The International System of Units

When the D&T 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.

From this list of words, state which are quantities and which are units: length, second, mass, metre, 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.

Write the name and symbol of the International System unit corresponding to each fundamental quantity: length, mass, time, temperature, electric current, and amount of substance.

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

On the label of Hugo's mobile charger it says "output: $2\ \text{A}$". a) What quantity is measured in amperes? b) Chemists use another fundamental quantity to count particles: what is it called and what is its International System unit?

Speed is calculated by dividing the distance travelled 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 metre 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 metre and write its symbol. b) Do the same for volume. The figure shows the cube referred to in part c:

1. c) The litre 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 metres $1\ \text{L}$ 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 millimetres are in a metre?

A team of scientists from Japan sends a report to another in Spain stating: "the cable measures $12$". a) What problem is there with this value? b) How is it solved if everyone uses the International System? c) Why do you think the SI is used worldwide instead of each country having its own?

For a long time, the "standard metre" 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?