Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
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.
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
