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Chapter 2: Problem 66

Express \(\frac{1}{20}\) of \(1 \%\) as a percent using decimal notation.

Short Answer

Expert verified
\(\frac{1}{20}\) of 1% is \(0.05\%\).

Step by step solution

01

Understanding Percentages

To begin, recall that 1% means 1 out of 100. So, 1% as a decimal is written as 0.01.
02

Applying the Part of a Quantity

We need to find \(\frac{1}{20}\) of 1%. This means multiplying the decimal form of 1%, which is 0.01, by \(\frac{1}{20}\).
03

Performing the Multiplication

Multiply \(0.01 \times \frac{1}{20}\). This multiplication requires multiplying the decimal 0.01 by the fraction \(\frac{1}{20}\), resulting in \(0.01 \times 0.05 = 0.0005\).
04

Converting Back to Percentage

Convert the decimal result back into a percentage. Multiplying the decimal 0.0005 by 100 to turn it into a percentage gives \(0.05\%\).

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Key Concepts

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

Decimal Notation
Decimal notation is a way to express numbers using a base-10 system. It is the most common numerical system that incorporates digits 0 through 9. In decimal notation, each digit has a place value, determined by its distance from the decimal point. For example, the number 0.01 is a decimal number, where the '0' left of the decimal represents units and the '1' in the second decimal place indicates one hundredth or 1/100.

Decimals are commonly used in various applications, such as representing currency or percentages. The advantage of decimal notation is its simplicity and the ease with which it handles fractional quantities.
Fraction to Decimal Conversion
Converting fractions to decimals is a useful skill that simplifies mathematical operations. To convert a fraction into a decimal, you divide the numerator by the denominator. This gives a representation of the fraction in decimal form.

Let's take the fraction \(\frac{1}{20}\) as an example. To convert \(\frac{1}{20}\) to a decimal, divide 1 by 20. Set up the division as 1 梅 20, which results in the decimal 0.05.
  • The numerator (1) is inside the division, while the denominator (20) acts as the divisor.
  • Perform the division to find that \(\frac{1}{20} = 0.05\).
This method of conversion helps when calculating percentages or when dealing with decimals in other computations.
Percentage Calculation
Calculating percentages involves converting a number into a percent by multiplying by 100. A percentage represents a fraction of 100, widely used to express how large one quantity is relative to another.

Let's examine how to express a decimal as a percentage. Suppose you have the decimal 0.0005 and you want to convert it into a percentage. To achieve this, multiply 0.0005 by 100, resulting in 0.05%.
  • The multiplication by 100 shifts the decimal point two places to the right, effectively converting a decimal into a percentage.
  • This calculation transforms the decimal value into a percentage that can be easily understood in terms of parts per hundred.
This technique is fundamental in many real-world contexts, such as financial calculations and data analysis.

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Most popular questions from this chapter

Solve each inequality or compound inequality. Write the solution set in interval notation and graph it. $$ -5 x+7 \leq 12 $$

Dry mixture problems. A scuba diver, hired by an amusement park, collected 121 dollar in nickels, dimes, and quarters at the bottom of a wishing well. There were 500 nickels, and 90 more quarters than dimes. How many quarters and dimes were thrown into the wishing well?

Dry mixture problems. A bag of peanuts is worth 0.30 dollar less than a bag of cashews. Equal amounts of peanuts and cashews are used to make 40 bags of a mixture that sells for 1.05 per bag. How much is a bag of cashews worth?

Solve each inequality or compound inequality. Write the solution set in interval notation and graph it. $$ 6<-2(x-1)<12 $$

Dry mixture problems. When a child emptied his coin bank, he had a collection of pennies, nickels, and dimes. There were 20 more pennies than dimes and the number of nickels was triple the number of dimes. If the coins had a value of 5.40 dollar, how many of each type coin were in the bank?
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