Question

The mass of a box measured by a grocer’s balance is 2.3 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. The total mass of the box is –
A) 2.30 kg
B) 2.340 kg
C) 2.34 kg
D) 2.3 kg

Answer 1

Hint: We need to understand the working of a physical weighing machine, its scaling and calibration techniques and the precision of the weighing machine to find the correct answer to this question. We can use the number of significant digits technique for this.

Complete Step-by-Step Solution:
We know that the weighing machines which we use in our daily life have different scales of measurement. The normal weight balance used in grocery stores and stalls can weigh up to 20 to 100 kg of mass, whereas the clinical weighing machines can measure up to 200 kg. The precision of the weighing machine depends on the number of digits the weighing machine will give us.

A digital weighing machine which can measure a minimum of 50g will display 0.000kg as long as the mass on the machine is less than 25g. For a mass greater than 25 g it will display as 0.050g.
We are given that the weighing machine shows 2.3 kg for a box kept on the device. This means that the least count of the instrument should be 100g. So, any mass greater than 50 g will only show 0.1kg on the display.
We are adding two masses of 20.15g and 20.17g into the box. The total mass of the box will be then –
\[\begin{align}
  & \text{Total mass = 2}\text{.3kg + 0}\text{.02015kg + }\text{0}\text{.02017kg} \\
 & \therefore Mass=2.34032kg \\
\end{align}\]
But the least count on the device is 100g. so only one digit after the decimal point will be displayed after rounding off to nearest hundreds, i.e., in this case, 2.3 kg itself.

Hence, the correct answer is option D.

Note:
We can see that the two options in this problem give solutions which are similar, i.e., 2.3 kg and 2.30 kg. We should be careful that the zero after the decimal has specific meaning and will give as a wrong answer as the mass is not accurate to 2.30kg.