Unit 5 · Topic 03 · Decimals
Two friends, Ishaan and Diya, raced to add 12.5 and 3.75 without a calculator.
Ishaan finished first and shouted '15.00!' Diya finished a moment later with '16.25'.
Only one tape measure was going to prove which of them had actually got it right.
It was sports day, and the two runners-up of the long jump were comparing combined distances: Ishaan's best jump was 12.5 m and his practice jump was 3.75 m. Whoever added them correctly first got to write the total on the board.
Ishaan wrote the numbers one under the other, right-aligned by the LAST digit, the way he lined up whole numbers: 12.5 on top, 3.75 below, with the 5 of 12.5 sitting above the 5 of 3.75.
5 plus 5 is 10, write 0 carry 1. 2 plus 7 plus 1 is 10, write 0 carry 1. 1 plus 3 plus 1 is 5. 15.00. He shouted it out.
Diya had written it differently. She lined up the DECIMAL POINTS first, then padded 12.5 with an extra zero to make 12.50, matching 3.75's two decimal places.
12.50 plus 3.75: hundredths 0+5=5, tenths 5+7=12 so write 2 carry 1, ones 2+3+1=6, tens 1. 16.25.
The gym teacher checked both jumps on the actual tape: 12.5 m plus 3.75 m of extra run-up. She confirmed 16.25.
"You lined up the wrong thing," Diya told Ishaan. "You matched the LAST digit, not the decimal point. My 5 is worth five tenths. Your 5 is worth five hundredths, because it's the second digit after your point. They're not the same size at all."
Ishaan redrew his columns, this time matching the points. He saw it immediately — his ones column had picked up a 7, which belonged in the tenths place one column to the right.
The teacher gave them a harder one to settle it for good: 20 minus 4.5. Ishaan tried straight away and got stuck — 20 had no decimal point to line up against.
"Give it one," said Diya. "20 is 20.0. Now line up the points and you've got a zero to borrow from, just like borrowing across a zero in whole numbers."
20.0 minus 4.5 became 19.10 minus 4.5 after borrowing a whole into the tenths column: 15.5.
"Same trick as always," said Ishaan. "Borrowing doesn't care whether there's a dot in the number or not."
Adding or subtracting decimals uses exactly the same column method as whole numbers, with one extra rule: line up the DECIMAL POINTS, never the last digit.
Once the points are aligned, pad the shorter decimal with trailing zeros so both numbers show the same number of decimal places. This makes every column line up with a column of the same size — tenths under tenths, hundredths under hundredths.
Carrying and borrowing work exactly as they do for whole numbers; the decimal point does not interrupt the process, it just travels straight down into the answer, staying in the same column.
A whole number with no visible decimal point can always be given one — 20 becomes 20.0 or 20.00 — which is essential whenever it needs to be added to or subtracted from a decimal.
Collect three real shop receipts or price tags and add up their totals by hand, lining up the decimal points on paper first.
Check your hand-added total against a calculator, then find and explain any column where you slipped.
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