Real Life Math
Singapore Haze 2026: Is PSI 192 Twice as Bad as 94?
Haze from fires in Sumatra and Kalimantan (Indonesia) is covering Malaysia and Singapore. Singapore haze 2026: on 9 Oct the PSI hit 192, the worst this year.…
Ages 13–17 · US Algebra 1 2:43
Step by step
- One cloud of smoke, three countriesThis week, one cloud of smoke covered three countries.
- Indonesia: fires in Sumatra and Kalimantan · visibility 150 mIn Indonesia, fires are burning in Sumatra and Kalimantan. In one city there, you could see only a hundred fifty meters.
- Malaysia: 38 of 68 stations unhealthy · schools closedIn Malaysia, thirty-eight of sixty-eight air stations read unhealthy. Schools closed in Johor, Selangor, Kuala Lumpur and more.
- Singapore, Oct 9: PSI 192, the worst this yearAnd in Singapore, on October ninth, the PSI hit one ninety-two. The worst this year.
- A week before: 94. So twice as bad?A week before, it was ninety-four. So the air is about twice as bad, right?
- In haze, PSI comes from PM2.5Hmm. Let's check the smoke itself. In haze, PSI comes from tiny particles called PM two point five.
- Oct 1: 50 µg/m³ · Oct 9: 143 µg/m³October first: fifty micrograms in every cubic meter of air. October ninth: one hundred forty-three.
- 143 ÷ 50 = ?One forty-three divided by fifty?
- Almost 3 times the smoke, not 2That's almost three times the smoke. Not two.
- So where does PSI come from?So where does the PSI number come from?
- NEA's reference tableSingapore's environment agency, NEA, publishes a reference table.
- Band edges: 12 → 50 · 55 → 100 · 150 → 200At the edge of each health band, they fixed a pair of numbers. Twelve micrograms means PSI fifty. Fifty-five means one hundred. One fifty means two hundred.
- Between two pairs: a straight lineThen, between two pairs, they draw a straight line.
- Piecewise function: straight piecesA rule made of straight pieces like this is called a piecewise function.
- 143 is on the third piece: 55 to 150Now read today's number. One forty-three sits on the third piece, between fifty-five and one fifty.
- How far along the piece?How far along that piece is it?
- 88 out of 95 ≈ 93% of the wayEighty-eight out of ninety-five. That's about ninety-three percent of the way.
- PSI: 93% of the way from 100 to 200…So the PSI goes ninety-three percent of the way from one hundred to two hundred...
- ≈ 193about one ninety-three.
- Each piece has its own slopeBut each piece has its own slope. Down low, a little smoke adds a lot of PSI. Higher up, it takes more smoke for each point.
- Double the PSI ≠ double the smokeSo doubling the PSI doesn't mean doubling the smoke.
- The real week: NEA dataHere's the real week, from NEA's own data.
- On a test: find the piece → slope → point-slopeOn a test: one forty-three is between fifty-five and one fifty, so use the third piece. Its slope is a hundred over ninety-five. PSI equals a hundred, plus eighty-eight times a hundred over ninety-five. That's about one ninety-three. NEA shows one ninety-two, because one forty-three is itself rounded.
- On a test, it looks like this: how far?On a test, it can look like this. How far did the taxi go?
Your turn
Your turn: PSI is one fifty. How much smoke is in the air?
Show the answer
Save NEA's table for the next haze day. And remember: see an index, think: pieces, not proportional.
Keep going
There are more short lessons on this topic, each with a full write-up.
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