Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
Sure! Let's go through each fraction step-by-step to find their decimal expansions and determine the type of decimal expansion they have.
### (i) [tex]\(\frac{42}{8}\)[/tex]
First, let's perform the division:
[tex]\[ \frac{42}{8} = 5.25 \][/tex]
The decimal expansion of [tex]\(\frac{42}{8}\)[/tex] is [tex]\( 5.25 \)[/tex].
- Type of Decimal Expansion: This is a Terminating decimal because the decimal terminates after 2 decimal places.
### (ii) [tex]\(\frac{5}{6}\)[/tex]
Next, let's perform the division:
[tex]\[ \frac{5}{6} = 0.8333333333\ldots \][/tex]
The decimal expansion of [tex]\(\frac{5}{6}\)[/tex] is [tex]\( 0.8333333333\ldots \)[/tex].
- Type of Decimal Expansion: This is a Non-Terminating, Repeating decimal because the digit 3 repeats endlessly.
### (iii) [tex]\(\frac{9}{11}\)[/tex]
Next, let's perform the division:
[tex]\[ \frac{9}{11} = 0.8181818181\ldots \][/tex]
The decimal expansion of [tex]\(\frac{9}{11}\)[/tex] is [tex]\( 0.8181818181\ldots \)[/tex].
- Type of Decimal Expansion: This is a Non-Terminating, Repeating decimal because the digits 81 repeat endlessly.
### (iv) [tex]\(\frac{37}{20}\)[/tex]
Next, let's perform the division:
[tex]\[ \frac{37}{20} = 1.85 \][/tex]
The decimal expansion of [tex]\(\frac{37}{20}\)[/tex] is [tex]\( 1.85 \)[/tex].
- Type of Decimal Expansion: This is a Terminating decimal because the decimal terminates after 2 decimal places.
### (v) [tex]\(\frac{4}{7}\)[/tex]
Next, let's perform the division:
[tex]\[ \frac{4}{7} = 0.5714285714\ldots \][/tex]
The decimal expansion of [tex]\(\frac{4}{7}\)[/tex] is [tex]\( 0.5714285714\ldots \)[/tex].
- Type of Decimal Expansion: This is a Non-Terminating, Repeating decimal because the digits 571428 repeat endlessly.
### (vi) [tex]\(\frac{43}{13}\)[/tex]
Next, let's perform the division:
[tex]\[ \frac{43}{13} = 3.3076923076\ldots \][/tex]
The decimal expansion of [tex]\(\frac{43}{13}\)[/tex] is [tex]\( 3.3076923076\ldots \)[/tex].
- Type of Decimal Expansion: This is a Non-Terminating, Repeating decimal because the digits 307692 repeat endlessly.
In summary, the results are:
- (i) [tex]\(\frac{42}{8} = 5.25\)[/tex] - Terminating
- (ii) [tex]\(\frac{5}{6} = 0.8333333333\ldots\)[/tex] - Non-Terminating, Repeating
- (iii) [tex]\(\frac{9}{11} = 0.8181818181\ldots\)[/tex] - Non-Terminating, Repeating
- (iv) [tex]\(\frac{37}{20} = 1.85\)[/tex] - Terminating
- (v) [tex]\(\frac{4}{7} = 0.5714285714\ldots\)[/tex] - Non-Terminating, Repeating
- (vi) [tex]\(\frac{43}{13} = 3.3076923076\ldots\)[/tex] - Non-Terminating, Repeating
Each fraction's decimal expansion and classification has been provided.
### (i) [tex]\(\frac{42}{8}\)[/tex]
First, let's perform the division:
[tex]\[ \frac{42}{8} = 5.25 \][/tex]
The decimal expansion of [tex]\(\frac{42}{8}\)[/tex] is [tex]\( 5.25 \)[/tex].
- Type of Decimal Expansion: This is a Terminating decimal because the decimal terminates after 2 decimal places.
### (ii) [tex]\(\frac{5}{6}\)[/tex]
Next, let's perform the division:
[tex]\[ \frac{5}{6} = 0.8333333333\ldots \][/tex]
The decimal expansion of [tex]\(\frac{5}{6}\)[/tex] is [tex]\( 0.8333333333\ldots \)[/tex].
- Type of Decimal Expansion: This is a Non-Terminating, Repeating decimal because the digit 3 repeats endlessly.
### (iii) [tex]\(\frac{9}{11}\)[/tex]
Next, let's perform the division:
[tex]\[ \frac{9}{11} = 0.8181818181\ldots \][/tex]
The decimal expansion of [tex]\(\frac{9}{11}\)[/tex] is [tex]\( 0.8181818181\ldots \)[/tex].
- Type of Decimal Expansion: This is a Non-Terminating, Repeating decimal because the digits 81 repeat endlessly.
### (iv) [tex]\(\frac{37}{20}\)[/tex]
Next, let's perform the division:
[tex]\[ \frac{37}{20} = 1.85 \][/tex]
The decimal expansion of [tex]\(\frac{37}{20}\)[/tex] is [tex]\( 1.85 \)[/tex].
- Type of Decimal Expansion: This is a Terminating decimal because the decimal terminates after 2 decimal places.
### (v) [tex]\(\frac{4}{7}\)[/tex]
Next, let's perform the division:
[tex]\[ \frac{4}{7} = 0.5714285714\ldots \][/tex]
The decimal expansion of [tex]\(\frac{4}{7}\)[/tex] is [tex]\( 0.5714285714\ldots \)[/tex].
- Type of Decimal Expansion: This is a Non-Terminating, Repeating decimal because the digits 571428 repeat endlessly.
### (vi) [tex]\(\frac{43}{13}\)[/tex]
Next, let's perform the division:
[tex]\[ \frac{43}{13} = 3.3076923076\ldots \][/tex]
The decimal expansion of [tex]\(\frac{43}{13}\)[/tex] is [tex]\( 3.3076923076\ldots \)[/tex].
- Type of Decimal Expansion: This is a Non-Terminating, Repeating decimal because the digits 307692 repeat endlessly.
In summary, the results are:
- (i) [tex]\(\frac{42}{8} = 5.25\)[/tex] - Terminating
- (ii) [tex]\(\frac{5}{6} = 0.8333333333\ldots\)[/tex] - Non-Terminating, Repeating
- (iii) [tex]\(\frac{9}{11} = 0.8181818181\ldots\)[/tex] - Non-Terminating, Repeating
- (iv) [tex]\(\frac{37}{20} = 1.85\)[/tex] - Terminating
- (v) [tex]\(\frac{4}{7} = 0.5714285714\ldots\)[/tex] - Non-Terminating, Repeating
- (vi) [tex]\(\frac{43}{13} = 3.3076923076\ldots\)[/tex] - Non-Terminating, Repeating
Each fraction's decimal expansion and classification has been provided.
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.
