Days, Weeks, Months, and Years

Understanding time-unit conversions

When a problem asks you to convert between days, weeks, months, and years, the goal is to express the same amount of time in a different unit. First, identify the starting unit and the target unit. Then use the standard relationships between the units, keeping track of whether you need to multiply or divide.

Method

1. Write the known quantity with its unit.
2. Choose the conversion direction:
   • larger to smaller units: multiply
   • smaller to larger units: divide
3. Apply the conversion step by step if more than one unit change is needed.
4. Simplify the final answer and include the correct unit.

Useful check

Make sure the answer is reasonable. For example, a number of weeks should usually be smaller than the equivalent number of days, and a number of years should be smaller than the equivalent number of months. If you convert back, you should recover the original amount.

Example of the reasoning

If you are converting from days to weeks, divide by the number of days in a week. If you are converting from months to years, divide by the number of months in a year. If a problem combines several steps, convert one unit at a time and keep the units aligned carefully.

Final tip

Always look for the simplest exact form before finishing. If the result is a whole number, write it directly. If not, leave it in the simplest exact form allowed by the exercise.