You Cannot Add Kilograms to Grams Until One of Them Changes

Because they are measured in different units, and $2.5+750$ means nothing at all. Convert the grams to kilograms first and the sum becomes easy:

$$2.5+0.75=3.25\text{ kg}$$

That one habit prevents most errors in this chapter. This page covers everything in the ICSE Class 7 Mathematics chapter's first part: decimal place value and conversion to fractions, comparing decimals, adding and subtracting across units, and multiplying and dividing decimals.

Each digit after the point has its own place value — tenths, hundredths, thousandths — each ten times smaller than the one before.

In $34.567$:

- 3 is 3 tens
- 4 is 4 ones
- 5 is 5 tenths, or $\frac{5}{10}$
- 6 is 6 hundredths, or $\frac{6}{100}$
- 7 is 7 thousandths, or $\frac{7}{1000}$

It is read as thirty-four point five six seven, naming the digits after the point one by one — never "five hundred and sixty-seven".

Decimal to vulgar fraction. Write the digits after the point over 1 followed by that many zeros, then reduce:

$$0.375=\frac{375}{1000}=\frac{3}{8}$$

Vulgar fraction to decimal. Divide the numerator by the denominator:

$$\frac{7}{8}=0.875$$

A shop bill for ₹34.50 is the everyday form — 34 rupees and 50 paise, where the 5 is five tenths of a rupee.

The fact that trips students up is that adding zeros at the end changes nothing. $0.5$, $0.50$ and $0.500$ are the same number, because those zeros sit in places that hold nothing. Adding a zero before the digits, as in $0.05$, changes the value completely.

Give every number the same number of decimal places by padding with zeros, then compare them digit by digit from the left.

Compare $0.5$, $0.45$ and $0.405$. Written with three decimal places each:

$$0.500,0.450,0.405$$

Now it is clear: $0.405<0.450<0.500$, so the ascending order is $0.405,0.45,0.5$.

Without the padding, $0.45$ looks bigger than $0.5$ because it has more digits — and that is exactly the error the padding removes.

Compare whole-number parts first. $3.9$ is greater than $3.15$, and $12.001$ is greater than $9.999$, because 12 beats 9 before any decimal is examined.

Petrol prices show the same logic: ₹94.50 per litre is more than ₹94.09, even though 50 has fewer digits than 09 suggests.

So the number of digits after the point says nothing about size. What matters is what each digit is worth, and equalising the places is what makes that visible.

Convert everything to one unit first, then line the decimal points up vertically and add or subtract as usual.

Money. A shopper pays ₹125.50 and ₹78.75:

$$125.50+78.75=₹204.25$$

Mass. A bag holds $2.5$ kg of rice and $750$ g of dal. Since $750g=0.75$ kg:

$$2.5+0.75=3.25\text{ kg}$$

Length. From a $3$ m cloth, $45$ cm is cut off. Since $45cm=0.45$ m:

$$3-0.45=2.55\text{ m}$$

Capacity. A jug holds $1.5$ L and $250$ mL is poured out. Since $250mL=0.25$ L:

$$1.5-0.25=1.25\text{ L}$$

The conversions to remember are $1kg=1000g$, $1m=100cm$, $1km=1000m$, $1L=1000mL$ and $₹1=100$ paise.

Lining the points up is the second essential habit. Writing $3$ as $3.00$ before subtracting $0.45$ makes the borrowing straightforward, whereas subtracting from a bare 3 is where digits get misplaced.

By a power of 10, move the point right for multiplication and left for division:

$$4.56\times 100=456,4.56÷100=0.0456$$

By a whole number, multiply as usual and keep the same number of decimal places:

$$3.4\times 7=23.8,9.6÷4=2.4$$

By another decimal, multiply ignoring the points, then give the answer as many decimal places as both factors have together:

$$1.2\times 0.25=0.3$$

since $12\times 25=300$ and $1+2=3$ places gives $0.300$.

Dividing by a decimal needs the divisor made whole first, by multiplying both numbers by the same power of 10:

$$4.5÷0.15=450÷15=30$$

A context check: $2.5$ kg of dal at ₹48.50 per kg costs $2.5\times 48.50=₹121.25$.

Estimate before you calculate and a misplaced point cannot survive. For $6.8\times 4.2$, note that $7\times 4=28$, so $28.56$ is right and $2.856$ is not. And note the direction of the last example: dividing by $0.15$, a number less than 1, made the answer much larger than $4.5$.