70\) plus \(\$ 10\) for each unit of time. Under what circumstances would it be more economical for a motorist to call Rick's?
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