This chapter extends the place value system below the units place to introduce decimals. To measure more precisely, a unit is split into ten one-tenths, each one-tenth into ten one-hundredths, and so on, so that \(1 = 10 \times \tfrac{1}{10}\) and \(\tfrac{1}{10} = 10 \times \tfrac{1}{100}\). A decimal point separates the whole-number part from the fractional part: \(70.5\) means \(7\times10 + 5\times\tfrac{1}{10}\), while \(7.05\) means \(7 + 5\times\tfrac{1}{100}\). You learn to read numbers like \(0.274\) as "zero point two seven four", to see that trailing zeros do not change a value \((0.2 = 0.20 = 0.200)\), and to locate and compare decimals on the number line by comparing digits place by place. The chapter connects decimals to everyday measurement — \(1\,\text{mm} = 0.1\,\text{cm}\), \(1\,\text{cm} = 0.01\,\text{m}\), \(1\,\text{g} = 0.001\,\text{kg}\), \(1\) paisa \(= \u20b90.01\) — and shows how to add and subtract decimals using the same column method as for whole numbers, plus a peek at the history of decimal notation.
Tenths, hundredths and thousandthsDecimal place value and notationLocating and comparing decimalsUnits of measurement (length, weight, money)Addition and subtraction of decimals
Key terms
Decimal point
The point "." that separates the whole-number part of a number from its fractional part.
Tenth
One of ten equal parts of a unit, written \(\dfrac{1}{10} = 0.1\).
Hundredth
One of a hundred equal parts of a unit, written \(\dfrac{1}{100} = 0.01\).
Thousandth
One of a thousand equal parts of a unit, written \(\dfrac{1}{1000} = 0.001\).
Decimal place value
The extension of the Indian place value system to tenths, hundredths, thousandths.
Equivalent decimals
Decimals with the same value although written differently, e.g. \(0.2 = 0.20 = 0.200\).
Extra questions & answers
Try one from this chapter
What does the decimal point separate in a number?
Flashcards & interactive practice
Practice quiz · A Peek Beyond the Point
Score on this chapter, climb the leaderboard, and get an AI diagnosis of your mistakes.
Double-checked questions Real exam pattern 1 free quiz every month, then ₹9 per quiz
#1
A Peek Beyond the Point
Start here
Maths 10 Qs · ~10 min
Instant score, answer review and weak-topic diagnosis
6.5/10avg score
8/10best
Data & insights
Trending in Class 7 this weekThe chapters students are reading most right now
