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How many zeros after the decimal point will be there in the decimal form of the number 10 -n ?
- a)n
- b)n+1
- c)n-1
- d)n/2
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
How many zeros after the decimal point will be there in the decimal fo...
Decimal Form of 10-n
To find the decimal form of 10-n, we need to divide 1 by 10-n.
1 ÷ 10-n = 10n
This means that the decimal form of 10-n will be a number with n zeros after the decimal point.
For example:
- When n = 3, 10-3 = 0.001, so the decimal form of 10-3 is 0.0001 (four zeros after the decimal point).
- When n = 5, 10-5 = 0.00001, so the decimal form of 10-5 is 0.000001 (six zeros after the decimal point).
Zeros After Decimal Point
Since the decimal form of 10-n has n zeros after the decimal point, the answer to the question "how many zeros after the decimal point will be there in the decimal form of the number 10-n?" is n-1.
This is because the first digit after the decimal point is not zero, so we need to subtract one from the total number of zeros to get the number of zeros after the decimal point.
For example:
- When n = 3, the decimal form of 10-3 is 0.0001, so there are 3-1 = 2 zeros after the decimal point.
- When n = 5, the decimal form of 10-5 is 0.000001, so there are 5-1 = 4 zeros after the decimal point.
Therefore, the correct answer is option C, n-1.
To find the decimal form of 10-n, we need to divide 1 by 10-n.
1 ÷ 10-n = 10n
This means that the decimal form of 10-n will be a number with n zeros after the decimal point.
For example:
- When n = 3, 10-3 = 0.001, so the decimal form of 10-3 is 0.0001 (four zeros after the decimal point).
- When n = 5, 10-5 = 0.00001, so the decimal form of 10-5 is 0.000001 (six zeros after the decimal point).
Zeros After Decimal Point
Since the decimal form of 10-n has n zeros after the decimal point, the answer to the question "how many zeros after the decimal point will be there in the decimal form of the number 10-n?" is n-1.
This is because the first digit after the decimal point is not zero, so we need to subtract one from the total number of zeros to get the number of zeros after the decimal point.
For example:
- When n = 3, the decimal form of 10-3 is 0.0001, so there are 3-1 = 2 zeros after the decimal point.
- When n = 5, the decimal form of 10-5 is 0.000001, so there are 5-1 = 4 zeros after the decimal point.
Therefore, the correct answer is option C, n-1.
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Community Answer
How many zeros after the decimal point will be there in the decimal fo...
10^-n = 1÷10^n
now let's take some examples
let's put the value of n
n=4 and n=5
first take n=4
then , 1÷10^4=1÷10000=0.0001 (i)
now let's take n=5,, 1÷10^5=1÷100000=0.00001 (ii)
in both case (i) and (ii) we see that zeroes after the decimal is 1 less than the exponent that n-1
That's why zeroes after the decimal point in the decimal form of 10^-n is n-1
now let's take some examples
let's put the value of n
n=4 and n=5
first take n=4
then , 1÷10^4=1÷10000=0.0001 (i)
now let's take n=5,, 1÷10^5=1÷100000=0.00001 (ii)
in both case (i) and (ii) we see that zeroes after the decimal is 1 less than the exponent that n-1
That's why zeroes after the decimal point in the decimal form of 10^-n is n-1
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