How to Find a Number Between 3.4 and 3.5
Learn to place decimals on a number line, compare them by place value rather than digit count, convert between units, and add and subtract without misaligning the point.
How many numbers fit between 3.4 and 3.5?
As many as you like. Between 3.4 and 3.5 lie 3.41, 3.42, 3.43 and so on — and between 3.41 and 3.42 lie 3.411, 3.412 and the rest. Every time you add a decimal place you find ten more numbers in the same gap, which never runs out.
This page covers everything in the CBSE Class 7 Mathematics chapter's second half: locating decimals on a number line, comparing them properly, converting units, and adding and subtracting them.
This page covers everything in the CBSE Class 7 Mathematics chapter's second half: locating decimals on a number line, comparing them properly, converting units, and adding and subtracting them.
How do you place a decimal on a number line?
Divide the gap between two whole numbers into ten equal parts, and each mark is one tenth.
To place 3.7, take the stretch from 3 to 4, divide it into ten, and count seven marks from 3.
For hundredths, zoom in. Take the stretch from 3.4 to 3.5, divide that into ten parts, and each mark is one hundredth — so 3.46 is six marks past 3.4.
This is exactly how you find a number between two decimals. Asked for a number between 3.4 and 3.5, zoom in one level and pick any of 3.41 to 3.49. Asked for one between 3.41 and 3.42, zoom again and pick 3.415.
For example, a ruler already does this for you: the centimetre marks are whole units and the ten small marks between them are tenths, which is why you can read 7.3 cm directly.
The idea that surprises students is that there is no "next" decimal after 3.4 — you can always squeeze another number in between.
To place 3.7, take the stretch from 3 to 4, divide it into ten, and count seven marks from 3.
For hundredths, zoom in. Take the stretch from 3.4 to 3.5, divide that into ten parts, and each mark is one hundredth — so 3.46 is six marks past 3.4.
This is exactly how you find a number between two decimals. Asked for a number between 3.4 and 3.5, zoom in one level and pick any of 3.41 to 3.49. Asked for one between 3.41 and 3.42, zoom again and pick 3.415.
For example, a ruler already does this for you: the centimetre marks are whole units and the ten small marks between them are tenths, which is why you can read 7.3 cm directly.
The idea that surprises students is that there is no "next" decimal after 3.4 — you can always squeeze another number in between.
Why is 0.5 greater than 0.45?
Because you compare place by place from the left, not by counting digits.
Compare 0.5 and 0.45. The tenths digits are 5 and 4. Since , we already know — the remaining digits cannot rescue it, because hundredths are too small to make up a whole tenth.
It helps to write them with the same number of places: , and is now obvious. Adding zeros on the right of a decimal never changes its value.
Another: compare and . Write the second as 2.310. The ones and tenths match, so move to the hundredths: 0 against 1. Since , we get — again the number with fewer digits is the larger one.
Order these ascending: 1.2, 1.02, 1.22, 1.002. Padded to 1.200, 1.020, 1.220, 1.002, they sort to 1.002, 1.02, 1.2, 1.22.
The trap is assuming more digits means a larger number. 0.45 has more digits than 0.5 and is smaller.
Compare 0.5 and 0.45. The tenths digits are 5 and 4. Since , we already know — the remaining digits cannot rescue it, because hundredths are too small to make up a whole tenth.
It helps to write them with the same number of places: , and is now obvious. Adding zeros on the right of a decimal never changes its value.
Another: compare and . Write the second as 2.310. The ones and tenths match, so move to the hundredths: 0 against 1. Since , we get — again the number with fewer digits is the larger one.
Order these ascending: 1.2, 1.02, 1.22, 1.002. Padded to 1.200, 1.020, 1.220, 1.002, they sort to 1.002, 1.02, 1.2, 1.22.
The trap is assuming more digits means a larger number. 0.45 has more digits than 0.5 and is smaller.
Formula
How do you convert between units using decimals?
Each conversion is a multiplication or division by a power of ten, which simply shifts the decimal point.
Going to a larger unit, divide — the point moves left:
Going to a smaller unit, multiply — the point moves right:
A combined one: express 2 km 350 m in kilometres. Since 350 m is 0.35 km, the answer is 2.35 km.
Check the direction before writing the answer: converting to a smaller unit must give a bigger number. If 3.4 m came out as 0.034 cm, the point went the wrong way.
Going to a larger unit, divide — the point moves left:
Going to a smaller unit, multiply — the point moves right:
A combined one: express 2 km 350 m in kilometres. Since 350 m is 0.35 km, the answer is 2.35 km.
Check the direction before writing the answer: converting to a smaller unit must give a bigger number. If 3.4 m came out as 0.034 cm, the point went the wrong way.
How do you add and subtract decimals?
Line up the decimal points, one under the other, so that tenths sit under tenths and hundredths under hundredths. Fill any short gaps with zeros, then add or subtract as usual and bring the point straight down.
Add 12.5 and 3.75:
The zero added to 12.5 keeps the columns aligned.
Subtract 4.8 from 10:
A word problem: you buy items for Rs 45.50, Rs 23.75 and Rs 8.25. The total is
Paying with Rs 100 leaves change of .
A measurement one: a rope 5.6 m long has 1.85 m cut off, leaving m.
The error to avoid is aligning the numbers by their right-hand edge instead of by the point — that puts hundredths under tenths and gives a wrong answer every time.
Add 12.5 and 3.75:
The zero added to 12.5 keeps the columns aligned.
Subtract 4.8 from 10:
A word problem: you buy items for Rs 45.50, Rs 23.75 and Rs 8.25. The total is
Paying with Rs 100 leaves change of .
A measurement one: a rope 5.6 m long has 1.85 m cut off, leaving m.
The error to avoid is aligning the numbers by their right-hand edge instead of by the point — that puts hundredths under tenths and gives a wrong answer every time.
Exam tip
Exam tip: padding with zeros before you compare or subtract
Most mistakes in this chapter come from decimals with different numbers of places sitting next to each other.
Make padding automatic. Before comparing, ordering, adding or subtracting, rewrite every number with the same number of decimal places by adding zeros on the right: 0.5 becomes 0.50, and 10 becomes 10.0 or 10.00 as needed.
This is safe because zeros on the right never change a decimal's value — only zeros on the left of the digits, like the one in 0.07, carry meaning.
Once padded, comparison is digit-by-digit and subtraction has no ragged columns. It costs one line of writing and removes the single commonest source of lost marks here.
Make padding automatic. Before comparing, ordering, adding or subtracting, rewrite every number with the same number of decimal places by adding zeros on the right: 0.5 becomes 0.50, and 10 becomes 10.0 or 10.00 as needed.
This is safe because zeros on the right never change a decimal's value — only zeros on the left of the digits, like the one in 0.07, carry meaning.
Once padded, comparison is digit-by-digit and subtraction has no ragged columns. It costs one line of writing and removes the single commonest source of lost marks here.
Did you know
Why does adding a zero on the right change nothing?
Because it fills a place with nothing. Writing 0.5 as 0.50 says there are five tenths and zero hundredths — which was already true; the zero was simply not written.
A zero on the left of the digits is different. In 0.07 it says there are no tenths, which pushes the 7 into the hundredths place and genuinely changes the number.
A zero on the left of the digits is different. In 0.07 it says there are no tenths, which pushes the 7 into the hundredths place and genuinely changes the number.
Key takeaways
Comparing and calculating with decimals: quick revision
- Between any two decimals lie infinitely many more; zoom in by one place to find them, as 3.41 sits between 3.4 and 3.5.
- On a number line, each gap between whole numbers divides into ten tenths, and each tenth into ten hundredths.
- Compare place by place from the left, not by digit count — 0.5 is greater than 0.45.
- Unit conversions shift the point: divide for a larger unit, multiply for a smaller one, and check the answer moved the right way.
- Add and subtract by lining up the decimal points and padding with zeros, never by aligning the right-hand edges.
You will remember all of this far better after answering five questions on it than after reading it twice.
- On a number line, each gap between whole numbers divides into ten tenths, and each tenth into ten hundredths.
- Compare place by place from the left, not by digit count — 0.5 is greater than 0.45.
- Unit conversions shift the point: divide for a larger unit, multiply for a smaller one, and check the answer moved the right way.
- Add and subtract by lining up the decimal points and padding with zeros, never by aligning the right-hand edges.
You will remember all of this far better after answering five questions on it than after reading it twice.