Unit 5 · Topic 01 · Decimals
The tailor's tape measure read 2.45 metres for the curtain fabric.
Pixel the class robot was building a table of measurements and needed to sort them smallest to largest.
It sorted 2.45 ABOVE 2.5, and nobody could work out why until they looked at what it was actually comparing.
The class was helping design a school notice board, and Ms. Rao sent Pixel — the little sorting robot that lived on the back shelf — off to arrange the fabric measurements in order: 2.45 m, 2.5 m, 2.09 m, 2.7 m.
Pixel printed its answer: 2.45, 2.7, 2.09, 2.5. Everyone frowned. Kabir checked it against the tape measure. It was wrong — 2.09 was clearly the shortest piece, not third.
"Show us how you sorted them," said Ms. Rao.
Pixel's screen displayed its method: it had compared the digits AFTER the point as if they were their own whole numbers. 45 against 5 against 09 against 7. Read that way, 45 looks bigger than 5, so 2.45 went above 2.5.
"There's the bug," said Anaya. "Point-four-five isn't forty-five of anything bigger than point-five is five of. They're different-sized pieces."
Ms. Rao drew a place-value chart stretching past the decimal point: ones, then a dot, then TENTHS, then HUNDREDTHS. "The first column after the point is tenths — cutting a whole into 10. The second is hundredths — cutting it into 100, ten times smaller pieces again."
She lined the four numbers up so every one had two decimal places: 2.45, 2.50, 2.09, 2.70. "Now compare column by column, tenths first, exactly like you would with whole numbers."
Kabir worked it: tenths digits were 4, 5, 0, 7. Smallest to largest: 2.09, 2.45, 2.50, 2.70.
"Fix Pixel," said Ms. Rao. "What went wrong in its rule?"
Anaya typed the correction: compare the TENTHS digit first, not the whole decimal part as one lump. If tenths tie, move to hundredths.
Pixel re-sorted instantly and got it right. Kabir noticed something else. "2.5 and 2.50 — are those the same length?"
"Try it on the tape measure," said Ms. Rao. Same mark, exactly. "A zero on the end of a decimal changes nothing. It's like writing 2 as 02 — the value doesn't move."
The place-value chart does not stop at the ones column. Past the decimal point it keeps going, each new column ten times smaller than the last: TENTHS (a whole cut into 10 pieces), then HUNDREDTHS (cut into 100), then THOUSANDTHS.
To compare two decimals, never compare the digits after the point as if they were their own whole number. Compare column by column from the LEFT, exactly as with whole numbers: tenths first, then hundredths, then thousandths — stop at the first column where they differ.
This is why 0.5 is bigger than 0.45, even though 45 looks bigger than 5: 0.5 has 5 in the tenths column and 0.45 only has 4 there, and that one column already settles it.
A zero added at the very end of a decimal changes nothing — 0.5, 0.50 and 0.500 are all exactly the same amount, the way 7 and 07 are the same whole number.
Shade 7 of 10 equal parts — write 7/10 and 0.7.
Write 45/100 as a decimal and compare 2.45 vs 2.50 using tenths first.
Order 2.45, 2.5, 2.09, 2.7 after lining up hundredths: 2.09, 2.45, 2.50, 2.70.
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