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

Question

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

1.7,105100,1314,0.7,120100 1.7,\frac{105}{100},\frac{13}{14},0.7,\frac{120}{100}

Video Solution

Step-by-Step Solution

To solve this problem, follow these steps:

  • Step 1: Recognize that 110%110\% is equivalent to 1.11.1 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 1.11.1 to sort.

Now, let's work through each step:

Step 1: Convert 110%110\% to a decimal: 110%=110100=1.1110\% = \frac{110}{100} = 1.1.

Step 2: Express each number in decimal form:

  • The number 1.71.7 is already a decimal.
  • 105100\frac{105}{100} becomes 1.051.05.
  • 1314\frac{13}{14} calculates to approximately 0.92860.9286.
  • The number 0.70.7 is already a decimal.
  • 120100\frac{120}{100} becomes 1.21.2.

Step 3: Compare each value against 1.11.1:

  • 1.7>1.11.7 > 1.1 (greater than 110%)
  • 1051001.05<1.1\frac{105}{100} \approx 1.05 < 1.1 (less than 110%)
  • 13140.9286<1.1\frac{13}{14} \approx 0.9286 < 1.1 (less than 110%)
  • 0.7<1.10.7 < 1.1 (less than 110%)
  • 120100=1.2>1.1\frac{120}{100} = 1.2 > 1.1 (greater than 110%)

Therefore, the organized groups are:

120100,1.7\frac{120}{100}, 1.7 are greater than 110%.

0.7,1314,1051000.7, \frac{13}{14}, \frac{105}{100} are less than 110%.

The problem's answer corresponds to choice 4:

120100,1.7>110%\frac{120}{100},1.7>110\%

0.7,1314,105100<110%0.7,\frac{13}{14},\frac{105}{100}<110\%

Answer

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

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