Question

Perform each of the following conversions within the metric system: a. \(4.15 \mathrm{~cm}\) to \(\mathrm{m}\) b. \(1458.4 \mathrm{~g}\) to \(\mathrm{kg}\) c. \(18.9 \mathrm{~cm}\) to \(\mathrm{mm}\)

Short answer

a. 4.15 cm = 0.0415 m, b. 1458.4 g = 1.4584 kg, c. 18.9 cm = 189 mm

Step-by-step solution

Convert centimeters to meters

To convert centimeters to meters, divide the number of centimeters by 100, because there are 100 centimeters in a meter. For 4.15 cm, the calculation would be 4.15 cm ÷ 100.

Convert grams to kilograms

To convert grams to kilograms, divide the number of grams by 1000, because there are 1000 grams in a kilogram. For 1458.4 g, the calculation would be 1458.4 g ÷ 1000.

Convert centimeters to millimeters

To convert centimeters to millimeters, multiply the number of centimeters by 10, since there are 10 millimeters in a centimeter. For 18.9 cm, the calculation would be 18.9 cm × 10.

Key concepts

Understanding Centimeters to Meters

When it comes to conversion between units, understanding the relationship between those units is crucial. Let's delve into converting centimeters to meters. Centimeters and meters are both units of length in the metric system, which is used worldwide for scientific and standard measurements. The metric system is based on the number 10, making conversions straightforward.

To put it simply, there are 100 centimeters in 1 meter. This means that to convert from centimeters to meters, you would divide the number of centimeters by 100. The underlying principle is to move from a smaller unit (centimeter) to a larger unit (meter), and dividing by 100 effectively reduces the number because meters are larger than centimeters.

For example, to convert 4.15 centimeters to meters, you divide 4.15 by 100, which gives you 0.0415 meters. It's helpful to remember that 'centi' denotes one-hundredth. Thus, 4.15 'hundredths' of a meter equals 0.0415 meters. Understanding this conversion factor is essential for accuracy in measurements and can be critical in fields such as engineering, physics, and everyday life.

Grams to Kilograms: Simplifying Mass Conversions

Converting units of mass, such as grams to kilograms, is a vital skill in various industries, including culinary arts, science, and engineering. The metric system simplifies these conversions by using multiples of 10. In this case, since 'kilo' means a 'thousand', there are 1,000 grams in a kilogram.

To convert grams to kilograms, you take the number of grams and divide it by 1,000. This step down-scales the unit of mass from a smaller unit (gram) to a larger unit (kilogram). Dividing by 1,000 reduces the quantity to reflect the change in magnitude of the unit. Let's apply this to a real example. If you have 1458.4 grams, dividing by 1,000 yields 1.4584 kilograms. The division simplifies the expression of mass, making it easier to manage larger quantities.

Remembering this ratio is instrumental when dealing with measurements that require precision, such as dosing medication or conducting experiments where the mass is a critical factor.

Centimeters to Millimeters and the Precision in Measurement

Modifying units within the metric system doesn't get simpler than converting centimeters to millimeters. This conversion is frequently used in industries that require precise measurements, such as manufacturing and engineering. A centimeter, being a smaller measurement unit than a meter, can be further broken down into millimeters.

In essence, one centimeter is equivalent to 10 millimeters. To convert centimeters to millimeters, you multiply the number of centimeters by 10. This is because you are moving from a larger unit to a smaller one - millimeters are smaller than centimeters. The multiplication by 10 adjusts the number to correspond with the increase in magnitude of units. For example, converting 18.9 centimeters to millimeters involves multiplying by 10 to get 189 millimeters. It's this type of simple math that clears the way toward understanding and applying measurements in more practical situations.

This conversion is very useful for finer measurements where even a small misstep could lead to significant discrepancies in results. Thus, mastery of the conversion of centimeters to millimeters is as crucial as the measurement itself.