Whole Numbers and Decimals ; Multiples and Factors

Here is a balanced class note on Whole Numbers and Decimals for JSS 2 students.

MATHEMATICS: Whole Numbers and Decimals

Welcome, JSS 2 students! Today, we will explore the fascinating world of numbers, specifically focusing on Whole Numbers and Decimals. Understanding these is crucial because they are the building blocks for most of the calculations you do every day, from counting items to dealing with money.

Core Concepts

1. Whole Numbers

Whole numbers are the basic counting numbers, including zero. They do not have any fractional or decimal parts. We use them to count complete items.

Definition: The set of numbers {0, 1, 2, 3, 4, 5, ...} extending infinitely.
Examples: 0, 7, 25, 100, 2024.
Place Value: Whole numbers have place values like Units (Ones), Tens, Hundreds, Thousands, and so on.
- For example, in the number 5,372:
  - 5 is in the Thousands place (value: 5 x 1000 = 5000)
  - 3 is in the Hundreds place (value: 3 x 100 = 300)
  - 7 is in the Tens place (value: 7 x 10 = 70)
  - 2 is in the Units (Ones) place (value: 2 x 1 = 2)

Image: A number line illustrating whole numbers from 0 to 10.

2. Decimals

Decimals are numbers that represent parts of a whole. They use a decimal point (.) to separate the whole number part from the fractional part. Decimals are closely related to fractions with denominators of 10, 100, 1000, etc.

Definition: A number that contains a decimal point, indicating a value that is not a whole number.
Examples: 0.5, 3.25, 12.001.
Connection to Fractions:
- 0.5 means 5 tenths, which is $\frac{5}{10}$ .
- 0.25 means 25 hundredths, which is $\frac{25}{100}$ .
- 0.001 means 1 thousandth, which is $\frac{1}{1000}$ .
Place Value: To the right of the decimal point, the place values are Tenths, Hundredths, Thousandths, and so on.

Image: A place value chart showing both whole number places and decimal places.

*   For example, in the number **4.836**:
    *   **4** is in the Units place (whole number part)
    *   **8** is in the Tenths place (value: 8 x $\frac{1}{10}$ = 0.8)
    *   **3** is in the Hundredths place (value: 3 x $\frac{1}{100}$ = 0.03)
    *   **6** is in the Thousandths place (value: 6 x $\frac{1}{1000}$ = 0.006)

Reading Decimals: We read the whole number part first, then say "point," and then read each digit after the decimal point separately.
- 3.14 is read as "three point one four."
- 12.056 is read as "twelve point zero five six."

Image: A grid showing 7 out of 10 squares shaded, representing 0.7 or 7 tenths.

3. Comparing Whole Numbers and Decimals

To compare numbers (decide which is larger or smaller), follow these steps:

Compare the whole number parts first:
- If the whole number parts are different, the number with the larger whole number part is the greater number.
  - Example: 15.7 is greater than 12.9 because 15 > 12.
If the whole number parts are the same, compare the digits after the decimal point, starting from the tenths place:
- Compare the tenths digits. The number with the larger tenths digit is greater.
  - Example: 5.82 is greater than 5.69 because 8 tenths > 6 tenths.
- If the tenths digits are the same, move to the hundredths digits, and so on.
  - Example: 3.45 is greater than 3.42 because the hundredths digit 5 > 2.

Real-World Example

When you go shopping, prices like ₦150.50 for a snack or ₦1,200.75 for a book are common. These are decimals because they represent naira and kobo, where kobo are parts of a naira. For instance, ₦150.50 means 150 naira and 50 kobo (which is 50 hundredths of a naira).

Nigerian Naira notes and coins Image: Various currency notes and coins, often involving decimal values.

Practice and Reflection

Consider the numbers 7.05, 7.5, and 7.005. Can you arrange them from the smallest to the largest? Think about their place values, especially the tenths, hundredths, and thousandths, to make your decision. For home practice, look at speed limits on road signs (whole numbers) or fuel prices at a petrol station (decimals) and identify their types and place values.