Answer :
To determine which number is greater than [tex]\(69 \frac{1}{6}\)[/tex], we need to compare each of the given numbers with [tex]\(69 \frac{1}{6}\)[/tex]. Here’s how we can do the comparison:
1. Convert the mixed number [tex]\(69 \frac{1}{6}\)[/tex] to a decimal:
- [tex]\(69 \frac{1}{6} = 69 + \frac{1}{6} = 69 + 0.1667 \approx 69.1667\)[/tex]
2. Next, we convert each of the other numbers to a decimal:
- [tex]\(69 \frac{5}{7} = 69 + \frac{5}{7} = 69 + 0.7143 \approx 69.7143\)[/tex]
- [tex]\(\frac{682}{10} = 68.2\)[/tex]
- [tex]\(68 \frac{7}{10} = 68 + \frac{7}{10} = 68 + 0.7 = 68.7\)[/tex]
- [tex]\(68 \frac{1}{4} = 68 + \frac{1}{4} = 68 + 0.25 = 68.25\)[/tex]
3. Now, we compare each of these numbers to [tex]\(69.1667\)[/tex]:
- [tex]\(69.7143 > 69.1667\)[/tex]
- [tex]\(68.2 < 69.1667\)[/tex]
- [tex]\(68.7 < 69.1667\)[/tex]
- [tex]\(68.25 < 69.1667\)[/tex]
From these comparisons, we see that the only number greater than [tex]\(69 \frac{1}{6}\)[/tex] is [tex]\(69 \frac{5}{7}\)[/tex].
Therefore, [tex]\(69 \frac{5}{7}\)[/tex] is the number greater than [tex]\(69 \frac{1}{6}\)[/tex].
1. Convert the mixed number [tex]\(69 \frac{1}{6}\)[/tex] to a decimal:
- [tex]\(69 \frac{1}{6} = 69 + \frac{1}{6} = 69 + 0.1667 \approx 69.1667\)[/tex]
2. Next, we convert each of the other numbers to a decimal:
- [tex]\(69 \frac{5}{7} = 69 + \frac{5}{7} = 69 + 0.7143 \approx 69.7143\)[/tex]
- [tex]\(\frac{682}{10} = 68.2\)[/tex]
- [tex]\(68 \frac{7}{10} = 68 + \frac{7}{10} = 68 + 0.7 = 68.7\)[/tex]
- [tex]\(68 \frac{1}{4} = 68 + \frac{1}{4} = 68 + 0.25 = 68.25\)[/tex]
3. Now, we compare each of these numbers to [tex]\(69.1667\)[/tex]:
- [tex]\(69.7143 > 69.1667\)[/tex]
- [tex]\(68.2 < 69.1667\)[/tex]
- [tex]\(68.7 < 69.1667\)[/tex]
- [tex]\(68.25 < 69.1667\)[/tex]
From these comparisons, we see that the only number greater than [tex]\(69 \frac{1}{6}\)[/tex] is [tex]\(69 \frac{5}{7}\)[/tex].
Therefore, [tex]\(69 \frac{5}{7}\)[/tex] is the number greater than [tex]\(69 \frac{1}{6}\)[/tex].
