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EMT 1150 Lab Experiment 1 Notes
- Course
- EMT 1150
- Institution
- New York City College Of Technology
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EMT1150 Lab Manual (08/2020)EMT1150 Lab Experiment 1
Math Review
Objective: Review and practice the necessary math for EMT1150
1.1 Powers of Ten
It should be apparent from the relative magnitude of the various units of measurement that very
large and very small numbers are frequently encountered in the sciences. To ease the difficulty of
mathematical operations with numbers of such varying size, powers of ten are usually employed.
This notation takes full advantage of the mathematical properties of powers of ten. The notation
used to represent numbers that are integer powers of ten is as follows:
1 = 100 1 0.1 = 10-1
10
=
10 = 101 1
= 0.01 = 10-2
100
100 = 102 1 0.001 = 10-3
1,000
=
1000 = 103 1 0.0001 = 10-4
10,000
=
where, an expression 104 is called a power, read “ten to the fourth power.” The exponent 4
represents the number of times the base 10 is used as a factor as shown below.
A quick method of determining the proper power of ten is to place a caret mark to the right of the
numeral 1 wherever it may occur; then count from this point to the number of places to the right
or left before arriving at the decimal point. Moving to the right indicates a positive power of ten,
whereas moving to the left indicates a negative power. For example,
1
,EMT1150 Lab Manual (08/2020)
1.1.1 P roperties of P ow
owers
ers of T
Ten
en
1) Zero exponent: 100 = 1
1 1
2) Negative exponent: 10𝑛 𝑛
, −𝑛𝑛 = 10𝑛𝑛
= 10−𝑛𝑛 10
Example 1.1
1
a. 104
= 10−4
1
b.
10−5
= 105
3) Product of powers of ten: (10𝑚𝑚 )(10𝑛𝑛 ) = 10(𝑚𝑚+𝑛𝑛)
Example 1.2
a. (1000)(10,000) = (103 )(104 ) = 10(3+4) = 107
b. (0.000001)(100) = (10−6 )(102 ) = 10(−6+2) = 10−4
10𝑚𝑚
4) Quotient of powers of ten: = 10(𝑚𝑚−𝑛𝑛)
10𝑛 𝑛
Example 1.3
100,000 105
a.
1000
= 103 = 10(5−3) = 102
0.0001 10−4
b. = = 10(−4−2) = 10−6
100 102
5) Power of a power of ten: (10𝑚𝑚 )𝑛 𝑛
= 10𝑚𝑚𝑛𝑛
Example 1.4
a. (1000)4 = (103 )4 = 103×4 = 1012
b. (0.00001)3 = (10−5 )3 = 10−15
2
, EMT1150 Lab Manual (08/2020)
Exercises 1.1 – Properties of Powers of Ten
1. (1000)(10,000) =
2. (0.001)(1000000) =
100
3. =
10,000
0.0000000001
4. =
1000
3
5. (100) =
6. (0.000001)5 =
Show work here:
1.2. Scientific and Engineering notation
In electronics, technicians very often have to deal with measurable values that might be very large
or very small numbers. For example, the distance from the Earth to the sun, which is 92960000
miles, or the thickness of the aluminum foil, which is 0.000963 inches. These numbers are
impractical to write out because of the length, the amount of space required, and the difficulty to
reading them. Due to it, scientists have developed a shorter method to write very large or very
small numbers. Those methods are known as scientific notation and engineering notation.
3
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