350% as a decimal and as a mixed number or fraction in simplest form.
The correct answer and explanation is:
To express 350% as a decimal and as a mixed number or fraction in simplest form, let’s break it down:
Step 1: Convert the percentage to a decimal
A percentage represents a value per 100. To convert a percentage into a decimal, divide the percentage by 100. 350%=350100=3.5350\% = \frac{350}{100} = 3.5
Thus, 350% as a decimal is 3.5.
Step 2: Convert the decimal to a mixed number
Next, we need to convert 3.5 into a mixed number. A mixed number is a combination of a whole number and a fraction. The number 3.5 can be split as: 3.5=3+0.53.5 = 3 + 0.5
Now, we express 0.5 as a fraction: 0.5=120.5 = \frac{1}{2}
Thus, 3.5 as a mixed number is 3 \frac{1}{2}.
Step 3: Convert the decimal to a fraction in simplest form
To convert 3.5 into a fraction, treat 3.5 as \frac{7}{2}. Here’s why:
First, write 3.5 as \frac{7}{2}: 3.5=723.5 = \frac{7}{2}
The fraction is already in its simplest form because 7 and 2 have no common factors other than 1.
Final Answers:
- As a decimal: 3.5
- As a mixed number: 3 \frac{1}{2}
- As a fraction: \frac{7}{2}
Explanation:
Percentages are based on a ratio of 100, so converting a percentage to a decimal simply involves dividing by 100. Converting the decimal to a mixed number involves separating the whole number part from the decimal part and converting the decimal part into a fraction. For instance, 0.5 is equivalent to \frac{1}{2}, so when combined with the whole number part, it forms a mixed number. To convert the decimal to a fraction, we multiply the decimal by 10 to remove the decimal point, then simplify the fraction if needed.