Revision Notes for Class 7 Maths Chapter 12: Another Peek Beyond the Point

Quick revision notes summarizing all key concepts from Class 7 Maths Chapter 12 “Another Peek Beyond the Point”. These Class 7 Mathematics Chapter 12 notes are ideal for quick revision just before exams.

Last Updated: September 23, 2026

• Decimal place value: digits after the decimal point represent tenths (1/10), hundredths (1/100), thousandths (1/1000), and so on.
• Multiplying decimals: multiply the numbers as whole numbers, then place the decimal point so the product has as many decimal digits as the total decimal digits in both factors combined.
• Multiplying by powers of 10: the decimal point shifts right by as many places as the number of zeros (×10 shifts 1 place, ×100 shifts 2 places).
• Size of the product: both factors > 1 → product > both factors; both factors between 0 and 1 → product < both factors; one factor between 0 and 1 and the other > 1 → product lies between the two.
• Dividing decimals by a whole number: divide as usual; the decimal point in the quotient lines up with the decimal point in the dividend.
• Dividing by a decimal divisor: multiply both the dividend and divisor by the same power of 10 to make the divisor a whole number, then divide — the quotient stays the same.
• Dividing by powers of 10: the decimal point shifts left by as many places as the number of zeros.
• Dividing by a number less than 1 always gives a quotient larger than the original number; dividing by a number greater than 1 always gives a smaller quotient.
• Terminating vs repeating decimals: a fraction gives a terminating decimal only if its lowest-terms denominator has no prime factors other than 2 or 5; otherwise the decimal repeats endlessly (e.g. 5/11 = 0.454545…).
• Real-life uses: billing and money, measuring lengths/weights/capacities, unit-rate price comparisons, and fuel-efficiency calculations all rely on decimal multiplication and division.

See also: NCERT Solutions for Class 7 Maths Chapter 12

Practice more: Extra Questions for Class 7 Maths Chapter 12

For the full chapter, see the Class 7 Maths Part 2 book page and the Class 7 Maths Formulas Handbook.

Frequently Asked Questions

How is multiplying two decimal numbers different from multiplying two whole numbers?
The numbers are first multiplied as whole numbers ignoring the decimal points, and then the decimal point is placed in the product based on the total number of decimal places in both original numbers.

Why does dividing a number by a decimal less than one give a bigger result than the original number?
Dividing by a decimal less than one is the same as multiplying by a number greater than one, which is why the quotient ends up larger than the original number.

Written by Satish

NCERTBooks.org is an independent educational resource run by a small team focused on making official NCERT textbooks easy to find, read, and download for students, parents, and teachers across India. We are not affiliated with NCERT or the Ministry of Education -- we organise publicly available NCERT content by class and subject, verify links against official sources, and build tools (like our in-browser reader) that make studying more convenient. Every guide we publish is written and reviewed by our team based on the actual NCERT curriculum and syllabus.