## Vernier Callipers

- The Vernier callipers has two scales.The
**main scale**is contained on the steel frame and is graduated in centimeters but also has millimeters divisions. The**Vernier scale**is contained on the sliding jaw and has 10 equal divisions. - The length of Vernier scale is 0.9cm implying that each division of the vernier scale is 0.09cm.
- The difference between the main scale division and the Vernier scale division is called the least count. This is the accuracy of the Vernier callipers i.e. (0.9-0.09)cm=0.01cm.
- Vernier callipers has inside jaws used to measure internal diameters and outside jaws used to measure external diameters.

### Using Vernier Calipers

- Place the object whose diameter(length) is to be measured between the outside jaws.
- Close the jaws till they just grip the object.
- Record the reading of the main scale, opposite and to the left of the zero mark of the vernier scale.
- Read the vernier scale mark that coincides exactly with a main scale mark and multiply it with the least count(accuracy) of the Vernier callipers. This is the Vernier scale reading.
- The sum of the vernier scale reading and the main scale reading gives the diameter(length) of the object.
**Vernier callipers reading = vernier scale reading + main scale reading**

#### Example

Main scale reading: 10.0 cm

Vernier scale reading: 0.02 cm (Alignment of scale lines)

Vernier Callipers reading = Main scale reading + Vernier scale reading: = 10.0 cm + 0.02 cm = 10.02 cm

#### Exercise

- Describe how you would measure the internal diameter of 100cm
^{3}beaker using vernier callipers. - Write down the vernier calipers reading in diagram (a)(b) and (c) showed below.

### Zero Error of the Vernier Callipers

- Vernier callipers is said to have a zero error if the zero marks of the main scale and vernier scale do not coincide when the jaws of the calipers are closed without an object.
- There are two types of errors:

#### i) Positive Error

- Occurs when the zero mark of the main scale is to the left of the zero mark of the vernier scale.

**Example**

This vernier callipers has a zero error of +0.13cm

**Correction of the Positive Error**

- The positive error is corrected by subtracting the zero error from the reading obtained.

#### (ii) Negative Error

- Occurs when the zero mark of the main scale is to the right of the zero mark of the vernier scale.

**Example**

This vernier callipers has a negative error of -0.02 cm

**Correction of the Negative Error**

- The negative error is corrected by adding zero error to the reading obtained.

**Exercise**

The figure below shows a vernier callipers

State the correct reading of the scale if the instrument has a zero error of –0.02cm.

## Micrometer Screw Gauge

- It is used to measure very small lengths such as the diameter of a thin wire.

- The micrometer screw gauge consist of a thimble which carries a circular rotating scale known as thimble scale and a spindle which moves forward and backwards when the thimble is rotated.
- The sleeve has a linear scale in millimeters and half millimeter called sleeve scale and the thimble has a circular scale of 50 or 100 equal divisions.
- The ratchet at the end of the thimble prevents the user from exerting more pressure on an object when the micrometer screw gauge is in use.
- The distance moved by the spindle in one complete rotation of the thimble is called the pitch of the micrometer. A spindle moves forward or backwards by 0.5mm per a complete rotation of the thimble with 50 divisions.
- Therefore each division of thimble scale represents a spindle travel of
^{0.5mm}/_{50}= 0.01mm - This means that if the thimble rotates through one division, the spindle moves backwards or forward by 0.01mm. This is the least count(accuracy) of the micrometer screw gauge.
- Least count of the screw gauge is defined as the distance moved bythe spindle when the thimble rotates through one division.

### Using a micrometer screw gauge

- Place the object whose diameter/length is to be measured between the anvil and the spindle.
- Close the micrometer using ratchet until the object is held gently between the anvil and the spindle. Note that the ratchet should slip only once when the grip is firm enough to give accurate reading.
- Read the sleeve scale and record it as:
**Sleeve scale reading**= --------------mm - Read the thimble scale and multiply it by the least count of the screwgauge(0.01mm) and record it as:
**Thimble scale reading**=……x0.01=………….mm - Micrometer reading=sleeve scale reading +thimble scale reading

**Example**

Sleeve scale reading: 2.5 mm

Thimble scale reading: 0.38 mm

Micrometer reading: 2.88 mm

### The zero error of the micrometer screwgauge

It occurs if the zero mark of the thimble scale does not coincide with the horizontal(centre) line of the sleeve scale when the micrometer is closed without an object.

#### Positive error of micrometer screw gauge

- Occurs when the zero mark of the thimble scale is below the horizontal line.
- The positive error is corrected by subtraction of the erro rfrom the reading given by the micrometer screw gauge.

#### Negative error

- It occurs when the zero mark of the thimble scale is above the horizontal line of the sleeve scale.
- The negative error is corrected by adding the error to the reading obtained by the screw gauge.

## Significant Figures

- Significant figures refer to the number of digits used to specify the accuracy of a value.

**Note**:

- The digits 1-9 are all significant when they appear in a number.
- The first digit from the left of a number is the first significant figures.
- The number of significant figures is determined by counting the number of digits from the first significant figure on the left.
- Zero may be significant or not depending on the position of the digit.
- If zero occurs between non- zero digits it is significant e.g.1004(4sf),15607(5sf),180.45(5sf)
- When zero occurs at the left end of a number it is not significant e.g.0.00546(3sf),0.0002(1sf)
- If the zero occurs at the right hand end of an integer it may or may not be significant. E.g.60000. It can be correct to 1 significant figure therefore the zeros are not significant. If all the zeros are counted(ended) then it will be correct to 6 significant figures.
- If the zero occurs at the right hand end after the decimal point,it is always significant e.g.2.000(4sf), 3.0(2sf)

**Exercise**

Write down the number of significant figures in each of the following

- 40000
- 609
- 0.000675
- 5237.8
- 0.0000600
- 0.002304

## Standard Form

- This is a way of writing a number especially a very large or very small number in which only one integer appears before the decimal point.
- A positive number is said to be in standard form when written as A x 10
^{n}, where A is such that 1≤A<10 and the index n is an integer e.g.3567=3.567x10^{3} - If the number lies between zero and 1 then the index n becomes a negative e.g.0.0003567=3.567x10
^{-4}

**Exercise**

Express the following in cm giving the answers in standard form