Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Experience the convenience of getting accurate answers to your questions from a dedicated community of professionals. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Write the decimal expansion of the following numbers and identify the type of decimal expansion each has:

(i) [tex]\(\frac{42}{8}\)[/tex]

(ii) [tex]\(\frac{5}{6}\)[/tex]

(iii) [tex]\(\frac{9}{11}\)[/tex]

(iv) [tex]\(\frac{37}{20}\)[/tex]

(v) [tex]\(\frac{4}{7}\)[/tex]

(vi) [tex]\(\frac{43}{13}\)[/tex]


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.
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.