Weight

Have you ever pondered the reasons behind why certain objects seem to have a significant heavy weight such as a car while others appear to be quite light weight such as a towel?

This chapter aims to introduce and explore the concept of weight.

What is Weight?

Weight is a measure of how heavy something is due to the pull of gravity.

Heavy and lightweight are terms used to describe the relative weight of objects. Here is a simple explanation of each:

Heavyweight: It is used to describe objects that have a significant amount of weight. These objects often feel burdensome due to their considerable weight.

For example, A basket of apples feels heavy because of its weight.

Lightweight: It is used to describe objects that have very little weight. These objects often feel easy to lift or carry due to their low weight.

For example, a balloon feels light because it has very little weight compared to the air around it.

These terms are relative and can vary depending on the context and what you are comparing the objects to.

Measuring Weights

Weighing balance and weighing scales are used to measure the weight which is displayed as follows:

Units of Weight

The weight can be measured in milligrams, decigrams, grams, kilograms, decagrams, quintals, pounds, ounces, etc.

Metric Units of Weight

Metric units for measuring weight provide a standardized way to quantify the heaviness or lightness of objects.

The primary metric units of weight are as follows:

1. Milligram (mg)
2. Centigram (cg)
3. Decigram (dg)
4. Gram (g)
5. Decagram (dag)
6. Hectogram (hg)
7. Kilogram (kg)

These metric units make it convenient to express weight in a consistent and easily understandable manner.

Non Metric Units of Weight

Non-metric units of weight are not based on grams as a standard of measurement.

The primary non-metric units of weight are as follows:

1. Pound (lb)
2. Ounce (oz)

Conversions of Units of Weight

When converting from a smaller unit of weight to a larger one, you can achieve this by multiplying the numerical value associated with the smaller unit by 10.

Conversely, when converting from a larger unit of weight to a smaller one, you can achieve this by dividing the numerical value associated with the larger unit by 10.

The conversion process of metric units can be visually represented as follows:

The conversion process of non-metric units can be visually represented as follows:

Here are some common units of weight and their conversion methods:

Kilograms (kg) to Grams (g):

→ 1 kg = 1000 g
→ To convert from kilograms to grams, multiply by 1000.
→ Example: 2.5 kg × 1000 = 2500 g

Grams (g) to Kilograms (kg):

→ 1 g =  1/1000 kg =  0.001 kg
→ To convert grams to kilograms, divide by 1000 or multiply by 0.001.
→ Example: 45000 g ÷ 1000 = 45 kg

Or

45000 g × 0.001 = 45000 g × (1/1000) = 45 kg

Kilograms (kg) to Hectograms (hg):

→ 1 kg =  10 hg
→ To convert from kilograms to hectograms, multiply by 10.
→ Example: 1.03 kg × 10 = 10.3 hg

Hectograms (hg) to Kilograms (kg):

→ 1 hg =  1/10 kg =  0.1 kg
→ To convert hectograms to kilograms, divide by 10 or multiply by 0.1.
→ Example: 130 hg ÷ 10 = 13 kg

Or

130 hg × 0.1 = 130 hg × (1/10) = 13 kg

Grams (g) to Milligrams (mg):

→ 1 g =  1000 mg
→ To convert grams to milligrams, multiply by 1000.
→ Example: 1.7 g × 1000 = 1700 mg

Milligrams (mg) to Grams (g):

→ 1 mg =  1/1000 g = 0.001
→ To convert milligrams to grams, divide by 1000 or multiply by 0.001.
→ Example: 82000 mg ÷ 1000 = 82 g.

Or

82000 mg × 0.001 = 82000 mg × (1/1000) = 82 g

Pounds (lbs) to Ounces (oz):

→ 1 pound (lb) =  16 ounces (oz)
→ To convert pounds to ounces, multiply by 16.
→ Example: 0.5 lb × 16 = 8 oz

Ounces (oz) to Pounds (g):

→ 1 ounce (oz) =  1/16 lb
→ To convert ounces to pounds, divide by 16.
→ Example: 1120 ounces ÷ 16 = 70 lbs

These conversions allow for easy transitions between different units of weight measurement.

Example 1: The fruit seller puts a watermelon and a jackfruit on the weighing machine. The machine shows an overall mass of 13 kg 900 g. What is the weight of the watermelon if the weight of the jackfruit is 7.2 kg 475 g?

a) 6 kg 025 g
b) 6 kg 125 g
c) 6 kg 225 g
d) 6 kg 325 g

Answer: c) 6 kg 225 g

Explanation: Total weight of watermelon and a jackfruit = 13 kg 900 g
                                                                                    = 13 kg + 900 g
                                                                                     = (13 × 1000) g + 900 g
                                                                                      = 13000 g + 900 g
                                                                                       = 13900 g  

Weight of the jackfruit = 7.2 kg 475 g
                                  = 7.2 kg + 475 g
                                   = (7.2 × 1000) g + 475 g
                                    = 7200 g + 475 g
                                     = 7675 g 

Weight of the watermelon = (13900 − 7675) g
                                       = 6225 g
                                        = 6000 g + 225 g
                                         = 6 kg + 225 g
                                          = 6 kg 225 g

Example 2: Mark went to the market and bought 65 pounds of rice. While returning home due to a hole in the bag, some rice was scattered out through the hole and 34 pounds 11 ounces of rice remained. What is the weight of a scattered quantity of rice in ounces?

a) 445 ounces
b) 485 ounces
c) 545 ounces
d) 585 ounces

Answer: b) 485 ounces

Explanation: Total weight of rice = 65 pounds
                                                    = 65 × 16 ounces
                                                    = 1040 ounces

Weight of rice that remained in the bag = 34 pounds 11 ounces
                                                           = 34 pounds + 11 ounces
                                                             = 34 × 16 ounces + 11 ounces
                                                               = 544 ounces + 11 ounces
                                                                 = 555 ounces 

Weight of a scattered quantity of rice = 1040 ounces − 555 ounces
                                                       = 485 ounces