Question

Convert units on the following time rates. 953 births per year to births per week.

Short answer

953 births per year is approximately 18.327 births per week.

Step-by-step solution

Understand the Conversion Factors

There are 52 weeks in a year. Therefore, to find the number of births per week, you need to divide the yearly rate by 52.

Perform the Division

Divide the total number of births per year by the number of weeks in a year to find the rate of births per week. So, the calculation would be 953 births per year / 52 weeks per year.

Calculate and Simplify

After performing the division, you will get the number of births per week. It may not be a whole number, and you may express it to a reasonable number of decimal places if needed.

Key concepts

Conversion Factors

When converting quantities from one unit to another, like turning annual data into weekly figures, conversion factors play a crucial role. They are the bridge that connects different units of measurement. For instance, if you know there are 365 days in a year, that piece of information becomes a conversion factor when you need to find out how many days are in a span of several years.

Similarly, recognizing that one year consists of 52 weeks provides us with the conversion factor needed to translate a yearly rate into a weekly rate. The key to using conversion factors effectively is to determine the relationship between the units involved. Here’s an easy-to-remember tip: To convert a larger unit to a smaller unit, you divide, and to go from smaller to larger, you multiply. Therefore, if you have a quantity given per year (a larger unit of time) and you need to know the equivalent per week (a smaller unit), you divide it by the number of weeks in a year—hence the conversion factor of 52.

Rate Conversions

Rate conversions are all about changing the unit of a rate without altering the rate itself. In our case, we're changing the frequency of births from per year to per week. While it might seem daunting at first, understanding that a rate, by definition, is a kind of ratio can simplify things. It represents how much of something occurs within a certain quantity of something else - in this case, time.

To perform a rate conversion, you maintain the proportion of the quantity measured against its unit of time. The year-to-week conversion entails dividing the yearly figure by the conversion factor, which is the number of weeks in a year. To ensure accuracy, always cross-check the time units you are converting between; this will help you to decide whether to multiply or divide. Any rate conversion boils down to manipulating the rate in a way that respects the initial ratio; keeping the 'per' relationship constant is critical.

Mathematical Division

Mathematical division is an essential operation when it comes to converting rates and units. It’s how you scale down or up a quantity to fit another set of units. The division allows us to spread a quantity evenly across multiple units. Think of it as slicing a cake: if you want to know how many pieces you can get from one cake, you divide the size of the cake by the size of each piece.

In our example, the 'cake' is the number of births per year, 953. The 'pieces' are the weeks in a year—52 in total. To find out how many 'slices' or births we get per week, we distribute the yearly total over the weeks by dividing. When performing division, especially with rates, it’s also important to consider significant figures and rounding. Since rates often deal with real-world measurements, like births, we sometimes round to a reasonable degree of accuracy, allowing the results to be more practical and relatable.