Import Question JSON

Current Question (ID: 8770)

Question:

$\text{In which of the following, the number of significant figures is different from that in the others?}$

Options:

1. $\text{2.303 kg}$
2. $\text{12.23 m}$
3. $0.002 \times 10^5 \text{ m}$
4. $2.001 \times 10^{-3} \text{ kg}$

Solution:

$\text{Hint: Recall the rules for significant figures.}$ $\text{Step 1: Recall the rules for significant figures.}$ $\text{(i) All zeros between 2 non-zero digits are significant}$ $\text{(ii) In numbers less than 1, all zeros between decimal places & non-zero digits are significant}$ $\text{(iii) In scientific notation, significant figures are given by numerical values.}$ $\text{Step 2: Find significant figures in all options.}$ $\text{To find the option where the number of significant figures is different from the others, let's analyze each option:}$ $\text{1. 2.303 kg, all digits are significant, so the number of significant figures is 4.}$ $\text{2. 12.23 m all digits are significant, so the number of significant figures is 4.}$ $\text{3. } 0.002 \times 10^5 \text{ m, the number 0.002 has only one significant figure because the leading zeros are not significant. Hence, the number of significant figures is 1.}$ $\text{4. } 2.001 \times 10^{-3} \text{ kg, all digits are significant, so the number of significant figures is 4.}$ $\text{Therefore, } 0.002 \times 10^5 \text{ m has 1 significant figure, while the others have 4 significant figures.}$ $\text{Hence, option (3) is the correct answer.}$

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
}