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

c)
`4.10^(6) cg`=40Kg

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)