Length

In the study of mathematics and physics, it is essential to distinguish between what we measure and the unit we use. Classify the following concepts in your notebook as either a quantity or a unit of measurement:

• Length

• Metre ($m$)

• Centimetre ($cm$)

• Width of a table

• Kilometre ($km$)

• Distance between two cities

To measure accurately, we must choose the most suitable unit. State which metric unit ($mm$, $cm$, $m$ or $km$) you would use to measure the following objects:

1. a) The length of a paperclip.
2. b) The height of your best friend.
3. c) The distance a school bus travels between two towns.
4. d) The thickness of a latest-generation smartphone screen.

The metric system is a base-10 decimal system because each unit is $10$ times larger than the previous one. Complete the following equalities by converting to the indicated unit:

1. a) $7\text{ m} = \dots\dots\dots\text{ dm}$
2. b) $25\text{ cm} = \dots\dots\dots\text{ mm}$
3. c) $1,5\text{ m} = \dots\dots\dots\text{ cm}$
4. d) $0,8\text{ dm} = \dots\dots\dots\text{ mm}$

When measuring large distances, we use multiples of the metre. Perform the following conversions:

1. a) $3.000\text{ m} = \dots\dots\dots\text{ km}$
2. b) $450\text{ m} = \dots\dots\dots\text{ hm}$
3. c) $12\text{ dam} = \dots\dots\dots\text{ m}$
4. d) $0,5\text{ km} = \dots\dots\dots\text{ hm}$

Three friends are comparing the distances they ran this morning while training for a charity race. Lucía says she ran $4,2 \text{ km}$, Marcos claims to have covered $38 \text{ hm}$ and $15 \text{ dam}$, and Sofía recorded a total of $4.050 \text{ m}$ on her smartwatch.

Order the three friends from greatest to shortest distance covered, expressing all measurements in metres to compare them.

Three friends compare the length of their headphone cables to see which one is longer. The measurements are:

• Marcos: $1,2\text{ m}$

• Lucía: $125\text{ cm}$

• Hugo: $11,5\text{ dm}$

Express all the measurements in centimeters and order them from smallest to largest using the symbol $<$.

A stage of a hiking route through the Sierra de Guadarrama is divided into two sections. The first section measures $3\text{ km y } 450\text{ m}$, and the second section measures $2.100\text{ m}$. How many kilometres is the complete stage?

Sara is designing a case for her tablet. She uses a ruler and observes that the length of the tablet is $24,5\text{ cm}$. If she wants to add a protective border of $5\text{ mm}$ to each of the two ends of the length, what will be the total length of the case in centimetres?

Calculate the perimeter (the sum of all its sides) of a five-a-side football pitch measuring $40\text{ m}$ in length and $200\text{ dm}$ in width. Express the final result in metres.

(Hint: Remember that to add measurements, they must all be in the same unit).

The perimeter of a go-kart track measures $0,85 \text{ km}$. During a race, a driver completed $12$ laps of the track.

Calculate the total distance covered by the driver and express it in compound form (using kilometres, hectometres and decametres).