Estimation: Sort into two groups

To solve this problem, we'll convert each given value into decimal form and compare it with $0.5$.

• $57\% = 0.57$, and since $0.57 > 0.5$, it is larger than $\frac{1}{2}$.
• $49\% = 0.49$, and since $0.49 < 0.5$, it is smaller than $\frac{1}{2}$.
• $0.54$ is already in decimal form, and since $0.54 > 0.5$, it is larger than $\frac{1}{2}$.
• $80\% = 0.80$, and since $0.80 > 0.5$, it is larger than $\frac{1}{2}$.
• $\frac{57}{100} = 0.57$, and since $0.57 > 0.5$, it is larger than $\frac{1}{2}$.

After comparing all the values, we classify them as follows:
- Smaller than $\frac{1}{2}$: $49\%$
- Larger than $\frac{1}{2}$: $57\%$, $0.54$, $80\%$, $\frac{57}{100}$

Therefore, the correct classification is:

$49\% < \frac{1}{2}$

$57\%, 0.54, 80\%, \frac{57}{100} > \frac{1}{2}$

To solve this problem, we'll convert each given value to a percentage and compare it with 25%.

• $\frac{13}{50}$: Calculate as $\left(\frac{13}{50}\right) \times 100 = 26\%$.
• $\frac{3}{4}$: Calculate as $\left(\frac{3}{4}\right) \times 100 = 75\%$.
• $34\%$: This value is already in percentage form as 34%.
• $\frac{24}{100}$: Calculate as $\left(\frac{24}{100}\right) \times 100 = 24\%$.
• $0.28$: Calculate as $0.28 \times 100 = 28\%$.

Now, we compare each percentage to 25%:

• $\frac{13}{50} = 26\%$ which is greater than 25%.
• $\frac{3}{4} = 75\%$ which is greater than 25%.
• $34\%$ which is greater than 25%.
• $\frac{24}{100} = 24\%$ which is less than 25%.
• $0.28 = 28\%$ which is greater than 25%.

Thus, grouping these values gives us:

• Values greater than 25%: $\frac{13}{50}, \frac{3}{4}, 34\%, 0.28$
• Values less than 25%: $\frac{24}{100}$

Therefore, the correct answer is:

\frac{13}{50},\frac{3}{4},34\%,0.28>25\% $$

\frac{24}{100}<25\%

$12\%=\frac{12}{100}=0.12$

Now we will convert all values into percentages and see which are greater and which are less than 12%.

$\frac{6}{40}\times\frac{2.5}{2.5}=\frac{15}{100}=15\%$

$\frac{11}{100}=11\%$

$0.1=\frac{10}{100}=10\%$

$0.13=\frac{13}{100}=13\%$

Now we can observe which are greater and less than 12%.

To categorize the numbers based on being greater than or less than 60%, we will first convert the fractions into decimals:

• $0.7$ is already a decimal, equivalent to $70\%$, which is greater than $60\%$.
• $\frac{67}{100} = 0.67$, equivalent to $67\%$, which is greater than $60\%$.
• $\frac{59}{100} = 0.59$, equivalent to $59\%$, which is less than $60\%$.
• $0.2$ is already a decimal, equivalent to $20\%$, which is less than $60\%$.
• $\frac{4}{5} = 0.8$, equivalent to $80\%$, which is greater than $60\%$.

Based on these conversions and comparisons, we organize them into two groups:

The numbers less than $60\%$ are $0.2$ and $\frac{59}{100}$.

The numbers greater than $60\%$ are $0.7$, $\frac{67}{100}$, and $\frac{4}{5}$.

Rechecking our work against the answer choices given confirms that the correct grouping is choice 3. Therefore, the solution is as follows:

0.2,\frac{59}{100}<60\%

0.7,\frac{67}{100},\frac{4}{5}>60\%

To solve this problem, we'll proceed with the following steps:

• Step 1: Convert each given value to a decimal form for consistent comparison.
• Step 2: Compare each decimal to 0.20, sort values into the categories: greater than 20% and less than 20%.

Let's convert each value:
- $\frac{18}{50} = 0.36$
- $0.24$ is already in decimal form.
- $0.19$ is already in decimal form.
- $45\%$ in decimal form is $0.45$.
- $\frac{28}{100} = 0.28$.

Now we compare each with 0.20:

• $\frac{18}{50} = 0.36$ is greater than $0.20$.
• $0.24$ is greater than $0.20$.
• $0.19$ is less than $0.20$.
• $45\%$ or $0.45$ is greater than $0.20$.
• $\frac{28}{100} = 0.28$ is greater than $0.20$.

Based on these comparisons, we organize them into two groups:

Greater than 20%: $\frac{18}{50}, 0.24, 45\%, \frac{28}{100}$

Less than 20%: $0.19$

Therefore, the values sorted into their respective categories are:

\frac{18}{50},0.24,45\%,\frac{28}{100}>20\%

0.19<20\%

To solve this problem, we'll follow these steps:

• Step 1: Convert all parts to decimals.

• Step 2: Compare each decimal to $0.2$ (the decimal form of $\frac{1}{5}$).

• Step 3: Organize the values based on whether they are greater or lesser than $0.2$.

Now, let's work through each step:

Step 1: Convert each value to a decimal.

• $\frac{5}{100} = 0.05$

• $24\% = 0.24$

• $50\% = 0.5$

• $\frac{1}{4} = 0.25$

• $0.5 = 0.5$

Step 2: Compare each decimal to $0.2$.

• 0.05 < 0.2

• 0.24 > 0.2

• 0.5 > 0.2

• 0.25 > 0.2

• 0.5 > 0.2

Step 3: Group the values:

• Parts less than $\frac{1}{5}$: $\frac{5}{100}$

• Parts greater than $\frac{1}{5}$: $24\%, 50\%, \frac{1}{4}, 0.5$

Therefore, the correct arrangement is:

\frac{5}{100}<\frac{1}{5}

24\%,50\%,\frac{1}{4},0.5>\frac{1}{5}

The problem requires us to organize values into two groups based on whether they are smaller or larger than $\frac{1}{8}$, which equals $0.125$.

First, convert the percentages to decimal form:

• $10\% = 0.10$

• $20\% = 0.20$

Now convert the fractions to decimal form:

• $\frac{11}{80} = 0.1375$

• $\frac{97}{800} = 0.12125$

The decimal $0.15$ is already given in decimal form.

We compare all values to $0.125$ (which is $\frac{1}{8}$):

• 0.10 < 0.125

• 0.20 > 0.125

• 0.1375 > 0.125

• 0.12125 < 0.125

• 0.15 > 0.125

Thus, we have:

Values smaller than $\frac{1}{8}$: $10\%$ and $\frac{97}{800}$.

Values larger than $\frac{1}{8}$: $20\%$, $\frac{11}{80}$, and $0.15$.

The correct grouping matches choice 1:
10\%, \frac{97}{800} < \frac{1}{8}
20\%, \frac{11}{80}, 0.15 > \frac{1}{8}

To solve this problem, we'll convert all given values to decimal form and compare them with 0.14.

• Convert $\frac{6}{20}$ to a decimal: $\frac{6}{20} = 0.3$.
• Convert $\frac{6}{40}$ to a decimal: $\frac{6}{40} = 0.15$.
• Convert $\frac{14}{95}$ to a decimal: $\frac{14}{95} \approx 0.1474$.
• Convert $\frac{1}{3}$ to a decimal: $\frac{1}{3} \approx 0.3333$.
• $0.1$ is already a decimal.

Now compare each value to 0.14:

• $0.1 < 0.14$
• $0.3 > 0.14$
• $0.15 > 0.14$
• $0.1474 > 0.14$
• $0.3333 > 0.14$

Therefore, grouping the values:

• Values greater than 14%: $\frac{1}{3}$, $\frac{6}{40}$, $\frac{6}{20}$
• Values less than 14%: $\frac{14}{95}$, $0.1$

In conclusion, the values greater than 14% are $\frac{1}{3}$, $\frac{6}{40}$, $\frac{6}{20}$ and less than 14% are $\frac{14}{95}$, $0.1$.

The correct answer choice is:

\frac{1}{3},\frac{6}{40},\frac{6}{20}>14\%

\frac{14}{95},0.1<14\%

To solve this problem, we'll convert each value to a decimal and compare it with $0.10$ (which represents $10\%$):

• Convert $19\%$ to a decimal: $19\% = 0.19$. Compare with $0.10$; 0.19 > 0.10.

• $0.9$ is already a decimal. Compare directly: 0.9 > 0.10.

• $0.09$ is already a decimal. Compare directly: 0.09 < 0.10.

• Convert $\frac{19}{100}$ to a decimal: $\frac{19}{100} = 0.19$. Compare with $0.10$; 0.19 > 0.10.

• Convert $\frac{1}{11}$ to a decimal: $\frac{1}{11} \approx 0.0909$. Compare with $0.10$; 0.0909 < 0.10.

Thus, the values can be grouped as follows:

Values less than $10\%$: $0.09, \frac{1}{11}$.

Values greater than $10\%$: $0.9, \frac{19}{100}, 19\%$.

The solution involves accurate conversion and comparison:

Therefore, the correct grouping is:

0.09, \frac{1}{11}<10\%

0.9, \frac{19}{100}, 19\% > 10\%

To solve this problem, follow these steps:

• Step 1: Recognize that $110\%$ is equivalent to $1.1$ when converted to decimal form.
• Step 2: Convert each given fraction to a decimal number for easy comparison, if necessary.
• Step 3: Compare each value with $1.1$ to sort.

Now, let's work through each step:

Step 1: Convert $110\%$ to a decimal: $110\% = \frac{110}{100} = 1.1$.

Step 2: Express each number in decimal form:

• The number $1.7$ is already a decimal.
• $\frac{105}{100}$ becomes $1.05$.
• $\frac{13}{14}$ calculates to approximately $0.9286$.
• The number $0.7$ is already a decimal.
• $\frac{120}{100}$ becomes $1.2$.

Step 3: Compare each value against $1.1$:

• $1.7 > 1.1$ (greater than 110%)
• $\frac{105}{100} \approx 1.05 < 1.1$ (less than 110%)
• $\frac{13}{14} \approx 0.9286 < 1.1$ (less than 110%)
• $0.7 < 1.1$ (less than 110%)
• $\frac{120}{100} = 1.2 > 1.1$ (greater than 110%)

Therefore, the organized groups are:

$\frac{120}{100}, 1.7$ are greater than 110%.

$0.7, \frac{13}{14}, \frac{105}{100}$ are less than 110%.

The problem's answer corresponds to choice 4:

$\frac{120}{100},1.7>110\%$

$0.7,\frac{13}{14},\frac{105}{100}<110\%$

To solve this problem, we need to compare each given value with $\frac{4}{2}$.

• Calculate $\frac{4}{2} = 2$.

Now, convert all given values to decimals:

• The value $1.3$ is already in decimal form: $1.3$.
• Convert $\frac{1}{2}$ to decimals: $0.5$.
• Convert $150\%$ to decimals by dividing by 100: $\frac{150}{100} = 1.5$.
• Calculate $\frac{74}{12} \approx 6.1667$.
• $0.5$ is already in decimal form: $0.5$.

Now, compare each value with $2$:

• Values less than $2$: $1.3, \frac{1}{2}, 150\%, 0.5$ (i.e., $1.3, 0.5, 1.5, 0.5$).
• Values greater than $2$: $\frac{74}{12}$ (i.e., approximately $6.1667$).

Therefore, the solution to the problem is:

$1.3, \frac{1}{2}, 150\%, 0.5 < \frac{4}{2}$

$\frac{74}{12} > \frac{4}{2}$

To solve this problem, we will convert all given values into decimals to compare with $\frac{6}{7}$.

Step 1: Convert $\frac{6}{7}$ into a decimal.
Calculate $\frac{6}{7} \approx 0.857$.

Step 2: Convert each value into a decimal.
- 84% = 0.84.
- 10% = 0.10.
- 0.4 is already a decimal.
- $\frac{14}{50} = 0.28$.
- 0.9 is already a decimal.

Step 3: Compare each value to $\frac{6}{7}$.
- $0.84 < 0.857$, so 84% is less than $\frac{6}{7}$.
- $0.10 < 0.857$, so 10% is less than $\frac{6}{7}$.
- $0.4 < 0.857$, so 0.4 is less than $\frac{6}{7}$.
- $0.28 < 0.857$, so $\frac{14}{50}$ is less than $\frac{6}{7}$.
- $0.9 > 0.857$, so 0.9 is greater than $\frac{6}{7}$.

Therefore, the solution is:

84\%,\frac{14}{50},0.4,10\%<\frac{6}{7}

0.9>\frac{6}{7}

To solve this problem, we first convert all the values to decimals to ease comparison with $\frac{3}{8} = 0.375$.

• $\frac{1}{3} \approx 0.333$
• $36\% = 0.36$
• $\frac{2}{3} \approx 0.667$
• $40\% = 0.40$
• $0.42$ remains the same.

Next, we compare each of these converted values to 0.375:

• $0.333 (\frac{1}{3}) < 0.375$
• $0.36 (36\%) < 0.375$
• $0.40 (40\%) > 0.375$
• $0.42 > 0.375$
• $0.667 (\frac{2}{3}) > 0.375$

Therefore, the values less than $\frac{3}{8}$ are $\frac{1}{3}$ and $36\%$, while the values greater than $\frac{3}{8}$ are $40\%$, $0.42$, and $\frac{2}{3}$.

The correct answer choice is:

36\%,\frac{1}{3}<\frac{3}{8}

0.42,40\%,\frac{2}{3}>\frac{3}{8}