Question

Convert units on the following unit prices. \(\$ 1.25\) per gram to dollars per kilogram.

Short answer

\$1250\ per\ kilogram

Step-by-step solution

Understand the Conversion Ratio

Recognize that there are 1000 grams in 1 kilogram. You will use this conversion ratio to scale up the price per gram to the price per kilogram.

Calculate Price per Kilogram

Since there are 1000 grams in a kilogram, multiply the given price per gram by 1000. The calculation is as follows: \(1.25 per gram times 1000 equals \)1250 per kilogram.

Key concepts

Measurement Units

Measurement units are the backbone of science, commerce, and daily life. They provide a standard way for us to quantify and communicate about quantities such as length, mass, and time.

For example, a gram is a unit of mass in the metric system used across the world for various purposes, from cooking to laboratory measurements. When we scale up from grams, we reach kilograms, which are likewise units of mass but represent a greater quantity. A kilogram consists of 1000 grams, making it a convenient measurement for larger quantities.

Understanding the appropriate use of measurement units and how they relate to each other is crucial. It ensures accuracy in calculations and helps to prevent errors in everyday transactions, such as purchasing goods that are priced by weight.

Mathematical Calculations

Mathematical calculations are the processes we use to manipulate numbers and equations to find answers. It's essential to approach these calculations with a systematic method to ensure precision and correctness.

Using the unit conversion exercise as our example, mathematical calculation involves multiplying the price per smaller unit (in this case, per gram) by the number of those smaller units in a larger unit (grams in a kilogram). It is a straightforward arithmetic operation: multiplication. However, even simple operations require attention to detail to ensure that the calculations are correct and the units are accurately converted.

Conversion Ratio

A conversion ratio is a factor used to convert one set of units to another, enabling us to compare or calculate things that are not initially expressed in the same units.

In our unit conversion exercise, the conversion ratio between grams and kilograms is 1000 grams per kilogram. When converting a price from per gram to per kilogram, you would multiply the price per gram by the conversion ratio (1000). Thus, using the conversion ratio in such mathematical calculations allows us to understand amounts and costs in different units and scales. Becoming comfortable with conversion ratios is crucial when working with different measurement systems or needing to reconcile different scales and units for comparison or computation.

It is beneficial to remember the most commonly used conversion ratios for quick and efficient problem-solving. For instance, knowing that there are 1000 grams in a kilogram, 12 inches in a foot, or 2.54 centimeters in an inch can save time and reduce potential errors in calculations involving these units.