Decimals - Introduction to Decimals

A decimal number consists of two parts: the whole number part and the fractional part, separated by a dot called the decimal point. Imagine a number line where the space between 0 and 1 is divided into 10 equal segments; each segment represents a tenth or $0.1$.

In the Decimal Place Value system, digits to the left of the decimal point represent whole numbers (Ones, Tens, Hundreds), while digits to the right represent parts of a whole (Tenths, Hundredths, Thousandths). Visually, a grid of 100 small squares can represent one whole, where a single column of 10 squares represents one tenth ($0.1$) and a single small square represents one hundredth ($0.01$).

Reading and Writing Decimals: We read the whole number part as usual, the decimal point as 'point', and the decimal part by naming each digit individually. For example, $23.45$ is read as 'twenty-three point four five'.

Equivalent Decimals are decimals that have the same value. Adding any number of zeros to the right end of a decimal does not change its value. For instance, $0.5$, $0.50$, and $0.500$ are all equal, much like how $\frac{5}{10}$ is equal to $\frac{50}{100}$.

Like and Unlike Decimals: Like decimals have the same number of decimal places (e.g., $1.25$ and $3.78$ both have two decimal places). Unlike decimals have a different number of decimal places (e.g., $4.5$ and $4.52$). Unlike decimals can be converted into like decimals by adding zeros at the end.

Conversion of Fractions to Decimals: A fraction with a denominator of 10, 100, or 1000 can be easily written as a decimal. The number of zeros in the denominator tells us how many digits should be to the right of the decimal point. For example, $\frac{7}{10} = 0.7$ and $\frac{9}{100} = 0.09$.

Expanded Form of Decimals: Decimals can be written as the sum of the place values of each digit. For example, $5.67$ can be written as $5 + \frac{6}{10} + \frac{7}{100}$ or $5 + 0.6 + 0.07$.