Pre – Algebra
8th Grade Math
Number System Study Guide
Section NS – 1: Rational and Irrational Numbers
- Rational Numbers: A number that can be written as the quotient of two integers (fraction)
o 7
o -10
o [pic]
- Irrational Numbers: A number that cannot be written as the quotient of two integers. The decimal form of an irrational number neither terminates or repeats
o [pic]
o [pic]
o 0.202002000…
- Decimal Expansions
o Tell whether a decimal expansion terminates or repeats by changing the fraction into a decimal
o 1/5 - .20 – Terminating Decimal
o 1/3 - .33333… - Repeating Decimal
Section NS – 2: Converting Decimals
- Converting terminating decimals
o Find the place value of the last digit in the terminating decimal. The Decimal value becomes the numerator and the place value becomes the denominator
▪ 0.7 – 7/10
▪ 3.05 - [pic]- [pic]
- Converting Repeating Decimals
o Take the number of repeating digits and place that number in the numerator and place the same number of nines in the denominator
▪ [pic]- [pic]- [pic]
Section NS – 3: Square Roots
- A perfect square is a number that is the square of an integer
o 144 - [pic]- 12
- Evaluating Expressions
o Evaluate the following when a is 12 and b is 4
▪ [pic]
▪ [pic]
- Solving Equations
o [pic]
o [pic]
- Estimate the value of irrational numbers
o Estimate the value of[pic]to the nearest tenths place
▪ [pic] is between the [pic]to
▪ So [pic] must be between 2 and 3
▪ [pic] is closer to [pic] so [pic] is close to 2
▪ Make a list and start squaring up to 2.5
• [pic] - 4.4
• 2.2[pic] - 4.8
• 2.3[pic] - 5.2
• 2.4[pic] - 5.7
• 2.5[pic]- 6.2
▪ 2.2 is the closest to 5 so 2.2 is the estimate of [pic]
Section NS – 4: Comparing and Ordering Rational Numbers
- Which value is greater 7.74596 or [pic]?
- Which value is greater [pic]or -3.5
- Order the numbers below from least to greatest
o 28%, -2.5, [pic], [pic]
Section NS – 5: Work with Rational Numbers
- Place the following numbers in order from least to greatest
o 3.24037…, [pic], [pic]
o Change all values to decimals then place in order
o Make sure to write values in final answer in correct format
o [pic], 3.24037…,[pic]
- Estimate the value of an expression
o [pic]- 9.86
o [pic]
- Estimate with Operations
o [pic]
o 6.56 – 0.64
o 5.92
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