Question

for a-d, choose yes or no if the pairs represent the same amount. the decimals are rounded to the nearest hundredth. a. \\(\frac{5}{9}\\) and 33.33% \\(\bigcirc\\)yes \\(\bigcirc\\)no b. 33.33% and \\(\frac{1}{2}\\) \\(\bigcirc\\)yes \\(\bigcirc\\)no c. 24% and \\(\frac{2}{4}\\) \\(\bigcirc\\)yes \\(\bigcirc\\)no d. \\(\frac{1}{3}\\) and 33.33% \\(\bigcirc\\)yes \\(\bigcirc\\)no

Explanation:

Step1: Analyze Option A

To check if $\frac{5}{9}$ and 33.33% are the same, first convert $\frac{5}{9}$ to a decimal. $\frac{5}{9} \approx 0.5556$. Now convert 33.33% to a decimal: $33.33\% = 0.3333$. Since $0.5556
eq 0.3333$, the answer for A is No.

Step2: Analyze Option B

Convert $\frac{1}{2}$ to a decimal: $\frac{1}{2} = 0.5$. Convert 33.33% to a decimal: $33.33\% = 0.3333$. Since $0.5
eq 0.3333$, the answer for B is No.

Step3: Analyze Option C

Convert $\frac{2}{4}$ to a decimal: $\frac{2}{4} = 0.5$. Convert 24% to a decimal: $24\% = 0.24$. Since $0.5
eq 0.24$, the answer for C is No.

Step4: Analyze Option D

Convert $\frac{1}{3}$ to a decimal: $\frac{1}{3} \approx 0.3333\ldots$. Convert 33.33% to a decimal: $33.33\% = 0.3333$. When $\frac{1}{3}$ is rounded to the nearest hundredth, it is $0.33$, but wait, actually $\frac{1}{3} \approx 0.3333$, and 33.33% is $0.3333$. Wait, no, $\frac{1}{3} = 0.\overline{3}$, which is approximately $0.3333$ when rounded to four decimal places, and 33.33% is $0.3333$. So when considering the nearest hundredth, $\frac{1}{3} \approx 0.33$? Wait, no, the problem says "the decimals are rounded to the nearest hundredth". Wait, $\frac{1}{3} \approx 0.3333\ldots$, rounded to the nearest hundredth is $0.33$? No, wait, the hundredth place is the second decimal. $0.3333\ldots$: the first decimal is 3 (tenths), second is 3 (hundredths), third is 3 (thousandths). So rounding to the nearest hundredth, look at the thousandth place, which is 3, so it stays $0.33$? But 33.33% is $0.3333$, which is $0.33$ when rounded to the nearest hundredth? Wait, no, 33.33% is exactly $0.3333$, and $\frac{1}{3} \approx 0.3333\ldots$. So when rounded to the nearest hundredth, both are $0.33$? Wait, no, the problem says "the decimals are rounded to the nearest hundredth". Wait, maybe the question is whether the fraction and the percentage represent the same amount when the decimal of the fraction is rounded to the nearest hundredth. Let's re - evaluate:

$\frac{1}{3}=0.3333\ldots$, rounded to the nearest hundredth is $0.33$? No, wait, the rule for rounding: look at the digit in the thousandth place. For $0.3333\ldots$, the thousandth digit is 3, which is less than 5? No, 3 is less than 5? Wait, no, 0.3333: the hundredth place is the second 3, the thousandth is 3. So to round to the nearest hundredth, we look at the thousandth digit. If it's 5 or more, we round up the hundredth digit. Since 3 < 5, we keep the hundredth digit as 3. So $\frac{1}{3}$ rounded to the nearest hundredth is $0.33$, and 33.33% is $0.3333$, which is $0.33$ when rounded to the nearest hundredth? Wait, no, 33.33% is $0.3333$, which is $0.33$ when rounded to the nearest hundredth? Wait, no, 0.3333 rounded to the nearest hundredth: the number is $0.3333$, the hundredth digit is 3, the thousandth is 3. So we round down, so it's $0.33$. And $\frac{1}{3}=0.3333\ldots$ rounded to the nearest hundredth is also $0.33$. So they are the same when rounded to the nearest hundredth. So the answer for D is Yes.

Answer:

A. No
B. No
C. No
D. Yes