Decimals - Comparing Decimals

Structure of Decimals: A decimal number consists of a whole number part and a fractional part, separated by a decimal point. Imagine the decimal point as a central divider: values to the left increase by powers of ten (ones, tens, hundreds), while values to the right decrease by powers of ten (tenths, hundredths, thousandths).

The Place Value Chart: To compare decimals effectively, understand the position of each digit. The first digit to the right of the decimal point is the tenths place, the second is the hundredths place, and the third is the thousandths place. Visualizing this, a tenth can be seen as one vertical strip in a square divided into ten equal strips, whereas a hundredth is one tiny square in a grid of 100 small squares.

Like and Unlike Decimals: Decimals having the same number of decimal places are called like decimals (e.g., $0.54$ and $0.82$). Decimals with different numbers of decimal places are unlike decimals (e.g., $0.1$ and $0.123$).

Annexing Zeros: You can add any number of zeros to the right of a decimal number without changing its value. For example, $0.5 = 0.50 = 0.500$. Visually, $0.5$ (5 out of 10 parts) occupies the same space as $0.50$ (50 out of 100 parts) on a hundred-square grid.

Order of Comparison: Always compare decimals starting from the leftmost digits. First, compare the whole number parts. If they are different, the number with the larger whole number is greater. If they are equal, move to the decimal part and compare the tenths digits, then hundredths, and so on.

The Number Line: Decimals can be visualized on a horizontal number line. A decimal point located to the right of another decimal point on the line always represents a larger value. For instance, $0.8$ is placed further to the right than $0.2$, confirming that $0.8 > 0.2$.