Question

express 7/3 as a decimal and tell their terminating and non terminating

Answer 1

Step-by-step explanation:

Given rational number is

80

7

.

We know,

q

p

is terminating if:

a) p and q are co-prime and

b) q is of the form of 2

n

×5

m

, where n and m are non-negative integers.

Firstly, we check whether the numerator and denominator are co-prime,

Numerator =7=7

1

Denominator =80=2

4

×5

1

⇒7 and 80 have no common factors.

Therefore, 7 and 80 are co-primes.

Now, we check whether q is in the form of 2

n

×5

m

,

Denominator =80=2

4

×5

1

So, the denominator is in the form 2

n

×5

m

, where n=4 and m=1.

Thus,

80

7

is a terminating decimal.

Now, multiplying and dividing by 5

3

=

2

4

×5

1

×5

3

7×5

3

=

2

4

×5

4

7×125

=

(2×5)

4

875

=

(10)

4

875

=

10000

875

=0.0875.

∴

80

7

=0.0875 is the decimal expansion

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Answer 2

Answer:

7/3 = 2.33333333333333

7/3 = non terminating but repeating decimal

Step-by-step explanation: