What is financial infrastructure?

The network of banks, payment systems and stock markets that helps manage money

What are the main things a bank does?

Holds deposits and lends money as loans

How do banks make money?

They pay lower interest on deposits and charge higher interest on loans

Earning interest on previous interest as well as on the original amount

How do you place the decimal point when multiplying two decimals?

The product has as many decimal places as the total in both factors.

Given \(596 \times 248 = 147808\), find \(5.96 \times 24.8\).

It is \(147.808\), with \(2 + 1 = 3\) decimal places.

How do you divide a decimal by 100?

Move the decimal point two places to the left.

Why does \(10 \div 3\) never end?

Each step leaves a remainder of 1, giving \(3.333\dots\) forever.

What is the repeating block in \(1 \div 7\)?

The block \(142857\), so \(1 \div 7 = 0.\overline{142857}\).

How do you handle a decimal divisor like 0.13?

Multiply dividend and divisor by 100 to make the divisor a whole number.

Is the product of 0.25 and 0.8 less than both?

Yes — \(0.25 \times 0.8 = 0.2\), which is less than both factors.

Why was the leap year introduced?

Because the Earth takes about \(365.2422\) days per revolution, needing an extra day roughly every 4 years.

When dividing, when is the quotient greater than the dividend?

When the divisor is a decimal less than 1, e.g. \(128 \div 0.4 = 320\).

Another Peek Beyond the Point

Class 7 Mathematics · Ganita Prakash Part 2 · Chapter 4

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Five congruence conditions to equations

Marks booster + cheatsheet: key concepts in 2 lines each
Integer sign rules, Ch 2
HCF and LCM by prime factors, Ch 3
Multiplying and dividing decimals, Ch 4
Mean, median and outliers, Ch 5
Ruler-and-compass constructions, Ch 6

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CBSE Class 7 · Mathematics

8 chapters: lakhs and crores to fractions

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Summary

This chapter extends decimal work to multiplication and division, treating decimals as the fractions they represent. To multiply two decimals, multiply the numbers as if there were no decimal points, then place the point so the number of decimal places in the product equals the sum of the decimal places in the factors — for example \(5.96 \times 24.8 = 147.808\). To divide by 10, 100, 1000, move the decimal point left by the number of zeros. Division uses the long-division (place-value) method: when ones are regrouped into tenths a decimal point is placed in the quotient, and regrouping continues into hundredths and thousandths. Some divisions never end, such as \(10 \div 3 = 3.333\dots\), revealing repeating decimals like \(1 \div 7 = 0.\overline{142857}\). When the divisor is itself a decimal, multiply both dividend and divisor by a power of 10 to make the divisor a whole number. The chapter ends with a fascinating real application: how leap-year rules (the \(0.2422\) extra days each year) keep our calendar aligned with the Earth's motion.

Recap of decimals; dividing by powers of 10Decimal multiplication and placing the pointDecimal division by long divisionRepeating decimals and decimal divisorsApplication: leap years and the calendar

Key terms

Decimal multiplication

Multiplying the numbers without the point, then placing the point by adding decimal places.

Decimal division

Dividing using long division and placing the point when ones become tenths.

Dividing by powers of 10

Moving the decimal point left by as many places as there are zeros in the divisor.

Repeating decimal

A decimal whose digits repeat without ending, e.g. \(1 \div 7 = 0.\overline{142857}\).

Decimal divisor

A divisor that is a decimal; make it a whole number by multiplying both numbers by a power of 10.

Leap year

A year with 366 days, added to keep the calendar aligned with the Earth's revolution.

Extra questions & answers

Try one from this chapter

When multiplying two decimals, the number of decimal places in the product equals:

Flashcards & interactive practice