Question
Is 3.78778777 font size decreased by 4 . font size decreased by 4 . font size decreased by 4 . a rational or irrational​ number?
Question content area bottom
Part 1
Choose the correct answer below.
rational number
irrational number
Question content area bottom
Part 1
Choose the correct answer below.
rational number
irrational number
Answers
GPT-4o mini
To determine whether \( 3.78778777 \) is a rational or irrational number, we need to understand how these types of numbers are defined:
- A rational number can be expressed as the quotient of two integers (a fraction) where the denominator is not zero. This includes both terminating and repeating decimals.
- An irrational number cannot be expressed as a simple fraction; its decimal representation is non-repeating and non-terminating.
The number \( 3.78778777 \) can be analyzed as follows:
1. **Identify the decimal expansion:** The decimal \( 3.78778777 \) is a decimal that starts with "3.78" and repeats "77" afterwards. The repeating nature of "77" indicates that it's a repeating decimal.
2. **Expressing as a fraction:** Since it is a repeating decimal, we can express it as a fraction. A repeating decimal like \( 3.78778777 \) can be converted to a fraction using algebra or direct methods.
Therefore, \( 3.78778777 \) is a rational number.
**Answer:** rational number
- A rational number can be expressed as the quotient of two integers (a fraction) where the denominator is not zero. This includes both terminating and repeating decimals.
- An irrational number cannot be expressed as a simple fraction; its decimal representation is non-repeating and non-terminating.
The number \( 3.78778777 \) can be analyzed as follows:
1. **Identify the decimal expansion:** The decimal \( 3.78778777 \) is a decimal that starts with "3.78" and repeats "77" afterwards. The repeating nature of "77" indicates that it's a repeating decimal.
2. **Expressing as a fraction:** Since it is a repeating decimal, we can express it as a fraction. A repeating decimal like \( 3.78778777 \) can be converted to a fraction using algebra or direct methods.
Therefore, \( 3.78778777 \) is a rational number.
**Answer:** rational number