Decimals

Lesson Objectives

Understand the concept of decimals and place values.
Convert between fractions and decimals.
Perform arithmetic operations with decimals.
Apply decimals in measurement and real-world problems.

Lesson Introduction

Decimals are numbers that have a whole part and a fractional part separated by a decimal point. They are used to represent parts of a whole, such as money, length, or weight.

For example, $3.5$ means 3 wholes and 5 tenths.

Lesson Content

Decimal Place Value

Each digit in a decimal has a place value based on its position. For example, in $4.237$ :

4 is in the units place
2 is in the tenths place
3 is in the hundredths place
7 is in the thousandths place

Converting Fractions to Decimals

To convert a fraction to a decimal, divide the numerator by the denominator.

Example: $\frac{3}{4} = 0.75$

Converting Decimals to Fractions

Write the decimal as a fraction with a power of 10 and simplify:

Example: $0.6 = \frac{6}{10} = \frac{3}{5}$

Comparing and Ordering Decimals

To compare decimals, align the numbers by their decimal points and compare digit by digit from left to right.

Arithmetic Operations with Decimals

Add/Subtract: Line up decimal points before adding or subtracting.
Multiply: Multiply normally, then count and place the decimal point.
Divide: Move decimal to make divisor whole, then divide normally.

Examples

Example: Convert $\frac{2}{5}$ to a decimal.

$2 \div 5 = 0.4$

Example: Convert $0.75$ to a fraction.

$0.75 = \frac{75}{100} = \frac{3}{4}$

Example: Add $3.14 + 2.6$

Line up decimals:
$3.14 + 2.60 = 5.74$

Example: Multiply $0.3 \times 0.2$

$3 \times 2 = 6$ → 2 decimal places: $0.06$

Example: Compare: Which is greater, $0.45$ or $0.405$ ?

Compare digits: 4 = 4, then 5 > 0 → $0.45 > 0.405$

Exercises

Write $0.25$ as a fraction in simplest form.
[WAEC] Convert $\frac{7}{8}$ to a decimal. (Past Question)
Add $2.35 + 1.45$
[JAMB] Multiply $0.6 \times 0.3$ (Past Question)
Which is greater: $0.7$ or $0.67$ ?
Convert $0.125$ to a fraction in simplest form.
[NECO] Subtract $3.6 - 1.85$ (Past Question)
Divide $4.8 \div 0.6$
[NABTEB] Express $\frac{9}{20}$ as a decimal. (Past Question)
Order the following: $0.45,\ 0.5,\ 0.405$

Conclusion/Recap

This lesson introduced decimals, showing how to convert, compare, and perform calculations with them. Decimals are essential for measurements, finance, and data, and mastery of them builds accuracy in real-life math use.