Decimals extend our number system to represent parts smaller than one. The decimal point separates the whole number part from the fractional part. Each place to the right of the decimal represents a smaller piece: tenths, hundredths, thousandths, and so on.

Decimals and fractions are two ways of expressing the same ideas. 0.5 equals 1/2, 0.25 equals 1/4, and 0.75 equals 3/4. Understanding both representations and being able to convert between them is an important skill for mathematical fluency.

Comparing decimals requires careful attention to place value. 0.5 is greater than 0.35 even though 35 is greater than 5. Looking at each decimal place from left to right helps determine which number is larger. Adding zeros after the last digit (0.5 = 0.50) can make comparisons clearer.

Decimal operations follow the same principles as whole number operations, with careful attention to the decimal point. When adding or subtracting, line up the decimal points. When multiplying, count the total decimal places in both factors to place the decimal in the product.