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Section 0.1. Rational 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….

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section 0 1

Section 0.1

Rational Numbers, Rounding, and Order of Operations

rational numbers
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 numbers1
Rational Numbers
  • Classify the following numbers as rational or irrational.

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

Solution:

Rational Numbers

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

Irrational Numbers

- this is a non repeating , non terminating decimal.

– this is always irrational

rounding and truncation
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 truncation1
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 truncation2
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
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 operations1
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 – 5

9 – 5

4

order of operations2
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 operations3
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

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