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Chapter 6: Problem 1

Write \(6 \%\) as a decimal. (a) 0.006 (b) 0.06 (c) 0.6 (d) 6.0

Short Answer

Expert verified
0.06; option (b).

Step by step solution

01

Understanding Percent

Percent means "per hundred," so 6% means 6 per 100 or 6 out of 100.
02

Convert Percent to Fraction

Express 6% as a fraction: \( \frac{6}{100} \).
03

Convert Fraction to Decimal

Divide 6 by 100 to convert the fraction to a decimal: \( \frac{6}{100} = 0.06 \). This means moving the decimal point two places to the left.
04

Choose the Correct Option

Identify the choice that equals the decimal \(0.06\). It is option (b) 0.06.

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Key Concepts

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

Percent to Fraction Conversion
To understand how to convert a percent into a fraction, remember that a percent is simply a part of a whole. A percent is out of 100, stemming from the term per centum, meaning per hundred.
Thus, when you have a percentage, such as 6%, you want to express this in terms of how many parts out of 100 it represents.
To convert 6% into a fraction, you simply place 6 over 100, giving you \( \frac{6}{100} \). This step places your percentage into a simple fractional form where the numerator is your percentage, and the denominator is always 100.
  • This step helps visualize the percentage as a part of a whole.
  • Always simplify fractions if you can, even though in the case of 6%, 6 and 100 share no common divisors other than 1.
Decimal Representation
Once you have the fraction \( \frac{6}{100} \), the next step is to express it as a decimal. Converting a fraction to a decimal involves division.
In this case, you divide the numerator (6) by the denominator (100). Doing this simple division calculation will provide you with the decimal form of the fraction. Calculating \( \frac{6}{100} = 0.06 \).
So, effectively, converting from a fraction to a decimal just involves division. This specific division鈥攂y 100鈥攊s crucial in percent conversions as it translates the part per hundred to a decimal point-of-view.
  • When dividing by 100, move the decimal two places to the left for quick conversion.
  • This change is the same as shifting from percent to decimal directly.
Basic Arithmetic Operations
Understanding basic arithmetic operations is pivotal when working with numbers and conversions. Division is a primary operation needed when converting fractions to decimals.
By recognizing percentages can be written as fractions over 100, arithmetic operations become a tool for transformation.
  • Division helps transition from a fraction to a decimal.
  • Moving the decimal is another way to perform division by powers of ten.
Mathematically, when percentages are involved, you're often dealing with divisions and multiplications of 100, because a percent is inherently an arithmetic relationship: parts out of 100.
Understanding this helps solidify how operations underlie simple conversions.

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Most popular questions from this chapter

Write \(125 \%\) as a fraction. (a) \(1 \frac{5}{8}\) (b) \(1 \frac{1}{4}\) (c) \(1 \frac{3}{4}\) (d) \(1 \frac{2}{5}\)

Write 0.511 as a percent. (a) \(0.511 \%\) (b) \(0.00511 \%\) (c) \(51.1 \%\) (d) \(511 \%\)

Write 0.39 as a percent. (a) \(0.39 \%\) (b) \(39 \%\) (c) \(0.039 \%\) (d) \(390 \%\)

Write \(54.8 \%\) as a decimal. (a) 0.548 (b) 5.48 (c) 0.0548 (d) 5480

6 is what percent of \(25 ?\) (a) \(150 \%\) (b) \(24 \%\) (c) \(41 . \overline{6} \%\) (d) \(72 \%\)
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