Brianna asked 45 students if they would vote for her to be student council president. She used her calculator to compare the number of students who said yes with the total number of students. Her calculator showed the result as 0.6222… 1. Write this number as a fraction (Steps) 2. How many students said they would vote for Brianna?
The Correct Answer and Explanation is:
1. Writing 0.6222… as a fraction:
The repeating decimal 0.6222… can be written as a fraction in a few simple steps:
Step 1: Let x=0.6222…x = 0.6222…x=0.6222…
This allows us to represent the repeating decimal as a variable.
Step 2: Eliminate the decimal by multiplying both sides of the equation by 10.
Multiply both sides by 10 to shift the decimal point one place to the right:10x=6.2222…10x = 6.2222…10x=6.2222…
Step 3: Subtract the original equation from the new equation.
Now subtract the first equation (x=0.6222…x = 0.6222…x=0.6222…) from the second equation (10x=6.2222…10x = 6.2222…10x=6.2222…):10x−x=6.2222…−0.6222…10x – x = 6.2222… – 0.6222…10x−x=6.2222…−0.6222…
This simplifies to:9x=5.69x = 5.69x=5.6
Step 4: Solve for xxx.
Now divide both sides of the equation by 9:x=5.69x = \frac{5.6}{9}x=95.6
Step 5: Simplify the fraction.
To eliminate the decimal point, multiply both the numerator and denominator by 10:x=5690x = \frac{56}{90}x=9056
Now simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2:x=56÷290÷2=2845x = \frac{56 \div 2}{90 \div 2} = \frac{28}{45}x=90÷256÷2=4528
Thus, 0.6222… as a fraction is 2845\frac{28}{45}4528.
2. How many students said they would vote for Brianna?
We know that Brianna asked 45 students, and 0.6222… represents the fraction of students who would vote for her. Therefore, to find the number of students who said yes, we multiply the total number of students (45) by the fraction 2845\frac{28}{45}4528:Number of students=45×2845=28\text{Number of students} = 45 \times \frac{28}{45} = 28Number of students=45×4528=28
Thus, 28 students said they would vote for Brianna.
Conclusion:
- The repeating decimal 0.6222… is equivalent to the fraction 2845\frac{28}{45}4528.
- 28 students said they would vote for Brianna.
