Fractions and Decimals

Four identical delivery vans have different amounts of fuel remaining in their tanks. Arrange the vehicles based on their remaining fuel fraction from the least amount to the greatest amount.

A civil supplies department procures three batches of edible oil weighing $0.\overline{6}$ metric tonnes, $1.\overline{3}$ metric tonnes, and $2.\overline{2}$ metric tonnes. The department intends to repackage the entire procured quantity into smaller, identical standardized containers. To minimize the number of containers used without mixing the batches, what should be the maximum capacity of each standardized container?

A jeweler is cutting equal-length pieces of gold wire from three different spools to make uniform necklace links without any wastage. The three spools contain gold wire of lengths $\frac{27}{2}$ cm, $\frac{45}{4}$ cm, and $\frac{63}{5}$ cm. What is the maximum possible length of each uniform gold wire piece that can be cut? (Provide your answer as a precise decimal)

A financial analyst is evaluating the long-term performance of four mutual funds. The average annualized yield rates of the funds are given below. Arrange the funds in descending order based on their yield rates (from highest to lowest).

A botanical research institute is preparing identical standardized nutrient doses for a plant growth experiment. They have three concentrated liquid nutrient solutions measuring $\frac{14}{3}$ liters, $\frac{35}{6}$ liters, and $\frac{21}{4}$ liters respectively. The researchers need to distribute these solutions into small testing vials such that every vial contains the exact same maximum possible volume of solution, without mixing the different types of nutrients, and leaving no solution behind in the original containers. What should be the volume capacity of each testing vial?

A civil engineer is evaluating the thickness of four different structural panels, measured in centimeters (cm). To meet safety standards, the panels must be stacked from the thinnest to the thickest. Arrange the following panel thicknesses in ascending order.

A highway construction company is contracted to pave a new road. In the first month, they complete exactly $0.\overline{3}$ of the total project length. In the second month, they pave $0.625$ of the *remaining* length. If there are exactly $21$ kilometers left to pave in the third month to finish the project, what is the total length of the highway in kilometers?

A specialized aerospace component is manufactured from a custom metal alloy weighing exactly $160$ kg. The alloy's composition by weight is $0.35$ aluminum and $\frac{5}{16}$ magnesium, with the remaining portion consisting entirely of titanium. What is the exact mass of titanium in this component?

Three automated drones patrol a large forest reserve and return to their base station for a rapid data sync at regular intervals. Drone A returns every $3.\overline{3}$ hours, Drone B returns every $2.5$ hours, and Drone C returns every $2.\overline{7}$ hours. If all three drones depart from the base station simultaneously, how many hours will it take for all three to meet at the base station again for a simultaneous data sync?

During a physical endurance test, four candidates completed different portions of a 10-kilometer cross-country course before a mandatory rest period. The fraction or decimal representing the portion of the course completed by each candidate is given below. Arrange the candidates in ascending order based on the portion of the course they completed (from least to most).

An agricultural research center is preparing experimental test plots. The facility has exactly $2 \frac{5}{8}$ kg, $2 \frac{11}{12}$ kg, and $3 \frac{1}{16}$ kg of three different premium organic soil additives. The lead researcher wants to distribute these additives into smaller, identical sample packets such that no material is left over from any of the three original quantities. To ensure efficiency, the packets must be as large as possible. What should be the exact weight capacity of each sample packet?

A civil contractor is tasked with upgrading a rural highway. In the first month, the crew successfully upgrades $0.275$ of the total highway length. During the second month, they upgrade $\frac{5}{12}$ of the remaining length. If the crew has exactly $10.15$ kilometers left to upgrade in the third month to complete the project, what is the total length of the highway in kilometers?

A specialized textile loom is weaving a highly detailed traditional tapestry. Different specialty threads are inserted at specific periodic intervals along the length of the fabric:
- Gold thread is inserted every $\frac{14}{15}$ of a millimeter.
- Silver thread is inserted every $\frac{21}{20}$ of a millimeter.
- Crimson thread is inserted every $\frac{35}{12}$ of a millimeter.

If all three threads are inserted simultaneously at the very beginning of the pattern, at what exact distance from the start will all three specialty threads be inserted at the exact same position again for the first time?

An aerospace engineering facility is calibrating a pressure sensor using four specialized metallic foils. To prevent calibration errors, a technician must stack these foils in strictly ascending order of their thickness (from thinnest to thickest).

The thicknesses of the four foils are:
- Foil P: $0.345$ mm
- Foil Q: $\frac{11}{32}$ mm
- Foil R: $0.\overline{34}$ mm
- Foil S: $\frac{7}{20}$ mm

Arrange the foils in the correct ascending order of their thickness.