Question

problems 1 - 4: determine the following values.
percent (%) decimal fraction

1. 6% 0.06
2. 400% 4.00
3. 50% 0.5
4. 60% 0.6
5. demetrius says that because percent means \out of 100,\ he needs to multiply by \\(\frac{1}{100}\\) to write a percentage that is equivalent to 3.7. help demetrius understand his mistake.
6. match each percent with its decimal equivalent.

a. 3.05% 0.305
b. 350% 3.5
c. 30.5% 0.035
d. 3.5% 0.0305

1. what is 0.7 expressed as a percentage?

Explanation:

Step1: Convert percentage to decimal

To convert a percentage to a decimal, divide by 100. For example, for \(a = 6\%\), \(a_{decimal}=\frac{6}{100}=0.06\).

Step2: Analyze Demetrius' mistake

To convert a number to a percentage, we multiply by 100, not \(\frac{1}{100}\). To write 3.7 as a percentage, we calculate \(3.7\times100 = 370\%\).

Step3: Match percentages and decimals

a. For \(3.05\%\), \(3.05\div100 = 0.0305\).
b. For \(350\%\), \(350\div100=3.5\).
c. For \(30.5\%\), \(30.5\div100 = 0.305\).
d. For \(3.5\%\), \(3.5\div100=0.035\).

Step4: Convert decimal to percentage

To convert 0.2 to a percentage, we multiply by 100: \(0.2\times100 = 20\%\).

Answer:

1. \(6\% = 0.06\)
2. \(400\%=4.00\)
3. \(50\% = 0.5\)
4. (Not clear from image, assume correct conversion based on steps above)
5. Demetrius should multiply by 100, not \(\frac{1}{100}\), so \(3.7 = 370\%\)
6. a. \(3.05\% - 0.0305\), b. \(350\% - 3.5\), c. \(30.5\% - 0.305\), d. \(3.5\% - 0.035\)
7. \(0.2\) expressed as a percentage is \(20\%\)