Advertisements
Advertisements
प्रश्न
Write down the decimal expansions of the following rational numbers by writing their denominators in the form 2m × 5n, where, m, n are non-negative integers.\[\frac{13}{125}\]
Advertisements
उत्तर
The given number is \[\frac{13}{125}\].
Clearly, 125 = 53 is of the form 2m × 5n, where m = 0 and n = 3.
So, the given number has terminating decimal expansion.
\[\therefore \frac{13}{125} = \frac{13 \times 2^3}{2^3 \times 5^3} = \frac{13 \times 8}{\left( 2 \times 5 \right)^3} = \frac{104}{\left( 10 \right)^3} = \frac{104}{1000} = 0 . 104\]
APPEARS IN
संबंधित प्रश्न
Consider the number 6n where n is a natural number. Check whether there is any value of n ∈ N for which 6n is divisible by 7.
Check whether 6n can end with the digit 0 for any natural number n.
Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.
State fundamental theorem of arithmetic?
Find the LCM and HCF of the following integers by applying the prime factorisation method:
40, 36 and 126
Write the exponent of 2 in the price factorization of 144.
Write the sum of the exponents of prime factors in the prime factorization of 98.
If the prime factorization of a natural number n is 23 ✕ 32 ✕ 52 ✕ 7, write the number of consecutive zeros in n.
Express the number as a product of its prime factor:
3825
Find the LCM and HCF of the following integers by applying the prime factorisation method.
8, 9 and 25
There is a circular path around a sports field. Priya takes 18 minutes to drive one round of the field. Harish takes 12 minutes. Suppose they both start at the same point and at the same time and go in the same direction. After how many minutes will they meet?
The product of two consecutive natural numbers is always ______.
If LCM(x, 18) = 36 and HCF(x, 18) = 2, then x is ______.
If two positive integers a and b are written as a = x3 y2 and b = xy3; x, y are prime numbers, then HCF (a, b) is ______.
If two positive integers p and q can be expressed as p = ab2 and q = a3b; a, b being prime numbers, then LCM (p, q) is ______.
Let a and b be two positive integers such that a = p3q4 and b = p2q3, where p and q are prime numbers. If HCF (a, b) = pmqn and LCM (a, b) = prqs, then (m + n)(r + s) = ______.
Show the 6n cannot end with digit 0 for any natural number 'n'.
Find the HCF and LCM of 26, 65 and 117, using prime factorisation.
(HCF × LCM) for the numbers 70 and 40 is ______.
If n is a natural number, then 8n cannot end with digit
