Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
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 hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.