Home / United States / Math Classes / Formulas / Units of Weight Conversion Formulas : Metric

We describe all objects with their different properties such as shape, size, height, weight, capacity, and so on. To quantify these properties precisely, units of measurement are used. The measurement of such properties is denoted with respect to a predetermined value according to the system of units used. Here we will focus on one particular system of units known as the metric system. Units in the metric system include millimeters, meters, liters, kilograms, and so on. We will learn more about the different units of measurement of weight and their conversion from larger to smaller values, or from smaller units to larger ones....Read MoreRead Less

All objects are made up of matter and the measure of the amount of matter in an object is called ** mass**. The term mass in our daily life is commonly referred to as

To avoid confusion or unnecessary complications, we will look at the description of the units of mass, but will refer to them as units of weight. This is because we usually adopt a common way of speaking instead of being technical.

Those students who would like to be more technical and precise, we would like to clarify that an object having a mass of 1 kg on earth will have a weight of 9.8 Newton (N). Suppose you buy 1 kg of sugar from a shop, so 1 kg is the mass of the sugar but the weight of the sugar is 9.8 Newton (N), technically.

The formula in the case of units of weight are related to the interconversion of larger to smaller units and *vice-versa*.

**Metric unit of mass:**

- 1 Kilogram (Kg) = 1,000 grams (g
**)** - 1 gram (g) = 1,000 milligrams (mg)

To convert from a larger unit to a smaller unit, we need to multiply

1 Kilogram (Kg) = 1,000 grams (g**) = 1,000,000 mg**

** **

Conversely, to convert from a smaller unit to a larger unit we need to divide. Therefore,

1 milligram (mg) = \(\frac{1}{1000}\) gram = \(\frac{1}{1000000}\) Kilogram

**Example 1: **Convert 5 kilograms to grams.

**Solution: **

To convert from a larger unit to a smaller unit, we need to multiply.

There are 1000 grams in 1 kilogram.

Therefore, 5 kilograms will have,

5 \(\times\) 1,000 = 5,000 grams

So there are 5,000 grams in 5 kilograms.

**Example 2:** Convert 12 kilograms to milligrams.

**Solution: **

To convert from a larger unit to a smaller unit, we need to multiply.

There are 1000 grams in 1 kilogram

Therefore, 12 kilograms will have

12 \(\times\) 1,000 = 12,000 grams

So there are 12,000 grams in 12 kilograms

Now, there are 1000 milligrams in 1 gram

Therefore 12 kilograms will have,

12,000 \(\times\) 1,000 = 12,000,000 milligrams

So, there are 12,000,000 milligrams in 12,000 grams

Hence, there are 12,000,000 milligrams in 12 kilograms.

**Example 3:** Fill in the blanks.

(a) 5300 g = ——– kg

(b) 9600 mg = ——– g

(c) 2700 mg = ——- kg

**Solution: **

(a) To convert from a smaller unit to a larger unit we need to divide. Therefore, 5300 g is:

\(\frac{5300g}{1000}=5.3kg\)

(b) To convert from a smaller unit to a larger unit we need to divide. Therefore, 9600 mg is:

\(\frac{9600mg}{1000}=9.6g\)

(c) To convert from a smaller unit to a larger unit we need to divide. Therefore, 2700 mg is:

\(\frac{2700mg}{1000000}=0.0027kg\)

**Example 4: **Mary has bought grocery items. She bought 3 packets of sugar of 2 kg each, 2 packets of salt of 500 grams each, 10 tablets of vitamin D of 350 milligrams each. Calculate the total weight of items in kg.

**Solution: **

Weight of 1 packet of sugar = 2 kg

Weight of 3 packets of sugar = 3 \(\times\) 2 = 6 kg

Weight of 1 packet of salt = 500 g

Weight of 2 packets of salt = 2 \(\times\) 500 = 1000g

Now, to convert from a smaller unit to a larger unit we need to divide. Therefore, 1000g is

\(\frac{1000g}{1000}=1.0kg\)

Weight of 1 tablet of vitamin D = 350 mg

Weight of 10 tablet of vitamin D = 10 \(\times\) 350 = 3500 mg

Now, to convert from a smaller unit to a larger unit we need to divide. Therefore, 3500 mg in g is

\(\frac{3500g}{1000}=3.5g\)

Now, 3.5 g in kg is

\(\frac{3.5kg}{1000}=0.0035kg\)

Therefore, the total weight of items = 6 + 1.0 + 0.0035

= 7.0035 kg

Frequently Asked Questions

The units of measurement in the metric system are called ** metric units** or SI units (International System of Units). The units include meter, kilogram, gram, milligrams, and so on.

The metric units of capacity include liters (L) and milliliters (mL). 1 liter is 1000 milliliters. Other units can be derived as well, such as kiloliter, dekaliter, hectoliter, and so on.

Mass and weight are not the same thing but for our simplicity, we consider them the same thing. Whenever we need to quantify the quantity of matter this assumption comes in handy. The reason behind it is that we always measure the weight of the object but not the mass. Also, we can not measure the mass of an object directly. Technically the standard unit of weight is “Newton” and the standard unit of mass is “kg”. Since the mass and weight are proportional to each other on earth so we commonly use mass and weight interchangeably.

**For Example: **If you weigh yourself on a weighing machine and its reading is 60. **Technically** your weight is 60 newton but you might **commonly **say that your weight is 60 kg or your mass is 60 kg.