{
  "schema": "vedokrok.public-item.v1",
  "release_id": "MHC-RPUB-20260920-75ad787a",
  "url": "/knowledge/set-a-rough-bound-before-trusting-the-exact-answer",
  "id": "MHC-D-RESEARCH-0256",
  "version": "0.1.0",
  "title": "Set a rough bound before trusting the exact answer",
  "summary": "An extra zero is less convincing when you already know the right neighborhood.",
  "kind": "heuristic",
  "body": "Estimate a simple lower and upper bound from the inputs before inspecting the precise result. Use the bound to catch impossible signs, scales or relationships. This is a second check, not a replacement for the full calculation.",
  "limits": [
    "Care is needed when operations reverse inequalities, such as dividing by negative values; an unjustified bound can mislead too."
  ],
  "topics": [
    "union-numerical-reasoning"
  ],
  "intents": [],
  "source_ids": [
    "RS-767005552D5DD114"
  ],
  "evidence": [
    {
      "claim": "Reasonableness checks can compare a percentage result with bounds implied by the original quantity.",
      "source_id": "RS-767005552D5DD114",
      "role": "supports",
      "note": "A plausible magnitude can still contain an error; this check supplements rather than replaces calculation.",
      "locator": "Check the answer; independent bounding examples"
    }
  ],
  "use_when": [
    "A calculator or spreadsheet returns a plausible-looking number that you have not independently checked."
  ],
  "avoid_when": [
    "Care is needed when operations reverse inequalities, such as dividing by negative values; an unjustified bound can mislead too."
  ],
  "example": "Ten percent of 480 is 48, so twelve percent must be a little larger than 48 and nowhere near 576.",
  "check": "The detailed answer satisfies an independently constructed magnitude check.",
  "sources": [
    {
      "id": "RS-767005552D5DD114",
      "title": "Prealgebra 2e, 6.2: Solve General Applications of Percent",
      "url": "https://openstax.org/books/prealgebra-2e/pages/6-2-solve-general-applications-of-percent"
    }
  ],
  "relations": [
    {
      "from": "MHC-D-RESEARCH-0256",
      "to": "MHC-D-RESEARCH-0252",
      "type": "useful_with",
      "url": "/knowledge/let-the-units-check-the-formula"
    }
  ],
  "collections": [
    {
      "id": "RC-D976097B2A42D9AC",
      "title": "Make the numbers answer the right question",
      "url": "/collections/make-the-numbers-answer-the-right-question"
    }
  ]
}