Import Question JSON

Current Question (ID: 7347)

Question:

$\text{The number of significant figures in the numbers 5005, 500.0, and 126,000 are, respectively:}$

Options:

1. $\text{2, 4, and 3}$
2. $\text{4, 1, and 3}$
3. $\text{4, 4, and 6}$
4. $\text{4, 4, and 3}$

Solution:

$\text{Hint: The term significant figures actually refers to particular digits in a number}$\n\n$\text{Significant figures are meaningful digits that are known with certainty plus one which is estimated or uncertain.}$\n\n$\text{The certain rule for determining the number of significant figures are as follows:}$\n\n$\text{Zeros between two non-zero digits are significant. Thus, 2.005 has four significant figures.}$\n\n$\text{Zeros at the end or right of a number are significant, provided they are on the right side of the decimal point. For example, 0.200 g has three significant figures. But, if otherwise, the terminal zeros are not significant if there is no decimal point.}$\n\n$\text{For example, 100 has only one significant figure, but 100. has three significant figures and 100.0 has four significant figures.}$\n\n$\text{Now let's apply these rules to the given numbers:}$\n\n$\text{5005: All digits are significant (there are no terminal zeros without a decimal point). So there are 4 significant figures.}$\n\n$\text{500.0: All digits are significant. The decimal point makes the trailing zeros significant. So there are 4 significant figures.}$\n\n$\text{126,000: Only the digits 1, 2, and 6 are significant. The three trailing zeros are not significant because there is no decimal point. So there are 3 significant figures.}$\n\n$\text{Hence, option fourth (4, 4, and 3) is the correct answer.}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}