Page 365 - Basic College Mathematics with Early Integers

342 C HAPTE R 4 I DECIMALS

Definitions and Concepts Examples

Section 4.4 Dividing Decimals

TO DIVIDE DECIMALS Divide: 1.118 , 2.6
Step 1: If the divisor is not a whole number, move the 0.43
decimal point in the divisor to the right until the 2.61.118
divisor is a whole number.
Step 2: Move the decimal point in the dividend to the –1 04
right the same number of places as the decimal 78
point was moved in Step 1. –78
Step 3: Divide.The decimal point in the quotient is directly 0
over the moved decimal point in the dividend.

Section 4.5 Fractions, Decimals, and Order of Operations

To write fractions as decimals, divide the numerator by 3
the denominator. Write as a decimal.
8
0.375
83.000
-24
60
-56
40
-40
0
ORDER OF OPERATIONS
1. Perform all operations within parentheses ( ), Simplify.
brackets [ ], or grouping symbols such as fraction -1.9(12.8 - 4.1) =-1.9(8.7) Subtract.
bars or square roots.
=-16.53 Multiply.
2. Evaluate any expressions with exponents.
3. Multiply or divide in order from left to right.
4. Add or subtract in order from left to right.

Section 4.6 Square Roots and the Pythagorean Theorem

SQUARE ROOTOFA NUMBER 29 = 3, 2100 = 10, 21 = 1
A square root of a number a is a number b whose square is
a.We use the radical sign 1 to indicate square roots.

PYTHAGOREAN THEOREM
2 2 2
1leg2 + 1other leg2 = 1hypotenuse2 Find the hypotenuse of the given triangle.
hypotenuse
3 in.
hypotenuse
leg
8 in.
2 2
hypotenuse = 21leg2 + 1other leg2
leg
2 2
= 2132 + 182 The legs are 3 and 8 inches.
TO FIND AN UNKNOWN LENGTH OF A RIGHT TRIANGLE Copyright 2012 Pearson Education, Inc.
= 29 + 64
2 2
hypotenuse = 21leg2 + 1other leg2
= 273 inches
2 2
leg = 21hypotenuse2 - 1other leg2 L 8.5 inches