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Express the following marks as a percentage:

1. 172 out of 9880
2. 100 out of 100
3. 36 out of 75
4. 0 out of 50
5. 11 out of 50

Convert the following:

1. 5 mm to cm
2. 74 g to kg
3. 30 ml to liters

Answer :

We begin by expressing each set of marks as a percentage and then perform the required conversions.

–––––––––––––––––––––––––––––––––––––––––––––––––––
Step 1. Expressing Marks as Percentages

1. For [tex]\(172\)[/tex] out of [tex]\(9880\)[/tex]:

[tex]\[
\text{Percentage}_1 = \frac{172}{9880} \times 100 \approx 1.7409\%
\][/tex]

2. For [tex]\(100\)[/tex] out of [tex]\(100\)[/tex]:

[tex]\[
\text{Percentage}_2 = \frac{100}{100} \times 100 = 100\%
\][/tex]

3. For [tex]\(36\)[/tex] out of [tex]\(75\)[/tex]:

[tex]\[
\text{Percentage}_3 = \frac{36}{75} \times 100 = 48\%
\][/tex]

4. For [tex]\(0\)[/tex] out of [tex]\(50\)[/tex]:

[tex]\[
\text{Percentage}_4 = \frac{0}{50} \times 100 = 0\%
\][/tex]

5. For [tex]\(11\)[/tex] out of [tex]\(50\)[/tex]:

[tex]\[
\text{Percentage}_5 = \frac{11}{50} \times 100 = 22\%
\][/tex]

–––––––––––––––––––––––––––––––––––––––––––––––––––
Step 2. Calculating the Overall Percentage

First, compute the total marks obtained and the total marks possible.

[tex]\[
\text{Total Obtained} = 172 + 100 + 36 + 0 + 11 = 319
\][/tex]

[tex]\[
\text{Total Possible} = 9880 + 100 + 75 + 50 + 50 = 10155
\][/tex]

Now, calculate the overall percentage:

[tex]\[
\text{Overall Percentage} = \frac{319}{10155} \times 100 \approx 3.1413\%
\][/tex]

–––––––––––––––––––––––––––––––––––––––––––––––––––
Step 3. Conversions

1. Converting [tex]\(5\)[/tex] mm to centimeters:

Since [tex]\(1\, \text{cm} = 10\, \text{mm}\)[/tex]:

[tex]\[
5\, \text{mm} = \frac{5}{10} = 0.5\, \text{cm}
\][/tex]

2. Converting [tex]\(74\)[/tex] g to kilograms:

Since [tex]\(1\, \text{kg} = 1000\, \text{g}\)[/tex]:

[tex]\[
74\, \text{g} = \frac{74}{1000} = 0.074\, \text{kg}
\][/tex]

3. Converting [tex]\(30\)[/tex] ml to liters:

Since [tex]\(1\, \text{L} = 1000\, \text{ml}\)[/tex]:

[tex]\[
30\, \text{ml} = \frac{30}{1000} = 0.03\, \text{L}
\][/tex]

–––––––––––––––––––––––––––––––––––––––––––––––––––
Final Answers

- The percentages for each set of marks are:
- [tex]\(1.7409\%\)[/tex] for [tex]\(172\)[/tex] out of [tex]\(9880\)[/tex],
- [tex]\(100\%\)[/tex] for [tex]\(100\)[/tex] out of [tex]\(100\)[/tex],
- [tex]\(48\%\)[/tex] for [tex]\(36\)[/tex] out of [tex]\(75\)[/tex],
- [tex]\(0\%\)[/tex] for [tex]\(0\)[/tex] out of [tex]\(50\)[/tex],
- [tex]\(22\%\)[/tex] for [tex]\(11\)[/tex] out of [tex]\(50\)[/tex].
- The overall percentage across all tests is approximately [tex]\(3.1413\%\)[/tex].
- Conversions:
- [tex]\(5\, \text{mm} = 0.5\, \text{cm}\)[/tex],
- [tex]\(74\, \text{g} = 0.074\, \text{kg}\)[/tex],
- [tex]\(30\, \text{ml} = 0.03\, \text{L}\)[/tex].

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