Compare Numbers with 6/7: Sorting Decimals, Percentages, and Fractions

Organise the following into two groups of parts smaller than

$\frac{6}{7}$ and parts larger than $\frac{6}{7}$:

$84\%,10\%,0.4,\frac{14}{50},0.9$

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:

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

$0.9>\frac{6}{7}$