Measuring Length with a Ruler

What you will learn

• Use a ruler to measure a length in centimetres, lining up zero correctly.
• Read the small marks between the numbers as millimetres.
• Find a length when the object does not start at zero.

Before you start: you should know that a unit is an agreed amount to measure with. Units of Measurement covers this, and Comparing Length, Mass and Capacity shows why equal units matter.

The idea

A ruler is a measuring stick with equal marks along it. Each mark is the same distance from the next, so you can count the marks instead of laying down paper clips. Most rulers show centimetres, written cm, and millimetres, written mm.

Reading a ruler

The long marks with numbers are centimetres. The distance from one number to the next is $1$ cm. The short marks in between are millimetres. There are $10$ millimetres between each pair of numbers, so $1$ cm $= 10$ mm. The mark halfway between two numbers is $5$ mm, which is half a centimetre.

Line up zero

Put one end of the object at the zero mark. Read the number at the other end. That number is the length.

Check three things every time. The ruler lies flat against the object. The object touches the ruler along its length. The end really is at zero, not at the edge of the ruler, because there is often a small gap before the zero mark.

When the object does not start at zero

Sometimes an object sits somewhere else on the ruler, or the ruler’s end is worn. You can still measure it. Read the number at each end and take the smaller from the bigger.

Count the gaps between marks, not the marks themselves. From $2$ to $8$ there are $6$ gaps, so the length is $6$ cm. Counting the marks gives $7$, which is one too many.

Between the numbers

Most lengths do not land exactly on a number. Look at the small marks. If an end is $4$ marks past the $3$, the length is $3$ cm and $4$ mm.

You can write this as a decimal, because each millimetre is a tenth of a centimetre. So $3$ cm and $4$ mm is $3.4$ cm, which is also $34$ mm.

Comparing with a ruler

Once you have measured in the same unit, you can compare. Find the difference by subtracting.

Worked examples

Example 1: A whole number of centimetres

A paper clip starts at $0$ and ends at $3$ on a ruler. How long is it?

1. The clip starts at zero.
2. The other end lines up with $3$.

Answer: $3$ cm.

Example 2: Starting somewhere else

A stick starts at the $4$ cm mark and ends at the $11$ cm mark. How long is it?

1. The stick does not start at zero, so subtract the readings.
2. $11 - 4 = 7$.
3. Check by counting gaps: from $4$ to $11$ there are $7$ gaps.

Answer: $7$ cm.

Example 3: Centimetres and millimetres

A bean is $2$ cm and $7$ mm long. Write its length in millimetres and as a decimal in centimetres.

1. $2$ cm is $2 \times 10 = 20$ mm.
2. Add the $7$ mm: $20 + 7 = 27$ mm.
3. As a decimal in cm: $27 \div 10 = 2.7$ cm.

Answer: $27$ mm, which is $2.7$ cm.

Do not start measuring at the end of the ruler. The first mark is often not zero, because of a small gap. Look for the number $0$ and line the object up with that.

Why it matters

Measuring with a ruler is how you check that a picture frame fits, cut paper to size or see how much a plant has grown. Doctors measure height, tailors measure cloth and builders measure wood. The same idea carries over to longer lengths in metres and kilometres. And because millimetres are tenths of a centimetre, reading a ruler is the first time many people use decimals.