The International System of Units

When the shop teacher says that the workshop table measures "6 handspans", she is comparing its length to that of her hand, as shown in the figure.

Explain in your own words what it means to measure a quantity and give a new example, different from the table.

Which quantity is measured with each of these instruments? Observe them in the figure:

1. a) A ruler.
2. b) A balance.
3. c) A stopwatch.
4. d) A thermometer.

From this list of words, state which are quantities and which are units: length, second, mass, meter, temperature, ampere, time, kilogram.

In the final of the $100\ \text{m}$ sprint, the scoreboard showed only this: "WINNER: $9.98$", as seen in the figure.

1. a) What is missing from this value for it to be a complete measurement? b) Complete the scoreboard with the appropriate unit and its symbol.

Emma's little brother wrote in his notebook: "My mass is $42\ \text{Kg}$ and my height is $1.45\ \text{M}$". There are two errors in the unit symbols. Find them and write the sentence correctly.

On the refrigerator at home there is a dial marked "$4\ \celsius$". a) What quantity does this dial regulate? b) What is the International System (SI) unit for this quantity? c) In what unit do we usually give it at home and on the news?

In a warehouse, three measurements without units are recorded: $3$; $40$; $45$. They correspond to the length of a shelving unit, the mass of a bag of animal feed, and the time taken for the freight elevator to go up, but they are out of order. Assign each number to its quantity and add the most suitable International System unit.

Speed is calculated by dividing the distance traveled by the time taken. a) Is it a fundamental or a derived quantity? Explain the difference. b) Deduce its unit in the International System from those of the meter and the second, and write its symbol correctly.

Classify these quantities as fundamental or derived: length, surface area, mass, volume, time, speed. Explain what criterion you used to decide.

Surface area is obtained by multiplying two lengths, and volume by multiplying three. a) Deduce the International System unit for surface area from the meter and write its symbol. b) Do the same for volume. The figure shows the cube referred to in part c:

1. c) The liter is not an SI unit, but it is widely used: knowing that $1\ \text{L}$ is the volume of a cube with an edge of $10\ \text{cm}$, calculate how many cubic meters $1\ \text{L}$ is equivalent to.

In the word "kilogram", the prefix "kilo-" appears, which means thousand. a) What do the prefixes in $\text{km}$, $\text{mm}$, and $\text{ms}$ mean? b) Write the full name of each unit and the quantity it measures. c) How many millimeters are in a meter?

In an American online store, a backpack weighs "$3\ \text{lb}$" (pounds) and measures "$18\ \text{in}$" (inches). a) Are these International System units? b) What do you need to know to get an idea of its weight and size? c) What advantage would there be if the store also provided kilograms and centimeters?

For a long time, the "standard meter" and "standard kilogram" existed: metal objects kept in a museum in Paris that served as the global reference. a) What problem arises if the standard kilogram gets dirty or wears down a little? b) Today units are defined using natural constants, such as the speed of light: why is this a better system? c) If all old standard prototypes in the world disappeared at once, would the units be lost? Explain your reasoning.

In 1999, the Mars Climate Orbiter space probe was lost on Mars because one team of engineers made calculations in pounds and another in newtons, and nobody converted the units. a) Explain in your own words what went wrong. b) If one pound-force is equal to about $4.45\ \text{N}$, how many newtons is a thrust of $100$ pounds-force equal to? c) The probe's computer expected the value in newtons and received the bare number $100$: was the applied thrust greater or smaller than expected? By how many times?