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{
  "topic": "absolute-value",
  "input_types": [
    "float"
  ],
  "input_labels": [
    "n"
  ],
  "input_values": [
    "-8"
  ],
  "type": "Calculate",
  "title": "Absolute Value",
  "category": "Arithmetic",
  "formula_mathjax": "\\( | n | \\)",
  "formula": "Math.abs( n )",
  "formula_captions": "<span>n</span> is an integer value.",
  "op_label": "Absolute Value",
  "explanation": "The absolute value of a given number is the magnitude of the given number. If -8 is the given number, then 8 is its absolute value. Similarly, if 12 is the given number, then 12 is its absolute value.",
  "content": "<h2>Understanding Absolute Value</h2>\n<p>The absolute value of a number represents its distance from zero on the number line, regardless of its direction. This value is always non-negative and is denoted by two vertical bars, as in \\( |n| \\).</p>\n<p>The formula for calculating the absolute value is:</p>\n<p>\\( |n| \\)</p>\n<p>where:</p>\n<ul>\n<li><b>n</b> is any real number, either positive or negative.</li>\n</ul><p>The absolute value is useful in various situations where only the magnitude of a number is needed, such as measuring distances, errors, or deviations.</p>\n\n<h2>Examples</h2><p>The following examples demonstrate how to calculate the absolute value in creative contexts.</p><div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">1.</span> A submarine dives 300 meters below sea level. What is the absolute value of its depth?</h3><h4 class=\"answer\">Answer</h4><p>Given:</p><ul><li><b>n</b> = -300 meters (since it's below sea level)</li></ul><p>The absolute value of -300 meters is calculated as:</p><p class=\"tabspace\">\\( | -300 | = 300 \\text{ meters} \\)</p><p>Even though the submarine is below sea level, the absolute value represents the distance from sea level, which is 300 meters.</p></div><div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">2.</span> During a game, a player gains 15 points and then loses 20 points. What is the absolute value of the player's net score?</h3><h4 class=\"answer\">Answer</h4><p>Given:</p><ul><li><b>n</b> = 15 - 20 = -5 points (net score)</li></ul><p>The absolute value of -5 points is calculated as:</p><p class=\"tabspace\">\\( | -5 | = 5 \\text{ points} \\)</p><p>While the player’s net score is negative, the absolute value shows the magnitude of the change, which is 5 points.</p></div><div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">3.</span> The temperature drops to -10°C overnight. What is the absolute value of the temperature drop?</h3><h4 class=\"answer\">Answer</h4><p>Given:</p><ul><li><b>n</b> = -10°C</li></ul><p>The absolute value of -10°C is calculated as:</p><p class=\"tabspace\">\\( | -10 | = 10 \\text{°C} \\)</p><p>The absolute value represents the magnitude of the temperature drop, which is 10°C.</p></div><div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">4.</span> An elevator moves 7 floors up and then 3 floors down. What is the absolute value of the elevator's final position relative to its starting point?</h3><h4 class=\"answer\">Answer</h4><p>Given:</p><ul><li><b>n</b> = 7 - 3 = 4 floors</li></ul><p>The absolute value of 4 floors is calculated as:</p><p class=\"tabspace\">\\( | 4 | = 4 \\text{ floors} \\)</p><p>Since the elevator’s final position is positive, the absolute value remains 4 floors.</p></div>"
}