Classify Numbers Above and Below 110%: Comparing Fractions and Decimals

Organise the values below into two groups of values greater than 110% and values less than 110%:

$$$1.7,\frac{105}{100},\frac{13}{14},0.7,\frac{120}{100}$

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:

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

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