Question

If \(N_A\), \(N_B\) and \(N_C\) are the number of significant figures in \(A=0.001204\text{ m}\), \(B=43120000\text{ m}\) and \(C=1.200\text{ m}\) respectively then

• A. \(N_A=N_B=N_C\)
• B. \(N_A\gt N_B\gt N_C\)
• C. \(N_A\lt N_B\lt N_C\)
• D. \(N_A\gt N_B\lt N_C\)

Hint:

Leading zeros are never significant, while zeros between non-zero digits and trailing zeros after a decimal point are significant.

Answer 1

The Correct Option is A

Step 1: Count significant figures in \(A=0.001204\).
Leading zeros are not significant.
The digits counted are \[ 1,\;2,\;0,\;4 \] Here, the zero between non-zero digits is significant.
Hence, \[ N_A=4 \]

Step 2: Count significant figures in \(B=43120000\).
Trailing zeros without a decimal point are not significant.
The significant digits are \[ 4,\;3,\;1,\;2 \] Hence, \[ N_B=4 \]

Step 3: Count significant figures in \(C=1.200\).
Trailing zeros to the right of a decimal point are significant.
Thus, the significant digits are \[ 1,\;2,\;0,\;0 \] Hence, \[ N_C=4 \]

Step 4: Compare the values.
We obtain \[ N_A=4,\quad N_B=4,\quad N_C=4 \] Therefore, \[ N_A=N_B=N_C \]

Step 5: Final Answer.
Hence, the correct option is \[ \boxed{N_A=N_B=N_C} \]