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Chapter 1: A. Basic Shop Math 9
Rational and Irrational Numbers
A rational number can be represented in fractional form. It either has a finite
number of decimal places or an infinite (never-ending) number of repeating decimal
places. For example, the numbers 0.37, 0.6894, 1.33562, 4.3 – , and 8.5 – 1 – 9 – are all
examples of rational numbers. The bar over the 3 in the number 4.3 implies that
the 3 repeats infinitely (4.333 . . .). Similarly, the bar over 519 in the number 8.519
implies that the sequence 519 repeats infinitely (8.519519519 . . .).
An irrational number is a number that has an infinite number of decimal places
that do not repeat. An example of an irrational number is p = 3.14159 . . . , since its
digits are nonrepeating and infinite.
Part I.A
Converting Decimals to Percentages
To convert a decimal into a percentage, multiply by 100 percent, as follows:
Adding and Subtracting Decimals
0. 375× 100% = 37. 5%
To add or subtract decimals, line up the numbers at their decimal places. For
example, the numbers 3.475, 11.55, and 2.2 can be added as follows:
+
3.
475
11.
55
22 .
17.
225
Multiplying and Dividing Decimals
To multiply or divide decimals, count the total number of decimal places in the
problem. The final answer will have that number of decimal places:
375 .
× 23 .
8.
625
2 decimal places
1 decimal place
3 decimal places
SQUARES AND SQUARE ROOTS
The square of a number is simply that number multiplied by itself. The square of a
number can also be written as that number to the second power. For example, the
square of 7 is calculated as
A square root is denoted as follows:
2
7× 7 = 7 = 49.
1
2 2
( ) =
25 = 25 = 5,since25 = 5×
5 5