Chapter 3: A Peek Beyond the Point

What lies beyond the decimal point? Smaller and smaller pieces: tenths, hundredths, thousandths. The decimal point is a tiny dot, but it opens up a vast world where numbers become precise , useful for measuring height, weight, time, money, and almost anything in science.

You already know money: $\rupee 12.75$ means $12$ rupees and $75$ paise, which is $\frac{75}{100}$ of a rupee. The same idea extends everywhere. The number $3.142$ means three wholes, $1$ tenth, $4$ hundredths, and $2$ thousandths.

In this chapter, you will learn how to read a decimal number, write it in expanded form, compare two decimals digit by digit, and finally add or subtract them with care. The key habit: line up the decimal points when stacking numbers.

You will also see decimals as fractions (so $0.5 = \tfrac{1}{2}$ and $0.25 = \tfrac{1}{4}$), and back. This two-way street between fractions and decimals is one of the most useful skills you can pick up at this age.

What's inside

1. Decimal place value , meaning of digits after the point.
2. Reading and writing decimals , connecting decimals and fractions.
3. Comparing and ordering decimals , digit-by-digit rule.
4. Adding and subtracting decimals , lining up the point.
5. Decimals in real life , money, measurement, time.

Key results

Place-value identity for a number like $4.328$: $4.328 = 4 + \frac{3}{10} + \frac{2}{100} + \frac{8}{1000}.$

How to read this chapter

Take a ruler and look at the $1$-mm marks: each is a tenth of a centimetre. Whenever a decimal appears in a problem, sketch it on a number line first. The point you mark gives you a quick intuition for how big or small the number is.