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Chapter 6: Problem 1

Write \(9 \%\) as a decimal. A. 0.009 B. 0.09 C. 0.9 D. 9.0

Short Answer

Expert verified
The decimal equivalent of 9% is 0.09 (Option B).

Step by step solution

01

Understanding the Percentage

Percentages represent a fraction of 100. In this problem, we have been given 9%, which means 9 per 100, or simply 9/100.
02

Converting Percentage to Fraction

To convert the percentage to a decimal, first express it as a fraction: \[ 9 ext{%} = \frac{9}{100} \] This fraction represents the equivalent value in tenths or hundredths.
03

Conversion from Fraction to Decimal

To convert the fraction \( \frac{9}{100} \) to a decimal, perform the division of 9 by 100. \[ \frac{9}{100} = 0.09 \] This gives the decimal equivalent of 9%.
04

Selecting the Correct Option

Now, compare the calculated decimal 0.09 with the given options: A. 0.009, B. 0.09, C. 0.9, and D. 9.0. The correct answer is option B, 0.09, as it matches our result.

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Key Concepts

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

Percentage
A percentage is a way of expressing a number as a fraction of 100. For instance, when we talk about 9%, we are referring to 9 out of every 100 pieces. This makes percentages an easy way to compare relative sizes because they relate a part to a large whole.
When you understand percentages, you are actually understanding parts of a whole - just like slices of a pie.
  • Relatable Example: Consider a classroom with 100 students. If 9% of them are wearing glasses, it means 9 students wear glasses.
  • General Formula: To express a number as a percentage, you multiply it by 100 and add the percent sign (%).
This percentage concept is the foundation when converting to other forms such as decimals.
Fraction to Decimal Conversion
Converting fractions to decimals is a fundamental arithmetic skill that connects different expressions of the same value. For the percentage 9%, we first convert it to a fraction, which is \[ \frac{9}{100} \]. This fraction represents 9 parts of 100.

The process of conversion from fractions to decimals involves division.
  • Divide the numerator (top number of the fraction) by the denominator (bottom number of the fraction).
  • In our example, divide 9 by 100 to get 0.09.
Now, the 0.09 is the decimal representation. Each of these conversions - percentage, fraction, and decimal - are different ways of communicating the same value.
Mathematical Problem-Solving
Mathematical problem-solving is not just about reaching the answer. It is about understanding the steps and operations needed to arrive at a solution. Let's apply these skills to our exercise:
Start by interpreting the percentage as a fraction. Next, perform the arithmetic operation - division to get the decimal.
  • Breaking Down: By breaking down the problem into parts, we made it easier to understand.
  • Checking Work: Always double-check your work by comparing your result with the provided choices.
In the context of our exercise, critical thinking helped us determine that the decimal equivalent of 9% is 0.09.
Basic Arithmetic Skills
Basic arithmetic skills such as division play a crucial role when converting percentages to decimals. These skills serve as the building blocks for solving more complex math problems.

The exercise required dividing 9 by 100, a simple arithmetic task that enhances your number senses.
  • Incremental Learning: Understanding such basic problems helps you tackle more advanced math confidently.
  • Arithmetic Operations: Being comfortable with division and multiplication aids in daily calculations and academic exercises.
Consistently practicing these skills ensures mastery, allowing for smoother learning transitions as mathematical tasks grow in complexity.

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Most popular questions from this chapter

Write 0.634 as a percent. A. \(63.4 \%\) B. \(0.00634 \%\) C. \(6.34 \%\) D. \(634 \%\)

8 is what percent of \(25 ?\) A. \(32 \%\) B. \(8 \%\) C. \(80 \%\) D. \(3.2 \%\)

Write \(145 \%\) as a decimal. A. 1.45 B. 0.145 C. 0.00145 D. 145

Write \(6 \frac{3}{4}\) as a percent. A. \(6.75 \%\) B. \(67.5 \%\) C. \(675 \%\) D. \(0.675 \%\)

Find \(75 \%\) of 250 . A. 187.5 B. 18.75 C. 1875 D. 18750
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