Organise the values below into two groups of values greater than 110% and values less than 110%:
1.7,100105,1413,0.7,100120
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%=100110=1.1.
Step 2: Express each number in decimal form:
- The number 1.7 is already a decimal.
- 100105 becomes 1.05.
- 1413 calculates to approximately 0.9286.
- The number 0.7 is already a decimal.
- 100120 becomes 1.2.
Step 3: Compare each value against 1.1:
- 1.7>1.1 (greater than 110%)
- 100105≈1.05<1.1 (less than 110%)
- 1413≈0.9286<1.1 (less than 110%)
- 0.7<1.1 (less than 110%)
- 100120=1.2>1.1 (greater than 110%)
Therefore, the organized groups are:
100120,1.7 are greater than 110%.
0.7,1413,100105 are less than 110%.
The problem's answer corresponds to choice 4:
100120,1.7>110%
0.7,1413,100105<110%
\frac{120}{100},1.7>110\%
0.7,\frac{13}{14},\frac{105}{100}<110\%