IDNLearn.com is your reliable source for expert answers and community insights. Whether your question is simple or complex, our community is here to provide detailed and trustworthy answers quickly and effectively.
Sagot :
Let's address each question step by step.
### Question 21
We need to determine which of the given mixed numbers has the same decimal value as [tex]\( 110 \frac{147}{168} \)[/tex].
1. Convert the mixed number [tex]\( 110 \frac{147}{168} \)[/tex] into a decimal:
- [tex]\( \frac{147}{168} \approx 0.875 \)[/tex]
- So, [tex]\( 110 \frac{147}{168} = 110 + 0.875 = 110.875 \)[/tex]
Now, let's convert each option to its decimal form and compare:
Option (A): [tex]\( 110 \frac{49}{56} \)[/tex]
- Convert [tex]\( \frac{49}{56} \approx 0.875 \)[/tex]
- Thus, [tex]\( 110 + 0.875 = 110.875 \)[/tex]
Option (B): [tex]\( 110 \frac{170}{180} \)[/tex]
- Convert [tex]\( \frac{170}{180} \approx 0.944444 \)[/tex]
- Thus, [tex]\( 110 + 0.944444 \approx 110.944444 \)[/tex]
Option (C): [tex]\( 110 \frac{56}{72} \)[/tex]
- Convert [tex]\( \frac{56}{72} \approx 0.777778 \)[/tex]
- Thus, [tex]\( 110 + 0.777778 \approx 110.777778 \)[/tex]
Option (D): [tex]\( 110 \frac{247}{268} \)[/tex]
- Convert [tex]\( \frac{247}{268} \approx 0.921642 \)[/tex]
- Thus, [tex]\( 110 + 0.921642 \approx 110.921642 \)[/tex]
Comparing these values:
- [tex]\( 110 \frac{49}{56} = 110.875 \)[/tex]
- [tex]\( 110 \frac{170}{180} \approx 110.944444 \)[/tex]
- [tex]\( 110 \frac{56}{72} \approx 110.777778 \)[/tex]
- [tex]\( 110 \frac{247}{268} \approx 110.921642 \)[/tex]
Thus, the correct answer is [tex]\( 110 \frac{49}{56} \)[/tex].
### Question 22
We need to analyze the statements about the negative fractions [tex]\( -\frac{4}{5} \)[/tex] and [tex]\( -\frac{5}{6} \)[/tex].
1. [tex]\( -\frac{4}{5} \)[/tex] expressed as a decimal:
- [tex]\( \frac{4}{5} = 0.8 \)[/tex]. It is a terminating decimal, not a repeating decimal.
2. [tex]\( -\frac{5}{6} \)[/tex] expressed as a decimal:
- [tex]\( \frac{5}{6} \approx 0.833333\ldots \)[/tex]. This is a repeating decimal where the digit 3 repeats indefinitely.
Statement Analysis:
- " [tex]\( -\frac{4}{5} \)[/tex] can be expressed as a repeating decimal.": False, because [tex]\( -\frac{4}{5} = -0.8 \)[/tex] is a terminating decimal.
- " [tex]\( -\frac{5}{6} \)[/tex] can be expressed as a repeating decimal.": True, because [tex]\( -\frac{5}{6} = -0.8333\ldots \)[/tex].
- "Both fractions can be expressed as repeating decimals.": False, as only [tex]\( -\frac{5}{6} \)[/tex] is a repeating decimal, not [tex]\( -\frac{4}{5} \)[/tex].
- "The digit that repeats is 3.": True for [tex]\( -\frac{5}{6} \)[/tex].
- "The digit that repeats is 8.": False, since 8 does not repeat in either fraction's decimal form.
So, the true statements are:
- [tex]\( -\frac{5}{6} \)[/tex] can be expressed as a repeating decimal.
- The digit that repeats is 3.
### Question 21
We need to determine which of the given mixed numbers has the same decimal value as [tex]\( 110 \frac{147}{168} \)[/tex].
1. Convert the mixed number [tex]\( 110 \frac{147}{168} \)[/tex] into a decimal:
- [tex]\( \frac{147}{168} \approx 0.875 \)[/tex]
- So, [tex]\( 110 \frac{147}{168} = 110 + 0.875 = 110.875 \)[/tex]
Now, let's convert each option to its decimal form and compare:
Option (A): [tex]\( 110 \frac{49}{56} \)[/tex]
- Convert [tex]\( \frac{49}{56} \approx 0.875 \)[/tex]
- Thus, [tex]\( 110 + 0.875 = 110.875 \)[/tex]
Option (B): [tex]\( 110 \frac{170}{180} \)[/tex]
- Convert [tex]\( \frac{170}{180} \approx 0.944444 \)[/tex]
- Thus, [tex]\( 110 + 0.944444 \approx 110.944444 \)[/tex]
Option (C): [tex]\( 110 \frac{56}{72} \)[/tex]
- Convert [tex]\( \frac{56}{72} \approx 0.777778 \)[/tex]
- Thus, [tex]\( 110 + 0.777778 \approx 110.777778 \)[/tex]
Option (D): [tex]\( 110 \frac{247}{268} \)[/tex]
- Convert [tex]\( \frac{247}{268} \approx 0.921642 \)[/tex]
- Thus, [tex]\( 110 + 0.921642 \approx 110.921642 \)[/tex]
Comparing these values:
- [tex]\( 110 \frac{49}{56} = 110.875 \)[/tex]
- [tex]\( 110 \frac{170}{180} \approx 110.944444 \)[/tex]
- [tex]\( 110 \frac{56}{72} \approx 110.777778 \)[/tex]
- [tex]\( 110 \frac{247}{268} \approx 110.921642 \)[/tex]
Thus, the correct answer is [tex]\( 110 \frac{49}{56} \)[/tex].
### Question 22
We need to analyze the statements about the negative fractions [tex]\( -\frac{4}{5} \)[/tex] and [tex]\( -\frac{5}{6} \)[/tex].
1. [tex]\( -\frac{4}{5} \)[/tex] expressed as a decimal:
- [tex]\( \frac{4}{5} = 0.8 \)[/tex]. It is a terminating decimal, not a repeating decimal.
2. [tex]\( -\frac{5}{6} \)[/tex] expressed as a decimal:
- [tex]\( \frac{5}{6} \approx 0.833333\ldots \)[/tex]. This is a repeating decimal where the digit 3 repeats indefinitely.
Statement Analysis:
- " [tex]\( -\frac{4}{5} \)[/tex] can be expressed as a repeating decimal.": False, because [tex]\( -\frac{4}{5} = -0.8 \)[/tex] is a terminating decimal.
- " [tex]\( -\frac{5}{6} \)[/tex] can be expressed as a repeating decimal.": True, because [tex]\( -\frac{5}{6} = -0.8333\ldots \)[/tex].
- "Both fractions can be expressed as repeating decimals.": False, as only [tex]\( -\frac{5}{6} \)[/tex] is a repeating decimal, not [tex]\( -\frac{4}{5} \)[/tex].
- "The digit that repeats is 3.": True for [tex]\( -\frac{5}{6} \)[/tex].
- "The digit that repeats is 8.": False, since 8 does not repeat in either fraction's decimal form.
So, the true statements are:
- [tex]\( -\frac{5}{6} \)[/tex] can be expressed as a repeating decimal.
- The digit that repeats is 3.
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for visiting IDNLearn.com. We’re here to provide dependable answers, so visit us again soon.
