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a real number ^ 3 into 3 power 2 into 7 to the power 3 into 54 by to the power 7 into 5 ^ 3 into 3 to the power 2 into 7 will have a terminating decimal or non-terminating decimal or non-terminating repeating decimal or non terminating non repeating
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a real number ^ 3 into 3 power 2 into 7 to the power 3 into 54 by to t...
Answer:
Given: a real number ^ 3 into 3 power 2 into 7 to the power 3 into 54 by to the power 7 into 5 ^ 3 into 3 to the power 2 into 7
To determine whether the given number is a terminating decimal or non-terminating decimal or non-terminating repeating decimal or non-terminating non-repeating decimal, we will simplify the given expression using the laws of exponents and then check its decimal representation.
Solution:
Simplifying the given expression by using the laws of exponents, we get:
= (3^3 * 7^3 * 2^3 * 3^3 * 2 * 3^3)/(5^3 * 3^2 * 7^3 * 2^7)
= (2^4 * 3^6)/(5^3 * 7^3)
Now, we can evaluate the decimal representation of the given expression to determine whether it is a terminating decimal or non-terminating decimal or non-terminating repeating decimal or non-terminating non-repeating decimal.
Using a calculator, we get:
= 0.13714285714285714
We can observe that the decimal representation of the given expression is a non-terminating repeating decimal, as it has a repeating block of digits (142857) that continues indefinitely.
Therefore, the given real number is a non-terminating repeating decimal.
Conclusion:
The given real number ^ 3 into 3 power 2 into 7 to the power 3 into 54 by to the power 7 into 5 ^ 3 into 3 to the power 2 into 7 is a non-terminating repeating decimal.
Given: a real number ^ 3 into 3 power 2 into 7 to the power 3 into 54 by to the power 7 into 5 ^ 3 into 3 to the power 2 into 7
To determine whether the given number is a terminating decimal or non-terminating decimal or non-terminating repeating decimal or non-terminating non-repeating decimal, we will simplify the given expression using the laws of exponents and then check its decimal representation.
Solution:
Simplifying the given expression by using the laws of exponents, we get:
= (3^3 * 7^3 * 2^3 * 3^3 * 2 * 3^3)/(5^3 * 3^2 * 7^3 * 2^7)
= (2^4 * 3^6)/(5^3 * 7^3)
Now, we can evaluate the decimal representation of the given expression to determine whether it is a terminating decimal or non-terminating decimal or non-terminating repeating decimal or non-terminating non-repeating decimal.
Using a calculator, we get:
= 0.13714285714285714
We can observe that the decimal representation of the given expression is a non-terminating repeating decimal, as it has a repeating block of digits (142857) that continues indefinitely.
Therefore, the given real number is a non-terminating repeating decimal.
Conclusion:
The given real number ^ 3 into 3 power 2 into 7 to the power 3 into 54 by to the power 7 into 5 ^ 3 into 3 to the power 2 into 7 is a non-terminating repeating decimal.
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