Question

what kind of decimal expansion does 37/8 have?​

Answer 1

Answer:

terminating

Step-by-step explanation:

Because this is full cut by 8

Answer 2

Step-by-step explanation:

Given that:37/8

To find: what kind of decimal expansion does it have.

Steps: To find what kind of decimal expansion does any rational number have,

1) first one have to check given number is simple rational number or not,i.e. numerator and denominator should don't have any common factor(Co-prime numbers).

here in 37/8,both numerator and denominator are Co-prime numbers.

2) Now do the prime factors of denominator,and check these must be in the form

${2}^{n} \times {5}^{m} \\ where \: m \: and \: n \: are \: positive \: integers$

So,here prime factors of 8 = 2×2×2

$8 = {2}^{3} \\ it \: can \: be \: expressed \: as \\ 8 = {2}^{3} \times {5}^{0} \\ \\ as \: {a}^{0} = 1$

So, the given number have terminating Decimal expansion.

Hope it helps you.