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Section 0.1

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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  1. Section 0.1 Rational Numbers, Rounding, and Order of Operations

  2. 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…..

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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.

  8. 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

  9. 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

  10. 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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