Mass

In the study of matter, it is essential not to confuse what we measure with the tool we use. Classify the following terms in the table according to whether they correspond to a quantity, a unit of measurement or a measuring instrument:

Mass, Gram, Balance, Kilogram, Scales, Capacity, Tonne, Dynamometer.

It is very important to know how to choose the appropriate unit depending on the object we are weighing. Match each of the following objects with the measurement that seems most realistic:

1. A worker ant.

2. A full can of drink.

3. A laptop.

4. A delivery lorry.

Possible measurements: $2\text{ kg}$, $8\text{ t}$, $3\text{ mg}$, $330\text{ g}$.

To convert from one unit to another in the metric system, we must multiply or divide by 1 followed by zeros. Complete the following equalities by converting to the indicated unit:

1. a) $45\text{ kg} = \dots\dots\dots\text{ g}$
2. b) $1.200\text{ mg} = \dots\dots\dots\text{ g}$
3. c) $0,5\text{ hg} = \dots\dots\dots\text{ dag}$
4. d) $34,7\text{ dg} = \dots\dots\dots\text{ cg}$

In a science laboratory, three students have weighed the same rock sample. Each has written down the result in a different unit:

• Student A: $0,45\text{ kg}$

• Student B: $4.200\text{ dg}$

• Student C: $46\text{ dag}$

Express all measurements in grams and order the students from lowest to highest according to the mass they obtained.

Express the following quantities in simple form (using a single unit), converting them to the unit indicated in each case:

1. a) $3\text{ kg y } 450\text{ g}$ $\rightarrow$ into grams.
2. b) $5\text{ dag, } 2\text{ g y } 8\text{ dg}$ $\rightarrow$ into decigrams.
3. c) $1\text{ t y } 200\text{ kg}$ $\rightarrow$ into kilograms.
4. d) $4\text{ hg y } 5\text{ cg}$ $\rightarrow$ into centigrams.

Order the following masses of electronic components used in manufacturing a smartphone from smallest to largest. To compare them, convert all units to milligrams ($mg$):

• Camera sensor: $0,0042\ kg$

• Main microchip: $1,85\ g$

• Fastening screw: $85\ cg$

• Charging connector: $12,4\ dg$

To prevent back injuries, it is recommended that a school backpack does not exceed $10 \%$ of the student's weight. Lucas weighs $45\ kg$ and has weighed the items he is carrying to class today:

• Books and notebooks: $2,8\ kg$

• Pencil case with stationery: $350\ g$

• English dictionary: $6,5\ hg$

• Full water bottle: $75\ dag$

Calculate the total mass of the backpack in kilograms and determine whether Lucas is carrying a safe weight for his back.

A delivery lorry has a maximum authorised load of $3,5\ t$. It is currently carrying $18$ pallets of milk boxes weighing $125\ kg$ each. The driver needs to pick up $12$ bags of animal feed weighing $450\ hg$ each at a warehouse.

Will he be able to load the bags of animal feed without exceeding the lorry's mass limit? Justify your answer by performing the calculations in kilograms.

A balance scale is in equilibrium. On the left pan there is a full jar of honey weighing $1,25$ $kg$. On the right pan there is a $5$ $hg$ weight, a $25$ $dag$ weight and the same jar of honey, but empty. Calculate the mass of the honey inside the jar and the mass of the empty jar separately, expressing both results in grams.