Question

used to indicate the digit or digit that repeat in a repeating decimal
11/2
-1/3
bar notation
repeating decimal

Answer 1

-2 3/8 × 8/5
a repeating decimal
b 11/2
c -19.59
d-3 4/5

Answer 2

To indicate that a digit or a set of digits repeat in a repeating decimal, bar notation is used. In bar notation, a horizontal bar is placed over the digit or set of digits that repeat.

For example:
- The decimal representation of 11/2 is 5.5, which means that the digit 5 repeats. So, it can be written as 5.5 with a bar over the 5: 5.5̅.
- The decimal representation of -1/3 is -0.3333..., where the digits 3 repeat. So, it can be written as -0.3̅.
- Repeating decimals can also be expressed using a set of digits that repeat. For example, 1/7 is equal to 0.142857142857..., where the set of digits 142857 repeat. So, it can be written as 0.1̅428̅57̅.

Answer 3

a. Since -2 3/8 is a mixed number, let's convert it to an improper fraction first.

-2 3/8 = (-2 * 8 + 3) / 8 = (-16 + 3) / 8 = -13/8

Now, multiply -13/8 by 8/5.

(-13/8) * (8/5) = -13/5

Since -13/5 is an improper fraction, let's represent it as a mixed number.

-13/5 = -2 3/5

So, the result is -2 3/5.

b. The decimal representation of 11/2 is 5.5. So, the result is 5.5.

c. The decimal representation of -19.59 does not contain any repeating digits. So, it is not a repeating decimal.

d. Since -3 4/5 is a mixed number, let's convert it into an improper fraction.

-3 4/5 = (-3 * 5 + 4) / 5 = (-15 + 4) / 5 = -11/5

So, the result is -11/5.