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

  1. One cloud of smoke, three countries
    This week, one cloud of smoke covered three countries.
  2. Indonesia: fires in Sumatra and Kalimantan · visibility 150 m
    In Indonesia, fires are burning in Sumatra and Kalimantan. In one city there, you could see only a hundred fifty meters.
  3. Malaysia: 38 of 68 stations unhealthy · schools closed
    In Malaysia, thirty-eight of sixty-eight air stations read unhealthy. Schools closed in Johor, Selangor, Kuala Lumpur and more.
  4. Singapore, Oct 9: PSI 192, the worst this year
    And in Singapore, on October ninth, the PSI hit one ninety-two. The worst this year.
  5. A week before: 94. So twice as bad?
    A week before, it was ninety-four. So the air is about twice as bad, right?
  6. In haze, PSI comes from PM2.5
    Hmm. Let's check the smoke itself. In haze, PSI comes from tiny particles called PM two point five.
  7. Oct 1: 50 µg/m³ · Oct 9: 143 µg/m³
    October first: fifty micrograms in every cubic meter of air. October ninth: one hundred forty-three.
  8. 143 ÷ 50 = ?
    One forty-three divided by fifty?
  9. Almost 3 times the smoke, not 2
    That's almost three times the smoke. Not two.
  10. So where does PSI come from?
    So where does the PSI number come from?
  11. NEA's reference table
    Singapore's environment agency, NEA, publishes a reference table.
  12. Band edges: 12 → 50 · 55 → 100 · 150 → 200
    At 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.
  13. Between two pairs: a straight line
    Then, between two pairs, they draw a straight line.
  14. Piecewise function: straight pieces
    A rule made of straight pieces like this is called a piecewise function.
  15. 143 is on the third piece: 55 to 150
    Now read today's number. One forty-three sits on the third piece, between fifty-five and one fifty.
  16. How far along the piece?
    How far along that piece is it?
  17. 88 out of 95 ≈ 93% of the way
    Eighty-eight out of ninety-five. That's about ninety-three percent of the way.
  18. 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...
  19. ≈ 193
    about one ninety-three.
  20. Each piece has its own slope
    But 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.
  21. Double the PSI ≠ double the smoke
    So doubling the PSI doesn't mean doubling the smoke.
  22. The real week: NEA data
    Here's the real week, from NEA's own data.
  23. On a test: find the piece → slope → point-slope
    On 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.
  24. 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.

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