# Measuring Length

## Introduction to Measuring Length

If I asked you how tall you are, you could say, ‘I am fairly tall'. If asked for a more specific idea, you could even say ‘My height is more than the height of most of the boys in my class'. However, to give me an accurate idea of how tall you are, you would need to use a number, like say 1.73 metres or 5 feet 8 inches. This is why we need to move away from qualitative measures of things and start to quantify them in standard terms. This allows for everyone to understand what is being talked about and allows us to be more accurate and informed about the decisions we make.

## The Big Idea: What Does Length Represent?

The length essentially represents how long an object is. Length could tell me how tall you are, or the length of the fence of your lawn, or the distance between those two places. It is one of the fundamental units of measurement, along with mass and time.

### Units of length

We spoke about how your height and the distance from your home to school are both lengths. But a length (or any dimension for that matter), cannot be expressed only by a number. I mean, if you tell me you are 1.73 tall, I wouldn’t understand what you are saying. But if you tell me you are 1.73 metres tall, I would understand. This is where the whole standard measure comes in. Internationally, the **metre** is the **standard unit of measurement for length**. Therefore, it removes any and all arbitrariness from a measurement when length is represented in metres, highlighting the importance and need for units.

We start from the small millimetre, go on to a centimetre, and then metre. This is the relationship between these metric units:

1 kilometre = 1000 metres

1 metre = 100 centimetres

1 centimetre = 10 millimete

Why do we need so many different units of measurement? Well, let’s take a look at an example:

Length of an earthworm = 350 mm = 35 cm = 0.35 m

Distance between New Delhi and New York City = 11747 km = 11,747,000 m = 11 .747 million metre

So, “Why are there so many units!?”. The simple explanation is that, an earthworm’s length could most easily be described in centimetres or millimetres, whereas the distance between two cities in two different continents can best be described in kilometres. That is why we need all these units.

### Conversion of Units

We spoke about the different units used to describe different lengths. But it is not enough to know what the units are, and we also need to know how to convert one unit to the other. A boy's height in metres might be the most convenient to measure and record, but sometimes this number is needed in centimetres. Again, your school might be at a distance of 1.5 kilometres from your house, but you might also want to describe that distance as 1500 metres.

So here are the rules again, for converting all the metric units, and we will move from the bigger to the smaller units.

So, if you need to convert 1.25 kilometres to smaller units, this is how the calculation would be done:

1.25 kilometre = (1.25 x 1000) metres = 1250 metres

1250 metres = (1250 x 100) centimetres = 125000 centimetres

125000 centrimetres = (125000 x 10) millimetres = 1250000 millimetre

What about the other way round? Say you want to convert 57 millimetres into bigger units? This is how the calculation would look like:

\(\begin{align} & 57{\text{ millimetres}} = \left( {\frac{{57}}{{10}}} \right){\text{ centimetres}} = 5.7{\text{ centimetres}}\\ & 5.7{\text{ centimetres}} = \left( {\frac{{5.7}}{{100}}} \right){\text{ metres}} = 0.057{\text{ metres}}\\ & 0.057{\text{ metres}} = \left( {\frac{{0.057}}{{1000}}} \right){\text{ kilometres}} = 0.000057{\text{ kilometres}} \end{align}\)

### How to Use a Standard Ruler

- A standard metric ruler is to be read from left to right, after aligning the zero mark of the ruler with the left extremity of the line segment whose length is to be measured.
- The basic unit in a metric ruler is a centimetre, and the centimetre values are written clearly beside each centimetre, and marked in longer lines.
- The distance between two consecutive centimetre lines is divided into ten smaller distances of 1 millimetre each because 1 centimetre = 10 millimetres.
- See which line the right extremity of the line segment aligns with. That is the length of your line segment.
- Another common misconception is that you need to start from the very edge of every ruler. You DON’T. The point that you should start measuring from is the point which is marked as 0 on the ruler for the most consistent and accurate results.