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   "source": [
    "# The *significance* of significant digits"
   ]
  },
  {
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    "As illustrated in the xx file, besides typical linguistic hedges (i.e. \"about 7\") which indicate uncertainty, the number (i.e. 7 or 7.0) per se indicate uncertainty as well. Significant digits are established ways among engineers to indicate how precise they can be about the measurements. With the concept of *uncertain number*, `pyuncertainnumber` facilitates the expression of such significance in computations."
   ]
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   "id": "190d453e-d8b7-4076-ac64-e1e98c1bad6b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pyuncertainnumber as pun\n",
    "from pyuncertainnumber.characterisation.utils import sgnumber"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3ce9c340-6b5f-4409-805a-1c4e4f2f4de0",
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Interpreting significant digits\n",
      "   200.000\t [199.9995, 200.0005]\n",
      "    200.00\t [199.995, 200.005]\n",
      "     200.0\t [199.95, 200.05]\n",
      "      200.\t [199.5, 200.5]\n",
      "     20.e1\t [195.0, 205.0]\n",
      "      1.23\t [1.225, 1.2349999999999999]\n",
      "    1.2300\t [1.2299499999999999, 1.23005]\n",
      "      12.3\t [12.25, 12.350000000000001]\n",
      "    1.23e8\t [122500000.0, 123500000.0]\n",
      "    12.3e2\t [1225.0, 1235.0]\n",
      "   12.3e-4\t [0.001225, 0.001235]\n",
      "     12300\t [12250.0, 12350.0]\n",
      "   12300e4\t [122500000.0, 123500000.0]\n",
      "         9\t [8.5, 9.5]\n",
      "       2e2\t [150.0, 250.0]\n",
      "       200\t [150.0, 250.0]\n",
      "        10\t [5.0, 15.0]\n",
      "      1000\t [500.0, 1500.0]\n",
      "   1000000\t [500000.0, 1500000.0]\n",
      "    123400\t [123350.0, 123450.0]\n",
      "     12000\t [11500.0, 12500.0]\n"
     ]
    }
   ],
   "source": [
    "print(\"\\n\\nInterpreting significant digits\")\n",
    "\n",
    "def unumber(s):\n",
    "    return pun.I(s).intervals\n",
    "\n",
    "def outs(s):\n",
    "    return \"{:>10}\\t\".format(s)\n",
    "\n",
    "s = \"200.000\"\n",
    "print(outs(s), sgnumber(s))  # [ 199.9995, 200.0005]\n",
    "s = \"200.00\"\n",
    "print(outs(s), sgnumber(s))  # [ 199.995, 200.005]\n",
    "s = \"200.0\"\n",
    "print(outs(s), sgnumber(s))  # [ 199.95, 200.05]\n",
    "s = \"200.\"\n",
    "print(outs(s), sgnumber(s))  # [ 199.5, 200.5]\n",
    "s = \"20.e1\"\n",
    "print(outs(s), sgnumber(s))  # [ 195, 205]\n",
    "s = \"1.23\"\n",
    "print(outs(s), sgnumber(s))  # 1.225, 1.235  # the extra nines are a 'feature' of Python\n",
    "s = \"1.2300\"\n",
    "print(outs(s), sgnumber(s))  # 1.22995, 1.23005\n",
    "s = \"12.3\"\n",
    "print(outs(s), sgnumber(s))  # 12.25, 12.35\n",
    "s = \"1.23e8\"\n",
    "print(outs(s), sgnumber(s))  # 122500000.0, 123500000.0\n",
    "s = \"12.3e2\"\n",
    "print(outs(s), sgnumber(s))  # 1225.0, 1235.0\n",
    "s = \"12.3e-4\"\n",
    "print(outs(s), sgnumber(s))  # 0.001225, 0.001235\n",
    "s = \"12300\"\n",
    "print(outs(s), sgnumber(s))  # 12250.0, 12350.0\n",
    "s = \"12300e4\"\n",
    "print(outs(s), sgnumber(s))  # 122500000.0, 123500000.0\n",
    "s = \"9\"\n",
    "print(outs(s), sgnumber(s))  # 8.5,9.5\n",
    "s = \"2e2\"\n",
    "print(outs(s), sgnumber(s))  # 150, 250\n",
    "s = \"200\"\n",
    "print(outs(s), sgnumber(s))  # 150,250\n",
    "s = \"10\"\n",
    "print(outs(s), sgnumber(s))  # 5,15\n",
    "s = \"1000\"\n",
    "print(outs(s), sgnumber(s))  # 500,1500\n",
    "s = \"1000000\"\n",
    "print(outs(s), sgnumber(s))  # 5e5,15e5\n",
    "s = \"123400\"\n",
    "print(outs(s), sgnumber(s))  # 123350,123450\n",
    "s = \"12000\"\n",
    "print(outs(s), sgnumber(s))  # 11500,12500\n"
   ]
  },
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