Textbook Question
Write each percent as a decimal. 4%
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0. Review of Algebra
Exponents
2:16 minutesProblem 160
Textbook Question
Write each percent as a decimal. 5 1/2%
Verified step by step guidance1
Convert the mixed number \(5 \frac{1}{2}\%\) into an improper fraction. This is done by multiplying the whole number by the denominator of the fraction and adding the numerator: \(5 \times 2 + 1 = 11\), so \(5 \frac{1}{2} = \frac{11}{2}\).
To convert a percentage to a decimal, divide by 100. So, divide \(\frac{11}{2}\) by 100.
This division can be expressed as \(\frac{11}{2} \times \frac{1}{100}\).
Multiply the numerators together and the denominators together: \(\frac{11 \times 1}{2 \times 100} = \frac{11}{200}\).
Convert the fraction \(\frac{11}{200}\) into a decimal by performing the division \(11 \div 200\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Percentages
A percentage is a way of expressing a number as a fraction of 100. It is often used to compare proportions and is denoted by the symbol '%'. For example, 25% means 25 out of 100, or 25/100. Understanding percentages is crucial for converting them into decimals or fractions.
Converting Percentages to Decimals
To convert a percentage to a decimal, you divide the percentage by 100. This process shifts the decimal point two places to the left. For instance, to convert 5.5% to a decimal, you calculate 5.5 ÷ 100, resulting in 0.055. This conversion is essential for performing calculations involving percentages.
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Mixed Numbers
A mixed number consists of a whole number and a proper fraction, such as 5 1/2. To work with mixed numbers, you often need to convert them into improper fractions or decimals. In this case, 5 1/2 can be converted to an improper fraction (11/2) or a decimal (5.5), which is necessary for further calculations.
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