Schooling · Class 7 · Mathematics · Another Peek Beyond the Point · Chapter on a page
CBSE Class 7 · Mathematics · NCERT Ganita Prakash-II
Another Peek Beyond the Point: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 26 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- A decimal number has two parts…
- Each place after the decimal point…
- Adding zeros at the end of the…
- To compare decimals, first compare…
- When adding or subtracting decimals…
- To multiply a decimal by 10, 100 or…
- To divide a decimal by 10, 100 or…
- Formulas and facts
- Place values after the point
- Comparing decimals
- Adding/subtracting decimals
- Multiplying by 10, 100, 1000
- Dividing by 10, 100, 1000
- Multiplying two decimals
- Dividing decimals
- Watch out for
- Thinking 4.12 is greater than 4.9…
- Forgetting to align decimal points…
- Moving the decimal point the wrong…
- Dropping the decimal point entirely…
- Writing 0.30 as smaller than 0.3
What this chapter is about
This chapter takes you deeper into the world of decimal numbers. You already know decimals from earlier classes. Now you will learn to work with them in more detail — comparing decimals, placing them on a number line, and doing all four operations (addition, subtraction, multiplication and division) with them.
Key ideas
- A decimal number has two parts separated by a decimal point: the whole number part (left of the point) and the decimal part (right of the point).
- Each place after the decimal point has a value: the first place is tenths (1/10), the second is hundredths (1/100), the third is thousandths (1/1000), and so on.
- Adding zeros at the end of the decimal part does not change the value: 3.5 = 3.50 = 3.500.
- To compare decimals, first compare the whole number parts. If they are equal, compare digit by digit after the point, moving left to right.
- When adding or subtracting decimals, line up the decimal points and fill empty places with zeros.
- To multiply a decimal by 10, 100 or 1000, move the decimal point to the right by 1, 2 or 3 places.
- To divide a decimal by 10, 100 or 1000, move the decimal point to the left by 1, 2 or 3 places.
- When multiplying two decimals, multiply as if they are whole numbers, then count the total decimal places in both numbers and put that many places in the answer.
Formulas and facts to remember
- Place values after the point: First place = tenths, second place = hundredths, third place = thousandths.
- Comparing decimals: Compare whole parts first; if equal, compare tenths, then hundredths, and so on.
- Adding/subtracting decimals: Align decimal points, add zeros if needed, then compute.
- Multiplying by 10, 100, 1000: Move the point right by 1, 2 or 3 places.
- Dividing by 10, 100, 1000: Move the point left by 1, 2 or 3 places.
- Multiplying two decimals: Total decimal places in the answer = sum of decimal places in the two numbers.
- Dividing decimals: Make the divisor a whole number by shifting points in both divisor and dividend equally.
Common mistakes
- Thinking 4.12 is greater than 4.9 because 12 > 9 → Compare place by place; 1 tenth is less than 9 tenths.
- Forgetting to align decimal points when adding, getting a wrong answer → Always line up the points first.
- Moving the decimal point the wrong way when multiplying or dividing by 10 → Multiplying makes the number bigger, so the point goes right; dividing makes it smaller, so the point goes left.
- Dropping the decimal point entirely after multiplication → Count total decimal places and place the point correctly.
- Writing 0.30 as smaller than 0.3 → They are equal; the trailing zero does not add value.
Quick revision
- Tenths, hundredths, thousandths are the first three places after the decimal point.
- To compare, go digit by digit from left to right after checking whole parts.
- Line up the decimal points before adding or subtracting.
- Multiplying by 10 shifts the point one place to the right.
- In decimal multiplication, add the decimal places of both numbers for the answer.
- Trailing zeros after the decimal point do not change a number's value.