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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?
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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?
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