Question

The decimal expansion of 17/8 will terminate after how many places of decimals?

Answer 1

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Answer 2

Given: The fraction is 17/8

To find The decimal expression of 17/8 and after how many places of decimals it will terminate

Solution:

• In mathematics, we convert fractions into decimal numbers and vice-versa. For this question, an improper fraction of 17/8 is given and we have to find the equivalent decimal number of that improper fraction.

• At first, on dividing 17/8, we have 2 in the quotient as (8×2=16) and leave 1 as the remainder.

• By giving a decimal point after the quotient that is after 2, the quotient becomes 2. and a zero is added after the remainder that is the new remainder becomes 10 and now we can divide by 8. Now the quotient is 2.1 as for 10/8 we multiply (8×1=8) which leaves a remainder 2.

• Then after the remainder 2, a zero is added after 2 and makes it 20 because of the decimal point we can take zero. Now we divide 20/8 and get 4 as the remainder(∵ 8×2=16) and the new quotient is 2.12 now.

• Similarly, a zero is added after the remainder 4 for the decimal point and now we divide 40/8 and we get zero as the remainder and the quotient is 2.125 (∵ 8×5=40).

• We stop the division of the improper fraction 17/8 here as the remainder becomes zero.

Hence the decimal expression of 17/8 is 2.125 and it will terminate after three decimal places.