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Chapter 8: Problem 23

Write each percent as a decimal number. $$16 \frac{1}{6} \%$$

Short Answer

Expert verified
Answer: The decimal equivalent of 16 1/6% is approximately 0.1617 when rounded to four decimal places.

Step by step solution

01

Convert the mixed number into an improper fraction

To convert the mixed number 16 1/6 into an improper fraction, we first multiply the integer part (16) by the denominator of the fractional part (6), and then add the numerator of the fractional part (1): $$16 \frac{1}{6} = \frac{16 \cdot 6 + 1}{6} = \frac{96+1}{6} = \frac{97}{6}$$ So, the improper fraction is 97/6.
02

Divide by 100 to get the decimal number

Now, to convert the fraction into a decimal, we'll divide the numerator (97) by the denominator (6) and then divide the result by 100, since the initial expression was in percentage: $$\frac{97}{6} \% = \frac{97 \div 6}{100} = \frac{16.1666666667}{100} = 0.1616666667$$ So, the decimal equivalent of 16 1/6% is approximately 0.1617 when rounded to four decimal places.

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Key Concepts

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

Mixed Numbers
Mixed numbers are a combination of whole numbers and fractions. They make it easier to express quantities that are not whole, for instance:
  • "16 1/6" is a mixed number with 16 being the whole number and 1/6 the fraction.
To work with mixed numbers, it's often useful to convert them to improper fractions. This involves:
  • Multiplying the whole number by the fraction's denominator.
  • Adding the result to the fraction's numerator.
This conversion makes further calculations simpler, especially when performing operations like addition or conversion to other forms.
Improper Fractions
An improper fraction is a type of fraction where the numerator (top number) is greater than or equal to the denominator (bottom number). This type of fraction often results from converting a mixed number, as it centralizes all parts of the number into one expression.
For example, converting "16 1/6" into an improper fraction gives us \[ \frac{97}{6} \].
Improper fractions are particularly handy:
  • They simplify division as both numerator and denominator are in integer form.
  • They are easier to convert into decimals.
Decimal Numbers
Decimal numbers are a way to express fractions using the base ten system. They provide precision and clarity, especially useful in percentages and financial calculations.

To convert fractions into decimals, divide the numerator by the denominator. From our example: \[ \frac{97}{6} = 16.1666... \]
Thus, fractions turn into decimal numbers through straightforward division, transforming data into formats easier to read or compare.
Division
Division, in mathematical terms, is the process of finding how many times a number (the divisor) is contained within another number (the dividend).
This is central to converting fractions into decimals. For instance:
  • When dividing 97 by 6, you get 16.1666... which signifies how many times 6 fits into 97.
  • This result can be further adjusted by dividing by 100 to convert percentages into their decimal form.
Mastering division is crucial to understanding fractions and decimals, especially when converting percentages.
Rounding Decimals
Rounding decimals is an important skill to simplify lengthy or repeating decimal numbers, ensuring they are presented in a more comprehensible form.
Rounding to a certain decimal place involves:
  • Looking at the digit just after the desired decimal place.
  • If this digit is 5 or higher, increase the last digit you're keeping by one.
  • If it鈥檚 less than 5, retain the last digit.
In our example, rounding 0.1616666667 to four decimal places gives 0.1617, smoothing out the number for easier understanding and presentation.

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Most popular questions from this chapter

Translate to an equation and solve. \(120 \%\) of what number is \(65.52 ?\)

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