Question
Add .
Solution — Step by Step
We write as — the value doesn’t change, but now both numbers have two decimal places. This is the key move that makes column addition possible.
2.35
+ 1.70
------The decimal points must sit in the same column. Every digit now has a clear partner to add with.
. Write 5 in the hundredths place. No carry.
. Write 0, carry 1 to the ones column.
. Bring down the decimal point. Final answer: 4.05.
2.35
+ 1.70
------
4.05Why This Works
Decimals are just fractions in disguise. means , and means . When we align decimal points, we’re making sure tenths add with tenths and hundredths add with hundredths — the same logic as adding hundreds with hundreds in whole numbers.
Writing as uses the fact that . Adding a trailing zero after the last decimal digit never changes the value — it just makes the column structure visible.
The decimal point in the answer goes directly below the decimal points in the question. It never shifts.
Alternative Method
We can convert both to fractions and add directly.
Same answer. This method is slower for calculation but useful when you need to verify or when the question appears in a fractions chapter.
For quick mental calculation: . Break the second number into its whole and decimal parts and add separately.
Common Mistake
Many students write the numbers right-aligned (like whole numbers) instead of decimal-point-aligned:
2.35
+ 1.7 ← WRONG alignment
------
3.05 ← wrong answerThis adds the 7 to the 3 (tenths + hundredths), which makes no sense — it’s like adding apples to oranges. Always align at the decimal point, not the last digit.