Question

Which of the following weights would you expect to be suitable for weighing on an ordinary bathroom scale?
a) 2500 μg
b) 5×10−4 kg
c) 4×106 cg
d) 5.5×108 dg
e) 2.0×107 mg

Answer 1

Answer:

c) $4.10^{6} cg$=40Kg

Step-by-step explanation:

To find the answer we have to put all the options in the same unit, so we are going to use Kg.

• a) 2500 μg

μ$=1.10^{-6}$

Replacing the value of μ:

$2500.1.10^{-6} g=\\ 2500.10^{-6} g$

Observation: 1 g = 0.001 Kg, 1 g=$1.10^{-3}$ Kg

$2500.10^{-6} g=\\ =2500.10^{-6}.10^{-3}Kg\\=2500.10^{-9}Kg$

$2500.10^{-9}Kg=0.000002500 Kg$

This number is very small so it's no suitable for weighing on an ordinary bathroom scale.

• b) $5.10^{-4}Kg$

This value is already in kilograms,

$5.10^{-4} kg=0,0005 Kg$

But it's small. It's not suitable for weighing on an ordinary bathroom scale.

• c) $4.10^{6} cg$

Centigrams: cg=$1.10^{-5} Kg$

Then,

$4.10^{6} cg=4.10^{6}.10^{-5}Kg\\ =4.10^{1} Kg\\ =40 Kg$

This value it's suitable for weighing on an bathroom scale.

• d) $5,5.10^{8} dg$

Decigrams: dg=$1.10^{-4} Kg$

Then,

$5,5.10^{8} dg=5,5.10^{8}.10^{-4}Kg\\ =5,5.10^{4} Kg\\ =55000 Kg$

This value is too big for a bathroom scale. Usually the limit for an ordinary bathroom scale is between 140-150 Kgs.

• e) $2,0.10^{7} mg$

Miligrams: mg=$1.10^{-6} Kg$

Then,

$2,0.10^{7} mg=2,0.10^{7}.10^{-6}Kg\\ =2,0.10^{1} Kg\\ =20 Kg$

This could be a right answer too but it all depends on the scale. There are some scales whose  minimum weight is 30Kg. So the right answer is c)