Section 0.1Rational Numbers, Rounding, and Order of Operations

Rational Numbers• Rational Numbers are any numbers that can be

written as a fraction.• That means:• Integers• Fractions• Decimals

Here are some examples:5, 1/3, -5.1234, -15

Here are some non-examples:, , 3.1245789…..

Rational Numbers• Classify the following numbers as rational or

irrational.

-3, 0, , , , 7.51, , -, 6.666666

Solution:Rational Numbers-3, 0, , 7.51, , -, 6.666666Irrational Numbers - this is a non repeating , non terminating decimal. – this is always irrational

Rounding and Truncation• Rounding – Look to the right of the specified

decimal place. If the number is 5 or greater, round up one. If the number is 4 or less, leave it alone. (You know this. You have been doing it forever!!!)

Round 7.356894 to 3 decimal places.7.356894 look at the number to the right of

the 6 it is higher than 5 so round up.

7.357

Rounding and Truncation• Truncation – Cutoff what you don’t want.

Approximate 7.456892 to 3 decimal places by truncation

7.456892 Cutoff everything past the “6”7.456

Rounding and Truncation• Approximate 17.368204 to two decimal places by

A) Rounding B) Truncation

• Approximate 23.02492 to two decimal places by A) Rounding B) Truncation

Solution:1. A) 17.37 B) 17.36 2. A) 23.02 B) 23.02

Order of Operations• You know this: PEMDAS• Parentheses• Exponents• Multiplication• Division• Addition• Subtraction

• Work left to right.• If you see division before multiplication, that is

okay do it first. Multiplication/division and addition/subtraction are done at the same time.

Order of operations• Example 1

7 – 2 * 5 + 4 * 3 – 5 No parentheses or exponents, so look for multiplication/division 1st.7 – 10 + 12 – 5 Go back to the beginning to do

addition/subtraction.-3 + 12 – 59 – 54

Order of Operations• Example 2 -3(x – y) + 4(3x – 2y) Here there are parentheses, but you cannot combine anything. You need to distribute 1st.

-3x + 3y + 12x - 8y Now combine like terms

9x – 5y

Order of operations• Try a few on your own. Ask a partner if they are

right, before I show you the answers. 1. 8 * 5 - 4 + 6 ÷ 2 2. -2(5 + 3) + 7(3 – 2 * 5)

3. 3(5x – 2y) – 7(x – 3y) 4. 6x(5 + 2 - 4) – (3 * 2 ÷ 3)

Solutions:1. 39 2. -65 3. 8x + 15y 4. 18x - 2