used to indicate the digit or digit that repeat in a repeating decimal
11/2
-1/3
bar notation
repeating decimal
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.
-2 3/8 × 8/5
a repeating decimal
b 11/2
c -19.59
d-3 4/5
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.
To represent repeating decimals, bar notation is used. This notation consists of placing a bar over the digit or digits that repeat.
For example, let's consider the fractions 11/2 and -1/3:
1. 11/2:
To convert this fraction into a decimal, divide 11 by 2:
11 ÷ 2 = 5.5
Since the division does not terminate and continues indefinitely, we can use bar notation to indicate the repeating decimal: 5.5 (the digit 5 repeats).
2. -1/3:
To convert this fraction into a decimal, divide -1 by 3:
-1 ÷ 3 ≈ -0.33333...
In this case, the digit 3 repeats. To represent this repeating decimal, we use bar notation: -0.3̅ (the digit 3 repeats).
Therefore, the repeating decimals for 11/2 and -1/3 using bar notation are 5.5 and -0.3̅, respectively.
To indicate the digit or digits that repeat in a repeating decimal, we use bar notation. Bar notation is a way of representing repeating decimals by placing a bar over the digits that repeat. For example, if a decimal number has a repeating digit of 3, we write it as 0.3̅. If a decimal number has two repeating digits of 27, we write it as 0.2727̅.
Now, let's consider the fractions you mentioned:
1. 11/2:
To convert the fraction 11/2 to a decimal, we perform division. We divide 11 by 2 and get 5.5 as the result. Since there are no repeating digits, we do not use bar notation.
2. -1/3:
To convert the fraction -1/3 to a decimal, we divide -1 by 3. The result is approximately -0.3333... (repeating). We can indicate the repeating digits by placing a bar over the '3', so the decimal can be represented as -0.3̅.
Therefore, while 11/2 does not have repeating digits, -1/3 can be represented as a repeating decimal using bar notation.