Science Metric System Problems and Solutions Mr. Benedict

Rahmir Science Mr. Benedict

How many milligrams are in one decigram?

Identify locations of milligrams and decigrams.

Decigrams (dg) are larger than milligrams (mg), so you expect there to be many mg in one dg.

Dg is 10 times larger than a cg, and a cg is 10 times larger than a mg.

Since you are going from a larger unit to a smaller unit, multiply.

1 dg · 10 · 10 = 100 mg

Multiply: 1 · 10 · 10, to find the number of milligrams in one decigram.

Answer There are 100 milligrams (mg) in 1 decigram (dg).

Example Problem Convert 1 centimeter to kilometers.

Identify locations of kilometers and centimeters.

Kilometers (km) are larger than centimeters (cm), so you expect there to be less than one km in a cm.

Cm is 10 times smaller than a dm; a dm is 10 times smaller than a m, etc.

Since you are going from a smaller unit to a larger unit, divide.

1 cm ÷ 10 ÷ 10 ÷ 10 ÷ 10 ÷ 10 = 0.00001 km

Divide: 1 ÷ 10 ÷ 10 ÷ 10 ÷ 10 ÷ 10, to find the number of kilometers in one centimeter.

Answer 1 centimeter (cm) = 0.00001 kilometers (km).

Once you begin to understand the metric system, you can use a shortcut to convert among different metric units. The size of metric units increases tenfold as you go up the metric scale. The decimal system works the same way: a tenth is 10 times larger than a hundredth; a hundredth is 10 times larger than a thousandth, etc. By applying what you know about decimals to the metric system, converting among units is as simple as moving decimal points.

Here is the first problem from above: How many milligrams are in one decigram? You can recreate the order of the metric units as shown below:

This question asks you to start with 1 decigram and convert that to milligrams. As shown above, milligrams is two places to the right of decigrams. You can just move the decimal point two places to the right to convert decigrams to milligrams: .

The same method works when you are converting from a smaller to a larger unit, as in the problem: Convert 1 centimeter to kilometers.

Note that instead of moving to the right, you are now moving to the left—so the decimal point must do the same: .

How many milliliters are in 1 liter?

A) 0.001

B) 0.1

C) 100

D) 1,000