Question

Perform the following conversions. (a) $1.55\mathrm{kg}=$________$\mathrm{g}$ (b) $642\mathrm{g}=$________$\mathrm{kg}$ (c) $2896\mathrm{mm}=$________$\mathrm{cm}$ (d) $0.086\mathrm{cm}=$________$\mathrm{mm}$

Short answer

(a) 1550 grams, (b) 0.642 kilograms, (c) 289.6 centimeters, (d) 0.86 millimeters

Step-by-step solution

Convert Kilograms to grams

To convert kilograms (kg) to grams (g) multiply by the conversion factor of 1000 (1kg = 1000g). So, $1.55\mathrm{kg}$ equals $1.55\times 1000=1550\mathrm{g}$

Convert grams to Kilograms

To convert grams (g) to kilograms (kg) divide by the conversion factor of 1000 (1kg = 1000g). So, $642\mathrm{g}$ equals $642÷1000=0.642\mathrm{kg}$

Convert millimeters to centimeters

To convert millimeters (mm) to centimeters (cm) divide by the conversion factor of 10 (1cm = 10mm). So, $2896\mathrm{mm}$ equals $2896÷10=289.6\mathrm{cm}$

Convert centimeters to millimeters

To convert centimeters (cm) to millimeters (mm) multiply by the conversion factor of 10 (1cm = 10mm). So, $0.086\mathrm{cm}$ equals $0.086\times 10=0.86\mathrm{mm}$

Key concepts

Metric System

The metric system is a universally adopted method of measurement that's founded on a simple decimal system. Its beauty lies in its ease of use, as it is based on units of ten. This makes conversions within the metric system straightforward and consistent.
When dealing with the metric system, you'll encounter units such as grams for mass and meters for length. These units are easily convertible because they scale by powers of ten. For instance, converting from one unit to another—say from kilograms to grams—only involves shifting the decimal point, which simplifies the process significantly.
Here's why the metric system is brilliant for scientific measures:

• It's a decimal-based system, making calculations easier.
• Most of the world uses it, promoting global standardization.
• Conversions within the system maintain simplicity and accuracy.

Overall, the metric system removes much of the complexity found in other measurement systems.

Mass Conversion

Mass conversion within the metric system is particularly straightforward, thanks to its decimal nature. Mass is typically measured in kilograms or grams, and converting between these units is a matter of shifting the decimal point.
To convert kilograms (kg) to grams (g), you multiply by 1000. This is because there are 1000 grams in a kilogram. For example, converting 1.55 kilograms to grams involves multiplying by the conversion factor 1000, resulting in 1550 grams: $$1.55\times 1000=1550g$$Conversely, converting from grams to kilograms involves dividing by 1000, due to the same conversion factor. For instance, changing 642 grams into kilograms would look like:$$642÷1000=0.642kg$$These straightforward calculations highlight the ease of converting mass within the metric system, allowing for quick and precise transitions between various scales of measurement.

Length Conversion

Length conversion in the metric system follows the same easy principles as mass conversion, using straightforward multiplication or division by factors of 10. Meters are often subdivided into centimeters and millimeters, making it simple to move between these units.
When converting millimeters (mm) to centimeters (cm), division by 10 is necessary, since there are 10 millimeters in a centimeter. For example, converting 2896 millimeters to centimeters involves this calculation:
$$2896÷10=289.6cm$$On the flip side, converting from centimeters to millimeters requires multiplication by 10. So, if you are converting 0.086 centimeters to millimeters, it would look like this:
$$0.086\times 10=0.86mm$$These conversions remind us how flexible and consistent the metric system is, streamlining complex measurements into simple arithmetic tasks which can be handled swiftly. This uniformity is one of the key benefits of using the metric system in scientific and general applications worldwide.