Question

Prime factorisation of the denominator of the rational number 52.9678 is
(a) of the form 2m × 5n where m, n are integers
(b) of the form 2m × 5n where m and n are positive integers
(c) of the form 2m × 5n where m, n are rational numbers
(d) not of the form 2m × 5n where m, n are non-negative integers

Answer 1

Answer:

Since 34.12345 has terminating decimal expansion. So, its denominator is of the form 2

m ×5 n

, where m, n are non-negative integers.

Step-by-step explanation:

same two be done with ur number

Answer 2

Option B is the correct answer.

• Any recurring and terminating decimal can be converted into the fractional form.
• Decimals can be converted into the fractional form using the following process,

=> Consider a decimal A.B, it is written in fractional form as (ab/10).

=> Consider a decimal A.BC, it is written in fractional form as ( ABC /100).

=> Consider a decimal A.BCD, it is written in fractional form as (ABCD/1000).

• The total amount of numbers after the decimal points is multiplied by 10 to the denominator to convert it into fractional form.

• The given number is 52.9678, it can be converted into fractional form as 529678/1000.
• The denominator is 1000, 1000 can also be writt$2^3$en as,

=> 1000 = 10 x 10 x 10,

=> 10 x 10 x 10 = 2 x 2 x 2 x 5 x 5 x 5,

=> 10 x 10 x 10 = $2^3$ x $5^3$.

• The final answer after rationalization is of form $2^m$x$5^n$, where m and n are positive integers.

Therefore, Option 2 is the correct answer.