MODULE A-1: POSITIVE AND NEGATIVE NUMBERS AND ROUNDING
MODULE A-1: POSITIVE AND NEGATIVE NUMBERS AND ROUNDING
I. Positive and Negative Numbers
A. Definitions
1. Number Line: A line on which every point represents a real number.
2. Real Number: The combined set of rational numbers and irrational numbers.
3. Origin: The point (0, 0) on a coordinate plane, where the x-axis and the y-axis intersect.
4. Positive Number: A real number greater than zero.
5. Negative Number: A real number that is less than zero.
6. Absolute Value: The distance of a number from zero.
7. Additive Inverse: The additive inverse of any number x is the number that gives zero when added to x. The additive inverse of 5 is -5.
B. Rules for working with Positive and Negative Numbers
1. Addition
a. Same signs - Add the absolute values of the numbers and give the answer the same sign as the original numbers.
b. Different signs – “Tug-O-War” Subtract smaller number’s absolute value from larger number’s absolute value and give answer the sign of the number with the larger absolute value.
2. Subtraction
a. Change sign of second number to it’s additive inverse and apply the addition rules
i. If second number is a positive number then change to negative.
• Example: -10 – 5 change to -10 + (-5) = -15
ii. If second number is a negative number then change to positive.
• 10 – (-5) change to 10 + (+5) = 15
3. Multiplication
a. Same signs - positive answer
b. Opposite signs - negative answer
4. Division
a. Same sign - positive answer
b. Opposite signs - negative answer
II. Rounding
A. Rounding Rules
1. Number of decimal places needed
|Size of number |# of decimal places used |# of decimal places used in |
| |when working |answer |
|Decimal |.XXX |.XX |
| |Three places |Two places |
|Small number |1.XX |1.X |
|< 100 |Two places |One place |
|Large number |111.X |111 |
|> 100 |One place |Zero places |
a. Calculator Use
i. If you do not have a calculator, round the numbers before performing the math then round the answers.
ii. If you have a calculator, do the math then just round the answer.
2. When to Round
a. If the number to be dropped is larger than or equal to 5, the preceding number is rounded up.
b. If the number to be dropped is smaller than 5, the preceding number stays the same.
3. Measurement & Precision
a. A calculation can only be as accurate as the accuracy of the measurements.
b. In most cases just follow the rounding rules.
c. Respiratory Therapy examples of exceptions to the rounding rules:
i. Temperature: Do not round 101.8 to 102
ii. Acid-Base measurement of pH: Do not round pH of 7.35 to 7.4
iii. Ideal body weight: Usually rounded to whole number (86 rather than 86.2)
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