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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