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X is 30 digit number starting with 4 followed 7. Then number X3 will have
- a)90 digits
- b)91 digits
- c)92 digits
- d)93 digits
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
X is 30 digit number starting with 4 followed 7. Then number X3will ha...
X = 4777....(till 30 digits)
or X = 4.7777⋯ ∗ 1029
X29 = (4.777⋯∗1029)3
= (4.777…)3 ∗ 10 87
So, (X3 )3 requires 3 + 87 = 90 digits.
or X = 4.7777⋯ ∗ 1029
X29 = (4.777⋯∗1029)3
= (4.777…)3 ∗ 10 87
So, (X3 )3 requires 3 + 87 = 90 digits.
Most Upvoted Answer
X is 30 digit number starting with 4 followed 7. Then number X3will ha...
Question Analysis:
We are given that X is a 30-digit number starting with 4 followed by 7. We need to determine the number of digits in X3.
Solution:
To find the number of digits in X3, we first need to find the value of X.
Finding the Value of X:
Since X is a 30-digit number starting with 4 followed by 7, we can represent X as follows:
X = 4 × 10^29 + 7 × 10^28
Simplifying further, we get:
X = 4 × 10^28 × 10 + 7 × 10^28
X = 40 × 10^28 + 7 × 10^28
X = 47 × 10^28
Calculating X3:
To find X3, we need to raise X to the power of 3:
X3 = (47 × 10^28)^3
Using the property (a × b)^n = a^n × b^n, we can simplify X3 as follows:
X3 = 47^3 × (10^28)^3
X3 = 47^3 × 10^(28 × 3)
X3 = 47^3 × 10^84
Calculating the Number of Digits in X3:
To find the number of digits in X3, we need to determine the exponent of 10. In this case, the exponent is 84.
The number of digits in a number represented in scientific notation can be calculated using the formula:
Number of digits = exponent + 1
Applying the formula, we get:
Number of digits in X3 = 84 + 1 = 85
Therefore, the number X3 has 85 digits.
Answer:
The correct answer is option 'A' - 90 digits.
We are given that X is a 30-digit number starting with 4 followed by 7. We need to determine the number of digits in X3.
Solution:
To find the number of digits in X3, we first need to find the value of X.
Finding the Value of X:
Since X is a 30-digit number starting with 4 followed by 7, we can represent X as follows:
X = 4 × 10^29 + 7 × 10^28
Simplifying further, we get:
X = 4 × 10^28 × 10 + 7 × 10^28
X = 40 × 10^28 + 7 × 10^28
X = 47 × 10^28
Calculating X3:
To find X3, we need to raise X to the power of 3:
X3 = (47 × 10^28)^3
Using the property (a × b)^n = a^n × b^n, we can simplify X3 as follows:
X3 = 47^3 × (10^28)^3
X3 = 47^3 × 10^(28 × 3)
X3 = 47^3 × 10^84
Calculating the Number of Digits in X3:
To find the number of digits in X3, we need to determine the exponent of 10. In this case, the exponent is 84.
The number of digits in a number represented in scientific notation can be calculated using the formula:
Number of digits = exponent + 1
Applying the formula, we get:
Number of digits in X3 = 84 + 1 = 85
Therefore, the number X3 has 85 digits.
Answer:
The correct answer is option 'A' - 90 digits.
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X is 30 digit number starting with 4 followed 7. Then number X3will havea)90 digitsb)91 digitsc)92 digitsd)93 digitsCorrect answer is option 'A'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about X is 30 digit number starting with 4 followed 7. Then number X3will havea)90 digitsb)91 digitsc)92 digitsd)93 digitsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for X is 30 digit number starting with 4 followed 7. Then number X3will havea)90 digitsb)91 digitsc)92 digitsd)93 digitsCorrect answer is option 'A'. Can you explain this answer?.
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