Carry out each of the following conversions: a. 25.5 m to km b. 36.3 km to m c. 487 kg to g d. 1.32 L to mL e. 55.9 dL to L f. 6251 L to cm
The Correct Answer and Explanation is:
Let’s solve each of the conversions step by step:
a. 25.5 meters to kilometers
To convert meters to kilometers, divide by 1,000.
25.5 m ÷ 1,000 = 0.0255 km
b. 36.3 kilometers to meters
To convert kilometers to meters, multiply by 1,000.
36.3 km × 1,000 = 36,300 m
c. 487 kilograms to grams
To convert kilograms to grams, multiply by 1,000.
487 kg × 1,000 = 487,000 g
d. 1.32 liters to milliliters
To convert liters to milliliters, multiply by 1,000.
1.32 L × 1,000 = 1,320 mL
e. 55.9 deciliters to liters
To convert deciliters to liters, divide by 10.
55.9 dL ÷ 10 = 5.59 L
f. 6251 liters to cubic centimeters (cm³)
Since 1 liter is equal to 1,000 cubic centimeters,
6251 L × 1,000 = 6,251,000 cm³
Explanation
Unit conversion is a fundamental skill in science and daily life. It involves changing a measurement from one unit to another without changing its actual quantity. Conversions within the metric system are straightforward because the system is based on powers of ten.
For instance, when converting from meters to kilometers, we note that there are 1,000 meters in a kilometer. Therefore, we divide the number of meters by 1,000 to get the value in kilometers. Conversely, to go from kilometers to meters, we multiply by 1,000.
The same logic applies to converting kilograms to grams. There are 1,000 grams in one kilogram, so multiplying the kilogram value by 1,000 gives the equivalent in grams.
For volume, converting liters to milliliters also uses a factor of 1,000 since there are 1,000 milliliters in a liter. However, when converting deciliters to liters, we use a different conversion factor. Since there are 10 deciliters in a liter, we divide by 10 to convert from dL to L.
Lastly, when converting liters to cubic centimeters, we rely on the fact that 1 liter equals 1,000 cubic centimeters. This is because one cubic centimeter is defined as the volume of a cube with 1 cm sides, and 1,000 of these fit into a liter. This conversion is particularly important in chemistry and medicine where liquid volumes often need to be converted to or from cm³.
Understanding these relationships ensures accuracy in scientific measurements and practical applications.
