5\ 6 in the decimal form is:\ (a) 0.8\bar{3} (b) 0.8\bar{33} (c) 0.6\bar{3} (d) 0.6\bar{33}\ Decimal representation of rational number 8\27 is:\ (a) 0.\bar{296} (b) 0.2\bar{96} (c) 0.29\bar{6} (d) 0.296
The Correct Answer and Explanation is:
Let’s break these two problems down step by step:
1. Decimal Representation of 5/6
To convert 5/6 into decimal form, we perform long division:
5 ÷ 6 gives:
- 6 goes into 50 eight times (6 × 8 = 48).
- Subtract 50 – 48 = 2.
- Bring down a zero, making it 20.
- 6 goes into 20 three times (6 × 3 = 18).
- Subtract 20 – 18 = 2.
- Notice the remainder repeats as 2.
The repeating part is “3”, so the decimal form of 5/6 is 0.83 repeating, or 0.8̅3.
Therefore, the correct answer is (a) 0.8̅3.
2. Decimal Representation of 8/27
Next, let’s convert 8/27 into decimal form using long division:
8 ÷ 27 gives:
- 27 goes into 80 two times (27 × 2 = 54).
- Subtract 80 – 54 = 26.
- Bring down a zero, making it 260.
- 27 goes into 260 nine times (27 × 9 = 243).
- Subtract 260 – 243 = 17.
- Bring down another zero, making it 170.
- 27 goes into 170 six times (27 × 6 = 162).
- Subtract 170 – 162 = 8, which repeats.
The repeating part is “296”, so the decimal form of 8/27 is 0.296̅.
Therefore, the correct answer is (a) 0.̅296.
Summary:
- The decimal form of 5/6 is 0.8̅3, and the correct answer is (a).
- The decimal form of 8/27 is 0.̅296, and the correct answer is (a).
