SI unit for length is metre (m). It is a scalar quantity.

**Things you need to know:**

- Accuracy refers to the maximum error encountered when a particular observation is made.
- Error in measurement is normally one-half the magnitude of the smallest scale reading.
- Because one has to align one end of the rule or device to the starting point of the measurement, the appropriate error is thus twice that of the smallest scale reading.
- Error is usually expressed in at most 1 or 2 significant figures.

### Tape

**Equipment:** It is made up of a long flexible tape and can measure objects or places up to 10 – 50 m in length. It has markings similar to that of the rigid rule. The smallest marking could be as small as 0.1 cm or could be as large as 0.5 cm or even 1 cm.

**How to use:** The zero-mark of the measuring tape is first aligned flat to one end of the object and the tape is stretched taut to the other end, the reading is taken where the other end of the object meets the tape.

**Accuracy:** ± 1 cm

### Rule

**Equipment:** It is made up of a long rigid piece of wood or steel and can measure objects up to 100 cm in length. The smallest marking is usually 0.1 cm.

**How to use: **The zero-end of the rule is first aligned flat with one end of the object and the reading is taken where the other end of the object meets the rule.

**Accuracy:** ± 0.1 cm

### Vernier Caliper

**Equipment:** It is made up of a main scale and a vernier scale and can usually measure objects up to 15 cm in length. The smallest marking is usually 0.1 cm on the main scale.

It has:

- a pair of external jaws to measure external diameters
- a pair of internal jaws to measure internal diameters
- a long rod to measure depths

**How to use:** The jaws are first closed to find any zero errors. The jaws are then opened to fit the object firmly and the reading is then taken.

**Accuracy:** ± 0.01 cm

**Note:** Check out How To Read A Vernier Caliper to learn how to read a vernier caliper.

### Micrometer Screw Gauge

**Equipment:** It is made up of a main scale and a thimble scale and can measure objects up to 5 cm in length. The smallest marking is usually 1 mm on the main scale (sleeve) and 0.01 mm on the thimble scale (thimble). The thimble has a total of 50 markings representing 0.50 mm.

It has:

- an anvil and a spindle to hold the object
- a ratchet on the thimble for accurate tightening (prevent over-tightening)

**How to use:** The spindle is first closed on the anvil to find any zero errors ( use the ratchet for careful tightening). The spindle is then opened to fit the object firmly (use the ratchet for careful tightening) and the reading is then taken.

**Accuracy:** ± 0.01 mm

** Note:** Check out How To Read A Micrometer Screw Gauge to learn how to read a micrometer screw gauge.

### Parallax Error

For accurate measurement, the eye must always be placed vertically above the mark being read. This is to avoid parallax errors which will give rise to inaccurate measurement.

Parallax errors affects the accuracy of the measurement. If you consistently used the incorrect angle to view the markings, your measurements will be displaced from the true values by the same amount. This is called **systematic error**.

However, if you used different angles to view the markings, your measurements will be displaced from the true values by different amounts. This is called **random error**.

#### Parallax error for micrometer screw gauge:

### Zero Error

#### Zero Errors of Vernier Caliper

When the jaws are closed, the vernier zero mark coincides with the zero mark on its fixed main scale.

Before taking any reading it is good practice to close the jaws or faces of the instrument to make sure that the reading is zero. If it is not, then note the reading. This reading is called “zero error”.

The zero error is of two types:

- Positive zero error; and
- Negative zero error.

##### Positive Zero Error

If the zero on the vernier scale is to the **right** of the main scale, then the error is said to be **positive** zero error and so the zero correction should be** subtracted** from the reading which is measured.

##### Negative Zero Error

If the zero on the vernier scale is to the **left** of the main scale, then the error is said to be **negative** zero error and so the zero correction should be **added** from the reading which is measured.

#### Zero Error for micrometer screw gauge

##### Positive Zero Error

If the zero marking on the thimble is below the datum line, the micrometer has a positive zero error. Whatever reading we take on this micrometer we would have to subtract the zero correction from the readings.

##### Negative Zero Error

If the zero marking on the thimble is above the datum line, the micrometer has a negative zero error. Whatever readings we take on this micrometer we would have to add the zero correction from the readings.

**Note:** You do not have to memorise positive error = subtract, negative error = add, just think this through for a while. It is rather straightforward and intuitive.

### Self-Test Questions

**How can you avoid parallax errors when measuring a length with a metre rule?**

### Show/hide answers

The first thing is to place the metre rule such that it’s edge is incident on the length, which will allow easy and accurate reading of the markings on the metre rule. The second thing is to place your eye vertically above the required points – “starting point” and “ending point”.

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