Question

Without actually performing the long division,state whether 77/210 will have a terminating decimal expansion or non-terminating repeating decimal expansion

Answer 1

Non-terminating repeating

Answer 2

the given number is 77/210

first HCF of (77,210)=7

∴ 77/210 = 77÷7/210 ÷7 = 11/30

here

11/30 is its simplest form

now,

11 = 1 ×11

30 = 2×3×5 is not in fome in $2^{m} *5^{n}$

so,the given no has a non-terminating repeating decimal expansion

IT is step of the question