Decimals extend the place value system to represent quantities less than one. Just as moving left multiplies by 10, moving right of the ones place divides by 10: the tenths place is 1/10, the hundredths place is 1/100. The decimal point separates the whole-number part from the fractional part. So 3.47 means 3 ones + 4 tenths + 7 hundredths. Decimals are fractions written in place-value notation -- 0.25 is simply 25/100 or 1/4. Students encounter decimals primarily through money (dollars and cents) and measurement.
Start with money: $0.50 is 50 cents, half a dollar. Use base-ten blocks where the flat represents 1 whole, the rod represents 1 tenth, and the small cube represents 1 hundredth. Practice reading decimals aloud correctly ("three and forty-seven hundredths" not "three point four seven"), as proper reading reinforces place-value understanding.
You already understand place value for whole numbers: each position in a number is worth ten times more than the position to its right. Ones, tens, hundreds, thousands — each step left multiplies by 10. The decimal point simply extends that pattern in the other direction. Each step right of the decimal point *divides* by 10: tenths (1/10), hundredths (1/100), thousandths (1/1000), and so on. The system is symmetric around the ones place. There is nothing new to memorize — the same base-ten logic you already know keeps on going past the point.
This means decimals are fractions in disguise — and you already know fractions too. The number 0.3 is not some mysterious new object; it is 3/10, three tenths. The number 0.47 is 47/100, forty-seven hundredths. Reading a decimal correctly forces you to say the denominator: "three tenths," "forty-seven hundredths." This is not just formality — it is exactly why 0.47 is *less* than 0.6. Written as fractions: 47/100 vs 6/10 = 60/100. Now it is obvious that 47/100 < 60/100. Students who read "point six" and "point forty-seven" as bare digits get confused; students who read "six tenths" and "forty-seven hundredths" almost never do.
Money gives you the most familiar example. You have been reading dollars and cents for years. $3.47 means 3 whole dollars, 4 dimes (tenths of a dollar), and 7 pennies (hundredths of a dollar). You already knew that 47 cents is less than 50 cents, which is half a dollar — you were reasoning about decimal place value without realizing it. Now you are just learning the formal notation that describes what you intuitively understand about coins.
The deepest idea here is that decimals and fractions are not two different kinds of numbers — they are two different notations for the same quantities. Every terminating decimal can be written as a fraction with a power-of-ten denominator, and vice versa. 0.25 = 25/100 = 1/4. This connection will be central when you start comparing, adding, and multiplying decimals. When in doubt about whether a decimal relationship makes sense, convert to a fraction and check your intuition against what you already know.