Fractions and Decimals

Arrange the following numerical values in ascending order (from smallest to largest).

A water storage tank is currently filled to $0.65$ of its total capacity. If the tank currently contains $130$ liters of water, what is the total capacity of the tank in liters?

Evaluate the following mathematical expression:

What is the correct resulting value?

Three electronic metronomes are set to tick at regular intervals of $\frac{2}{3}$ of a second, $\frac{3}{4}$ of a second, and $\frac{4}{5}$ of a second, respectively. If they all tick simultaneously at a given moment, after how many seconds will they next tick together simultaneously?

Compute the exact Highest Common Factor (HCF) for the fractions $\frac{6}{25}$ and $\frac{9}{10}$. Express your final result as a decimal.

During a materials testing process, the density of four composite alloys (A, B, C, and D) is recorded in grams per cubic centimeter ($\text{g/cm}^3$):

- Alloy A: $2.\overline{15}$
- Alloy B: $\frac{15}{7}$
- Alloy C: $2.1\overline{5}$
- Alloy D: $\frac{28}{13}$

Arrange the alloys in ascending order based on their density, from the lowest to the highest.

A local water reservoir was initially filled to exactly $0.\overline{3}$ of its maximum capacity. After several days of heavy rainfall, an additional $14.4$ million liters of water flowed into the reservoir, bringing the water level to $0.6$ of its maximum capacity.

Currently, a nearby town consumes water from the reservoir at a steady rate of $1\frac{1}{2}$ million liters per day. Additionally, an undiscovered leak at the base of the reservoir drains water at a constant rate of $0.05$ million liters per hour.

If the reservoir were completely full and no further water was added, in how many days would it become completely empty?

A municipal corporation is distributing its annual infrastructure development fund. Exactly $0.\overline{5}$ of the total fund is allocated to urban housing projects. From the remaining fund, $\frac{3}{7}$ is assigned to public transportation. The rest of the fund is distributed equally between two sectors: renewable energy and public parks. If the amount allocated to renewable energy is $\$3.2$ million, what is the total annual infrastructure development fund?

During a system stress test, four data processing modules record their average latency per transaction (in seconds) as given below. Arrange the modules in ascending order based on their latency times (from fastest to slowest).

An industrial chemical plant stores a specialized solvent in three large cylindrical vats. The first vat contains $53.\overline{3}$ liters, the second contains $71.\overline{1}$ liters, and the third contains $26.\overline{6}$ liters of the solvent. The plant manager wants to completely transfer the solvent from all three vats into identical, smaller drums such that every drum is completely filled, no solvent is left over in any vat, and solvents from different vats are not mixed. What should be the maximum possible capacity of each drum?

A large agricultural cooperative is dividing a massive tract of land for different crops. They allocate $0.\overline{428571}$ of the total land to cultivate sunflowers, $0.1\overline{6}$ of the total land to cultivate maize, and $0.0\overline{5}$ of the total land to cultivate organic vegetables. The remaining land, which measures exactly $110$ hectares, is preserved as a wildlife reserve. What is the total area of the tract of land, in hectares?

A digital communications system transmits data packets of three specific sizes: $\frac{35}{18}$ MB, $\frac{7}{4}$ MB, and $\frac{49}{24}$ MB. To optimize the network buffer, the engineers must define a standardized base unit size. Every transmitted packet must be an exact multiple of this base unit. To maximize efficiency, what is the largest possible size for this base unit?

An agronomist is comparing the soil moisture retention rates of four different agricultural plots. The rates, measured in liters per cubic meter per day, are given below. Arrange the plots in ascending order of their moisture retention rates.

In a highly automated manufacturing plant, three different robotic assembly lines are synchronized by a central control system. Line A completes a specific micro-calibration cycle every $\frac{4}{15}$ of a minute. Line B completes its calibration cycle every $\frac{6}{25}$ of a minute, and Line C completes its cycle every $\frac{8}{35}$ of a minute. If all three lines complete a calibration cycle simultaneously at a given moment, what is the shortest time interval that must elapse before all three lines complete their calibration cycles together again?

A civil engineering team is installing three different types of sensor cables along a newly constructed bridge. The standard supplier rolls for these cables come in lengths of $\frac{55}{2}$ meters, $\frac{77}{4}$ meters, and $\frac{121}{5}$ meters. To ensure modular replacement without any waste, the team must cut all the rolls into smaller, equal-length segments. What is the maximum possible length, in meters, of each segment?

At a metropolitan central station, three express commuter trains depart simultaneously at 6:00 AM on Monday. The Green Line completes its round trip every $2 \frac{1}{4}$ hours, the Blue Line every $3 \frac{3}{8}$ hours, and the Red Line every $4 \frac{1}{2}$ hours. Assuming continuous operation without delays, how many hours will it take for all three trains to depart simultaneously from the central station again?

Arrange the following real numbers in ascending order (from smallest to largest):

Three quantities are given as $0.\overline{6}$, $\frac{12}{25}$, and $1.4$. What is the exact ratio of the Least Common Multiple (LCM) of these three quantities to their Highest Common Factor (HCF)?

A district officer allocates a development fund among four sectors: Health, Education, Infrastructure, and Agriculture. Health receives a fraction equal to $0.1\overline{6}$ of the total fund. Education receives $\frac{3}{8}$ of the remaining fund after the Health allocation. Infrastructure is directly allocated $0.4\overline{3}$ of the original total fund. The remaining amount is given to Agriculture. If the amount allocated to Infrastructure exceeds the amount allocated to Education by ₹ $87,000$, what is the total development fund in Rupees?

What is the Highest Common Factor (HCF) of the fractions $\frac{3}{4}$ and $\frac{9}{10}$?