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Applied Math I

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Overview

In this lesson you will learn about:

● The different kinds of calipers.

● The components of a typical caliper.

● Caliper usage.

● Reading English and metric

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Introduction

● Calipers are tools used in home, small

shop, and industrial settings.

● They are used to make precise length

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Introduction

● Some reasons for their popularity

include:

● Wide measuring range (usually 0 - 6”).

English and metric scales are usually

found on the same instrument.

● Many different kinds of measurements

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Introduction

● While both micrometers and calipers

can make outside length

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Introduction

● Calipers can also make inside

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Introduction

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Introduction

● There are three types of calipers.

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Introduction

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Introduction

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Introduction

● In this lesson, we will concentrate on

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Introduction

● These are the main features of a typical

vernier caliper:

Jaws (for outside measurements)

Small jaws (for inside measurements)

Metric vernier scaleMetric fixed scale

English vernier scaleEnglish fixed scale Beam

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Reading a Caliper: English

● To determine the length of an object in

inches, you must be able to read the English scale on the caliper.

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Reading a Caliper: English

● Most of the measurement information is

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Reading a Caliper: English

● Where do you start?

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Reading a Caliper: English

● The zero line acts as a pointer, and tells

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Reading a Caliper: English

● Reading a caliper is a process of

collecting measurements from the fixed scale and the vernier scale.

● To stay organized, write down each

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Reading a Caliper: English

● The largest fixed scale divisions are the

one-inch intervals, so start there first.

Since the zero line is between 1” and 2”, we know the object being measured is at least 1” long.

Measurements

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Reading a Caliper: English

● The one-inch intervals are broken down

into ten smaller ones. Each of these is worth a tenth of an inch (0.1”).

0.1” Measurements

1 0.2”0.3”0.4”0.5”

Because the zero line did not go beyond any of the one-tenth lines, you won’t add any of these to the measurement total.

0.0

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Reading a Caliper: English

● Notice that between any one-tenth

interval, there are four spaces. Each of

these is 0.025” (0.1” ÷ 4 = 0.025” )

0.025” Measurements

1

0.050”0.075”

0.0

The zero line has gone past two

of 0.025 lines but it hasn’t quite

gone beyond the third one.

Two 0.025” lines equals 0.050”. Add that to your measurement total.

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Reading a Caliper: English

● The last step is to get a reading from

the vernier scale.

0.001” Measurements 1 0.002” 0.003” 0.0

Each line on the vernier scale is worth 0.001”

0.050

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Reading a Caliper: English

● What you are looking for is a place

where one of the lines on the vernier “lines up” with a line on the fixed scale.

Measurements

1 0.0 0.050

It might be difficult to see on the computer screen, but

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Reading a Caliper: English

● Add the vernier scale number to your

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Reading a Caliper: English

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Reading a Caliper: English

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Reading a Caliper: English

● Determine the number of whole

inches...

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Reading a Caliper: English

● ...the number of tenths (0.1”)...

1 0.0

The zero line did not go

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Reading a Caliper: English

● ...the number of 0.025” lines...

1 0.0

The zero line is beyond the second 0.025” line but not the third.

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Reading a Caliper: English

● …and finally the vernier reading.

1 0.0

The 0.020” line seems to line up best with a

division on the fixed scale. 0.050

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Reading a Caliper: English

● The sum of all these measurements is

1.070”.

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● Let’s obtain a reading from this caliper:

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Reading a Caliper: English

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Reading a Caliper: English

● Determine the number of whole

inches...

0

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Reading a Caliper: English

● …the number of tenths (0.1”)...

0

The zero line on the vernier scale has gone beyond the 0.5” line.

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Reading a Caliper: English

● …the number of 0.025” lines...

0

The zero line on the vernier scale has gone beyond the first 0.025” line but not the second.

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Reading a Caliper: English

● …and finally the vernier reading.

0 0.5

0.025 The 0.019” line

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Reading a Caliper: English

● The sum of all these measurements is

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● Let’s obtain a reading from this caliper:

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Reading a Caliper: English

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Reading a Caliper: English

● Determine the number of whole

inches...

1

The zero line has gone

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Reading a Caliper: English

● …the number of tenths (0.1”)...

1 The zero line on the vernier scale has gone beyond the 0.6” line but not quite to the 0.7” line

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Reading a Caliper: English

● …the number of 0.025” lines...

1 The zero line on the vernier scale has gone beyond three

of the 0.025” lines. This is equal to 0.075”.

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Reading a Caliper: English

● …and finally the vernier reading.

1 0.6 0.075

The 0.014” line

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Reading a Caliper: English

● The sum of all these measurements is

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● Do this problem on your own. Click to

see the answer.

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Reading a Caliper: English

● Determine the number of whole

inches...

4

The zero line has gone

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Reading a Caliper: English

● …the number of tenths (0.1”)...

4 The zero line on the vernier

scale has gone beyond the 0.5” line but not the 0.6” line

(53)

Reading a Caliper: English

● …the number of 0.025” lines...

4 The zero line on the vernier scale has gone beyond two

of the 0.025” lines. This is equal to 0.050”.

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Reading a Caliper: English

● …and finally the vernier reading.

4 0.5 0.050

The 0.013” line

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Reading a Caliper: English

● The sum of all these measurements is

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Introduction and

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Reading a Caliper: metric

● As you are about to see, working with

the metric portion of a vernier caliper is a bit easier to deal with.

● You only need to make two readings:

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Reading a caliper: metric

● Start by obtaining a measurement from

the fixed scale...

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Reading a caliper: metric

● Use the zero line on the vernier to

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Reading a caliper: metric

Each number printed on the

metric scale represents centimeters.

6 cm

However, since your final reading is supposed to be in millimeters, you need view these amounts as millimeters.

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Reading a caliper: metric

One “trick” is to mentally add a 0 (zero) behind each centimeter number.

0

60 mm

0 0 0 0

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Reading a caliper: metric

Since there are ten spaces between each

numbered interval, these smallest spaces must be 1 mm each.

For example, note the ten spaces in this interval. The smallest interval on this

scale is 1mm. For example, this

(63)

Reading a caliper: metric

As you can see in this problem, we have a fixed scale measurement of 63 mm.

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Reading a caliper: metric

To finish we must obtain a reading from the metric vernier scale.

On this scale, each line represents 0.05 mm.

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Reading a caliper: metric

Just as we did on the English vernier scale, we need to look for a place where a line from the fixed scale “lines up” with a line on the vernier.It appears that these two

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Reading a caliper: metric

So based upon the two readings (one from the fixed scale, and one from the ruler) the length must be 63 mm + .50 mm = 63.50 mm

63 mm

.50 mm +

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Reading a caliper: metric

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Reading a caliper: metric

● First take a reading from the fixed scale.

Use the zero line from the vernier to help.

Remember that we need to read the fixed scale in terms of millimeters. The zero line is close, but not quite up to the 20 mm line. It has gone beyond the 19 mm line however.

19 mm

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19 mm

Reading a caliper: metric

● To finish, read the vernier scale.

It appears that these two lines, “line up” the best.

This is read as .35 mm

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19 mm

Reading a caliper: metric

● The final reading then is 19.35 mm.

.35 mm +

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Reading a caliper: metric

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Reading a caliper: metric

● Use the zero line from the vernier scale

to help get a reading on the fixed scale.Remember that we need to read the

fixed scale in terms of millimeters. The zero line is directly above the

8 mm line.

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Reading a caliper: metric

● That’s it! Since the zero line on the

vernier matched up with a line on the fixed scale, you quit right there.

(76)
(77)

Reading a caliper: metric

● Do this one on your own. Click to see

(78)

● Start with the fixed scale reading.

Remember that we need to read the fixed scale in terms of millimeters. The zero line is close, but not quite to the 97 mm line. It has gone

beyond the 96 mm line however.

96 mm

0 0 0

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96 mm

Reading a caliper: metric

● To finish, read the vernier scale.It appears that these two lines, “line up” the best.

This is read as .60 mm

(80)

96 mm

Reading a caliper: metric

● The final reading then is 96.60 mm.

.60 mm +

References

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