1.1 Number Line

Question 1

bar notation

Answer 1

The table below shows some examples of repeating decimals and their bar notations:

Decimal Bar Notation
0.1666666666… 0.16 (line bar over the 6)
0.3535353535… 0.35 (line bar over the 5)
12.688888888… 12.68 (line bar over the 8)

Question 2

Irrational Number

Answer 2

A number that cannot be written as a fraction a/b
(where b ≠ 0), a repeating decimal, or a terminating decimal.

[Examples include π,√3, and 0.1345698876623…]

Question 3

The set of real numbers can be divided into …..

Answer 3

two groups: rational numbers and irrational numbers

Question 4

Rational Number

Answer 4

A number that can be written as a fraction a/b
(where b ≠ 0), a repeating decimal, or a terminating decimal.

Question 5

But, how do you reverse this process and convert a repeating decimal into a rational number?

Answer 5

One approach is to notice that rational numbers with denominators of 9 repeat a single digit.
3/9 =0.333333333…

Denominators of 99 repeat two digits, denominators of 999 repeat three digits, and so on.
74/99=0.7474747474… or 237/999=0.237237237237237…

Question 6

How do you convert a repeating decimal into a rational number?

Answer 6

From this pattern, you can go in the opposite direction; the number of digits that repeats determines the number of 9s that should be in the denominator.

0.134134134…=134/999

Question 7

Terminating Decimal

Answer 7

A decimal that, when dividing, ends with a remainder of zero.

Question 8

Repeating Decimal

Answer 8

A decimal where, when dividing, a digit or group of digits repeats without end in the quotient; there is a pattern in the digits that repeat without end.