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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

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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) RoundingB) Truncation

  • Approximate 23.02492 to two decimal places by

    A) RoundingB) Truncation

Solution:

1. A) 17.37 B) 17.362. 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 – 5Go 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. 392. -653. 8x + 15y4. 18x - 2


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