DOCUMENT RESUME
ED 327 701
CE 056 763
AUTHOR
TITLE
INSTITUTION
SPONS AGENCY
PUB DATE
CONTRACT
NOTE
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Engelbrecht, Nancy; And Others
Rounding Decimal Numbers to a Designated Precision.
Fundamentals of Occupational Mathematics. Module
2.
Central Community Coll., Grand Island, NE.
Office of Vocational and Adult Education (ED) ,
Washington, DC.
90
V199A90067
lOp.; For related modules, see CE 056 762-773.
Guides - Classroom Use - Materials (For Learner)
(051)
EDRS PRICE MFOl/PCOl Plus Postage.
DESCRIPTORS Arithmetic; Community Colleges; ^Decimal Fractions;
Individualized Instruction; Learning Modules;
^Mathematical Applications; ^Mathematics Instruction;
^Measurement; Number Concepts; Numbers; Pacing; Two
Year Colleges; Vocational Education
IDENTIFIERS *Job Related Mathematics; ^Precision (Mathematics)
ABSTRACT
This module is the second in a series of 12 learning
modules designed to teach occupational mathematics. Blocks of
informative material and rules are followed by examples and practice
problems. The solutions to the practice problems are found at the end
of the module. Specific topics covered include rounding off,
precision of measurement, and the concept of least precise
measurement . ( YLB)
* Reproductions supplied by EDRS are the best that can be made
* from the original document.
Ptx^0ctDlr9ctor
Ron Vofd^strasse
Prol9ct30emtMry
Jan Wisiakjwski
T$ehnle*t ContuiUnt
Ray PfaMtton
Technical Wrttm
Nancy EnQotbrecht
LyrmeGmt
Ann Hunter
StaceyOekes
^opynght. Central Community Coilege
3
1
Module 2 — ROUNDING DECIMAL NUMBERS TO A
DESIGNATED PRECISION
Rounding off a decimal niimber means rewriting the nximber in
a shorter form to represent an approximation of the number. The
symbol used for values that are approximately equal, but not
exactly equal is In measuring the length of an object, it
could be measured to the nearest 1 mm, the nearest 0.1 mm, the
nearest 0.01 mm or even closer. Measurements are never exact.
The precision with which the technician needs a measurement
depends upon the particular application. The measurement a
person records is a nxamber which has been read only as close as
needed and therefore, represents a rounded off value.
The number pi = jc = 3.141592653589793238 is a never
ending decimal. It is necessary to round it off somewhere.
Various possibilities includa:
nearest
^ 3
nearest
tenth
^ 3.
1
neazest
hundredth
^ 3.
14
nearest
thousandth
^ 3.
142
nearest
ten-thousandth
. . . 7C
^ 3.
1416
The proper value to select depends upon the demand for pr€.cision.
The process called rounding off will follow the commonly
used stops in what is called the rule--of-5. For example, when
the number 748.537 is rounded to the units place, it is written
as 749. Rounded to the nearest tenths, 748.537 becomes 748.5,
and rounding to the nearest hundredth makes it 748.54. The
following is the usual rule-of-5 for rounding a number written
out in detail.
4
2
RULE FOR ROUNDING DECIMAlL NUMBERS
ROUNDING TO TEN OR HIGHER PIACE
To round a number to a particular place value, called the
rounding place, that is in the ten (10) place or greater
1. If the digit immediately to the right of the rounding
place is less than 5 (0,1,2,3,4), then
(a) do not change the digit in the rounding place or
any digits to the left of it.
(b) replace, with zeros, all the digits to the right
of the rounding place until the decimal point
location is reached.
(c) do not write the decimal point.
(d) drop all digits which were to the right of the
decimal point (do not replace them with zeros) .
2. If the digit iimnediately to the right of th^ rounding
place is 5 or greater (5,6,7,8,9), then
(a) add 1 (one) to the digit in the rounding place.
When adding 1 to a 9 digit, add the 1 to the two
digit number which ends in that 9. This has the
effect of changing the 9 into 0 and the digit to
its left will become 1 greater.
(b) replace, with zeros, all the digits to the right
of the rounding place until the decimal point
location is reached.
(c) do not write the decimal point,
(d) drop all digits which wera to the right of the
decimal point (ao not replace them with zero) .
To round a number to a particular place value that is in the
units place or to the right of the decimal point:
3. If the digit immediately to the right of the rounding
place is less than 5 (0,1,2,3,4), then
(a) do not change the digit in the rounding place or
any digits to the left of it.
(b) drop all the digits to the right of the rounding
place.
(c) do not replace dropped digits with zeros.
4. If the digit immediately to the right of the rounding
place is 5 or greater (5,6,7,8,9), then
(a) add 1 (one) to the digit in the rounding place.
When adding 1 to a 9 digit, add the 1 to the two
di jit number which ends in that 9. This has the
effect of changing the 9 into 0 and the digit to
its left will become 1 greater.
(b) drop all the digits to the right of the rovnding
place .
(c) do not replace dropped digits with zeros.
ERIC
5
3
EXAMPLE i: Round each number in the left-hand column to the
place value (precision) indicated in each column
heading .
decimal
ten
unit
tenth
hundredth
thousandth
275.8103
280
276
275.8
275.81
275.810
43. 9618
40
44
44.0
43.96
43.962
27.8205
30
28
27.8
27. 82
27.821
7.0261
10
7
7.0
7.03
7.026
A special case arose when 7.0261 was rounded to the nearest
ten. The original tens digit is considered to be 0 so that
7.0261 = 07.0261. Since the digit immediately to the right
of the ten digit is 7 (5 or more), then the tens digit of 0
is to be increased by 1 to form 10. Rounding 7.0261 to the
nearest ten produced lU.
PRACTICE PROBLEMS: Round each number in the left-hand column to
the place value indicated in each column
heading .
Decimal hundred ten unit tenth
1. 685.31
2. 1728.47
3. 475.296
4. 88.972
Round each number in the left-hand column to the
place value indicated in each column heading.
Deciraal tenth hundredth thousandth ten-thousandth
5. 1.70062
6. 0.39491
7. 3.06177
8. 6.07939
9. 0.17316
10. 0.05592
6
4
A ruler, caliper and micrometer are three different devices
used to make a length measurement. The biggest difference in
these three instruments is the precision with which you are able
to determine size. A person trained to use these might record
the following for the measurement of the length of a pin.
The PRECISION of each measurement is the place value of the
last digit recorded by the measuring instrument and the unit of
measure used by the instrument.
The last digit of the metric caliper reading is the 3 of
17.3 mm. This 3 is in the tenths or 0.1 place value position.
The precision of the 17.3 mm caliper reading is stated as 0.1 mm.
An English caliper reading for length of the same pin is
0,68 in. The last digit 8 of 0.68 in. is in the hundredths or
0,01 place value position. The precision of the 0.68 in. English
caliper reading is stated as 0.01 in.
EXAMPLE 2: The precision of the measurements given for the pin
length by the various types of instruments is
summarized in the table.
Type of Metric Metric English English
Device Measure Precision Measure Precision
ruler 17mm 1mm 0.7 in. 0.1 in.
caliper 17.3 mm 0.1 mm 0.68 in. 0.01 in.
micrometer 17.274 mm 0.001 mm 0.6801 in. 0.0001 in.
As one learns production skills of machining, it is
necessary to match the quality demanded of the craftsmanship to
the precision of the measurements required to meet those quality
standards .
ruler, metric 17 mm
caliper, metric 17.5 mm
micrometer, metric 17.274 mm
ruler, English 0.7 in.
caliper, English 0.68 in.
micrometer, English 0.6801 in.
ERIC
PRACTICE PROBLEnS: State the precision of the following
measurements. Do not forget to include the
unit of measurement with your niimber value.
11. 2.4 in.
13. 1.931 in
IS. 7.09 in.
17. 91.0 mm
19, 0.81 in.
12. 6.08 mm
14. 12.280 mm
16. 91 mm
18. 91.000 mm
20. 0.810 in.
The English length of pin measurements of Example 2 show
that different instruments have different precisions. The least
precise English measure is achieved by the English ruler as
0.7 in., while the most precise English measure is 0.6801 in.
obtained by the English micrometer.
The LEAST PRECISE of two or more measurements is the
measure whose last recorded digit is farthest left
(higher place value) .
EXAMPLE 3: The diameter of a pin has been recorded as 0.25 in.
and as 0.248 in. What is the precision of each
measurement and which measurement is the least
precise?
Solution:
0.25 in. has precision 0.01 in.
0.248 in. has precision 0.001 in.
The least precise is 0.25 in.
EXAMPLE 4: The thickness of a steel plate has been recorded as
9.78 mm, 9.780 mm and as 9.8 mm. What is the
precision of each measurement and which measurement
is the least precise?
Solution:
9.78 mm has precision 0.01 mm
9.780 mm has precision 0.001 mm
2^.8 mm has precision 0.1 mm
The least precise is the 9.8 mm.
8
6
PRACTICE PROBLEMS: Identify the least precise of each set of
measurements :
21. 2.181 in., 2.18 in., 2.1814 in.
22. 7.23 mm, 7.2346 mm, 7.2 mm, 7.235 mm.
23. 1230 mm, 1200 mm, 1232.1 mm, 1232 mm
24. 6.26 in., 6 in., 6.3 in., 6.277 in.
25. 4.00 in., 4.0 in., 4.000 in., 4 in.
The widi-h of 3 separate steel plates are recorded below.
Identify the least precise of each set of measurements.
26. 0.3 in., 2.56 in., 1.772 in.
27. 12.3 mm, 10.44 mm, 13 mm
28. 6.002 mm, 10.92 mm, 15.8 mm.
29. 14.125 in., 3.25 in., 0.875 in.
30. 9.40 mm, 27.900 mm, 316.0 mm
ERIC
9
7
SOLUTIONS TO PRACTICE PROBLEMS — MODULE 2
Decimal
hundred
ten
unit
tenth
1.
685.31
700
690
685
685.3
2.
1728.47
1700
1730
1728
1728.5
3.
475.296
500
480
475
475.3
4.
88.972
100
90
89
89.0
Decimal
tenth
hundredth
thousandth
ten-thou
5.
1.70862
1.7
1.71
1.709
1.7086
6.
0.39491
0.4
0.39
0.395
0.3949
7.
3.06177
3.1
3.06
3.062
3.0618
8.
6.07939
6.1
6.08
6.079
6.0794
9.
0.17316
0.2
0.17
0.173
0.1732
10.
0.05592
0.1
0.06
0.056
0.0559
11. 0.1 iu.
14. 0.001 mm
17. 0.1 mm
20. 0.001 in
23. 1200 mm
26. 0.3 in.
29. 3.25 in.
12. 0.01 mm
15. 0.01 in.
18. 0.001 mm
21 . 2.18 in.
24. 6 in.
27. 13 mm
30. 316.0 mm
13. 0.001 in
16. 1 mm
19. 0.01 in.
22. 7.2 mm
25. 4 in.
28. 15.8 mm
ERIC
10
1/
U.S. Dept. of Education
Office of Educational
Research and Improvement (OER!)
Date Filmed
July 17, 1991
