Let's Learn About Mass! (g/kg)

Hello, young mathematicians! Have you ever tried to pick up your school bag and thought, "Wow, this is heavy!"? Or have you ever held a tiny feather and thought about how light it is? In mathematics and science, the amount of matter in an object is called its mass (often called weight in daily life). In this chapter, we are going to become experts at measuring, converting, and solving problems with mass!


Section 1: Standard Units of Mass

To measure mass accurately, we use standard units. The two most important units are the gram (g) and the kilogram (kg).

The Gram (g) - For Light Objects

A gram is very light. Think about the mass of a single paperclip. That is about 1 gram!

We use grams to measure lighter objects:

  • A single piece of paper
  • A small coin
  • A strawberry

The short symbol for gram is g. So, 10 grams is written as 10 g.

The Kilogram (kg) - For Heavy Objects

A kilogram is much heavier than a gram. A big bag of sugar or a 1-litre bottle of water has a mass of about 1 kilogram.

We use kilograms to measure heavier objects:

  • A large watermelon
  • Your school bag packed with books
  • A bicycle

The short symbol for kilogram is kg. So, 5 kilograms is written as 5 kg.

The Golden Conversion Rule

Here is the essential rule connecting kilograms and grams:

1 kilogram is equal to 1000 grams.

\(1 \text{ kg} = 1000 \text{ g}\)


Section 2: Reading Weighing Scales

We use weighing scales to measure mass. Dial scales have tick marks or gradations. Before reading a scale, always find out what each tick mark stands for!

Steps to read a scale:

1. Look at the numbers on the scale (e.g., from 0 to 100 g, or 0 to 1 kg).
2. Count the number of smaller spaces between the numbers.
3. Determine the value of each interval (such as 20 g, 50 g, 100 g, or 200 g).
4. Read where the pointer points.

Example: If there are 5 equal spaces between 0 and 100 g, each space represents \(100 \text{ g} \div 5 = 20 \text{ g}\). If the needle is 3 marks past 0, the mass is \(3 \times 20 \text{ g} = 60 \text{ g}\).


Section 3: Converting Between Units of Mass

We often write mass in compound units (both kg and g) or in single units (grams only).

1. Converting from kg and g to g

To convert compound units like 2 kg 150 g into pure grams:

Step 1: Convert the kilograms to grams: \(2 \text{ kg} = 2 \times 1000 \text{ g} = 2000 \text{ g}\).

Step 2: Add the remaining grams: \(2000 \text{ g} + 150 \text{ g} = 2150 \text{ g}\).

Common Mistake Alert!

When you see 3 kg 50 g, do not write 350 g! Remember that 3 kg = 3000 g, so the total is \(3000 \text{ g} + 50 \text{ g} = 3050 \text{ g}\).

2. Converting from g to kg and g

To convert single units like 3450 g back into kilograms and grams:

Step 1: Split the number into thousands and remaining grams: \(3450 \text{ g} = 3000 \text{ g} + 450 \text{ g}\).

Step 2: Convert the thousands into kilograms: \(3000 \text{ g} = 3 \text{ kg}\).

So, \(3450 \text{ g} = 3 \text{ kg } 450 \text{ g}\).


Section 4: Solving Word Problems on Mass

We can add, subtract, multiply, and divide mass when solving real-world word problems.

Example 1: Addition of Mass

A baker bought 2 kg 400 g of white flour and 1 kg 750 g of wholemeal flour. What was the total mass of flour bought?

Step 1: Add the kilograms: \(2 \text{ kg} + 1 \text{ kg} = 3 \text{ kg}\).
Step 2: Add the grams: \(400 \text{ g} + 750 \text{ g} = 1150 \text{ g}\).
Step 3: Regroup the grams: \(1150 \text{ g} = 1 \text{ kg } 150 \text{ g}\).
Step 4: Combine: \(3 \text{ kg} + 1 \text{ kg } 150 \text{ g} = 4 \text{ kg } 150 \text{ g}\).

The total mass of flour bought was 4 kg 150 g.

Example 2: Subtraction of Mass

A basket of apples has a mass of 3 kg 200 g. The empty basket has a mass of 650 g. What is the mass of the apples?

Step 1: Convert total mass into grams: \(3 \text{ kg } 200 \text{ g} = 3200 \text{ g}\).
Step 2: Subtract the basket mass: \(3200 \text{ g} - 650 \text{ g} = 2550 \text{ g}\).
Step 3: Convert back to kg and g: \(2550 \text{ g} = 2 \text{ kg } 550 \text{ g}\).

The mass of the apples is 2 kg 550 g.


Chapter Review: Quick Facts!

  • Mass tells us how heavy an object is.
  • We use grams (g) for light objects and kilograms (kg) for heavy objects.
  • The golden rule is: \(1 \text{ kg} = 1000 \text{ g}\).
  • To read dial scales accurately, check the value of each gradation interval first.
  • We can convert between compound units (\(2 \text{ kg } 150 \text{ g}\)) and single units (\(2150 \text{ g}\)).