Write each percent as a decimal. 5 1/2%

Verified step by step guidance

1. Convert the mixed number $5\frac{1}{2}\mathrm{\%}$ 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 $5\frac{1}{2}=\frac{11}{2}$.
2. To convert a percentage to a decimal, divide by 100. So, divide $\frac{11}{2}$ by 100.
3. This division can be expressed as $\frac{11}{2}\times \frac{1}{100}$.
4. Multiply the numerators together and the denominators together: $\frac{11\times 1}{2\times 100}=\frac{11}{200}$.
5. Convert the fraction $\frac{11}{200}$ into a decimal by performing the division $11÷200$.

Key Concepts

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.

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.