State whether the following rational number will have a terminating or non termining decimal -0-03945 auraus wat hulle (2) 96 terminating 25 (3) 229 \2^3 x 3²x5^7
Answers
Answer:
TERMINATING.
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Answer:
Let's analyze each of the given rational numbers to determine if their decimal representation is terminating or non-terminating.
-0.03945
The number has five decimal places. To determine if it is terminating or non-terminating, we need to check if there is a repeating pattern after the decimal point. In this case, there is no repeating pattern, and the number does not extend infinitely. Therefore, the decimal representation of -0.03945 is terminating.
96
The number 96 can be written as 96.0000 (with infinite zeros after the decimal point). Since there are no non-zero digits after the decimal point, the number is terminating.
25
The number 25 can be written as 25.0000 (with infinite zeros after the decimal point). Like the previous example, there are no non-zero digits after the decimal point, making the number terminating.
229 / (2^3 * 3^2 * 5^7)
To determine if this rational number has a terminating or non-terminating decimal representation, we need to simplify it:
229 / (2^3 * 3^2 * 5^7) = 229 / (8 * 9 * 78125)
To check if the decimal representation is terminating or non-terminating, we need to find out if there is a repeating pattern when this rational number is represented as a decimal. However, calculating this division manually would be quite complex due to the large prime factors.
Nonetheless, since the denominator consists of prime factors 2, 3, and 5, and none of these factors can divide evenly into the numerator (229), the decimal representation will be non-terminating and non-repeating (a non-repeating decimal is also known as an irrational number).
In summary:
-0.03945 is a terminating decimal.
96 is a terminating decimal.
25 is a terminating decimal.
229 / (2^3 * 3^2 * 5^7) is a non-terminating, non-repeating (irrational) decimal.
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