Digits, Grade 8, Volume 1, Homework Helper

# Unit A: Number and Operations

## Topic 1: Rational and Irrational Numbers

### 1-1: Exploring Irrational Numbers

#### Key Concept

A rational number is a number that can be written in the form eh over b , where a and b are integers and b ≠ 0. Rational numbers can also be written in decimal form. Think of eh over b as a fraction. To write eh over b as a decimal, you divide a by b. A rational number in decimal form is either a terminating or a repeating decimal.

A terminating decimal has a decimal expansion that terminates in 0's. All integers can be written with a 0 following a decimal point. So, all integers are terminating decimals.

Examples:

table with 2 rows and 2 columns , row1 column 1 , 9 fifths , equals 1.8 , column 2 negative , 4 100ths , equals negative , 0.04 , row2 column 1 , 1 fourth , equals , 0.25 , column 2 5 equals , 5 over 1 , equals 5.0 , end table

A repeating decimal has a decimal expansion that repeats the same digit, or block of digits, without end. A bar indicates the repeating digit, or block of digits. So, 0. , 3 bar , equals , 0.3333 , dot dot dot

Examples:

table with 2 rows and 2 columns , row1 column 1 , 1 third , equals , 0.3333 , dot dot dot equals 0. , 3 bar , column 2 negative , 4 ninths , equals negative , 0.4444 , dot dot dot equals negative 0. , 4 bar , row2 column 1 , 7 fifteenths , equals , 0.4666 , dot dot dot equals 0.4 , 6 bar , column 2 49 over 33 , equals , 1.4848 , dot dot dot equals 1.4 , 8 bar , end table

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