220% as a decimal and mixed number or fraction.
The Correct Answer and Explanation is:
To express 220% as a decimal and a mixed number or fraction, we need to break it down step by step.
Step 1: Convert 220% to a decimal
To convert a percentage to a decimal, divide the percentage by 100. This is because “percent” means “per hundred.” So, we perform the following operation:220%=220100=2.2220\% = \frac{220}{100} = 2.2220%=100220=2.2
So, 220% as a decimal is 2.2.
Step 2: Convert 220% to a mixed number or fraction
To express 220% as a fraction, we start with the value 220100\frac{220}{100}100220. Next, simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 220 and 100 is 20. So we divide both by 20:220100=220÷20100÷20=115\frac{220}{100} = \frac{220 \div 20}{100 \div 20} = \frac{11}{5}100220=100÷20220÷20=511
Thus, 220% as a fraction is 115\frac{11}{5}511.
Step 3: Convert the fraction 115\frac{11}{5}511 to a mixed number
A mixed number consists of a whole number and a fraction. To convert 115\frac{11}{5}511 into a mixed number, divide the numerator by the denominator. When 11 is divided by 5, the quotient is 2 with a remainder of 1. This means:115=215\frac{11}{5} = 2 \frac{1}{5}511=251
Thus, 220% as a mixed number is 2152 \frac{1}{5}251.
Summary:
- As a decimal, 220% is 2.2.
- As a fraction, 220% is 115\frac{11}{5}511.
- As a mixed number, 220% is 2152 \frac{1}{5}251.
This is how we can express 220% in decimal, fraction, and mixed number forms.
