Find the sums of the given fractions.

To solve the given problems, we need to add fractions. The key steps involve finding a common denominator and then performing the addition. Let's solve each part step by step.

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Part (a): $\frac{9}{10} + \frac{8}{100}$

1. Find a common denominator:
- The denominators are 10 and 100.
- The least common denominator (LCD) is 100.

2. Convert each fraction to have the common denominator:
- $\frac{9}{10} = \frac{9 \times 10}{10 \times 10} = \frac{90}{100}$
- $\frac{8}{100}$ remains $\frac{8}{100}$.

3. Add the fractions:
$$
\frac{90}{100} + \frac{8}{100} = \frac{90 + 8}{100} = \frac{98}{100}
$$

4. Simplify the result:
- $\frac{98}{100}$ can be simplified by dividing both numerator and denominator by their greatest common divisor (GCD), which is 2.
$$
\frac{98 \div 2}{100 \div 2} = \frac{49}{50}
$$

Answer for (a): $\boxed{\frac{49}{50}}$

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Part (b): $\frac{7}{100} + \frac{3}{10}$

1. Find a common denominator:
- The denominators are 100 and 10.
- The least common denominator (LCD) is 100.

2. Convert each fraction to have the common denominator:
- $\frac{7}{100}$ remains $\frac{7}{100}$.
- $\frac{3}{10} = \frac{3 \times 10}{10 \times 10} = \frac{30}{100}$.

3. Add the fractions:
$$
\frac{7}{100} + \frac{30}{100} = \frac{7 + 30}{100} = \frac{37}{100}
$$

Answer for (b): $\boxed{\frac{37}{100}}$

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Part (c): $\frac{2}{10} + \frac{41}{100}$

1. Find a common denominator:
- The denominators are 10 and 100.
- The least common denominator (LCD) is 100.

2. Convert each fraction to have the common denominator:
- $\frac{2}{10} = \frac{2 \times 10}{10 \times 10} = \frac{20}{100}$.
- $\frac{41}{100}$ remains $\frac{41}{100}$.

3. Add the fractions:
$$
\frac{20}{100} + \frac{41}{100} = \frac{20 + 41}{100} = \frac{61}{100}
$$

Answer for (c): $\boxed{\frac{61}{100}}$

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Part (d): $\frac{23}{100} + \frac{7}{10}$

1. Find a common denominator:
- The denominators are 100 and 10.
- The least common denominator (LCD) is 100.

2. Convert each fraction to have the common denominator:
- $\frac{23}{100}$ remains $\frac{23}{100}$.
- $\frac{7}{10} = \frac{7 \times 10}{10 \times 10} = \frac{70}{100}$.

3. Add the fractions:
$$
\frac{23}{100} + \frac{70}{100} = \frac{23 + 70}{100} = \frac{93}{100}
$$

Answer for (d): $\boxed{\frac{93}{100}}$

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Part (e): $\frac{7}{10} + \frac{20}{100}$

1. Find a common denominator:
- The denominators are 10 and 100.
- The least common denominator (LCD) is 100.

2. Convert each fraction to have the common denominator:
- $\frac{7}{10} = \frac{7 \times 10}{10 \times 10} = \frac{70}{100}$.
- $\frac{20}{100}$ remains $\frac{20}{100}$.

3. Add the fractions:
$$
\frac{70}{100} + \frac{20}{100} = \frac{70 + 20}{100} = \frac{90}{100}
$$

4. Simplify the result:
- $\frac{90}{100}$ can be simplified by dividing both numerator and denominator by their greatest common divisor (GCD), which is 10.
$$
\frac{90 \div 10}{100 \div 10} = \frac{9}{10}
$$

Answer for (e): $\boxed{\frac{9}{10}}$

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Part (f): $\frac{1}{10} + \frac{9}{100} + \frac{13}{10} + \frac{21}{100}$

1. Find a common denominator:
- The denominators are 10 and 100.
- The least common denominator (LCD) is 100.

2. Convert each fraction to have the common denominator:
- $\frac{1}{10} = \frac{1 \times 10}{10 \times 10} = \frac{10}{100}$.
- $\frac{9}{100}$ remains $\frac{9}{100}$.
- $\frac{13}{10} = \frac{13 \times 10}{10 \times 10} = \frac{130}{100}$.
- $\frac{21}{100}$ remains $\frac{21}{100}$.

3. Add all the fractions:
$$
\frac{10}{100} + \frac{9}{100} + \frac{130}{100} + \frac{21}{100} = \frac{10 + 9 + 130 + 21}{100} = \frac{170}{100}
$$

4. Simplify the result:
- $\frac{170}{100}$ can be simplified by dividing both numerator and denominator by their greatest common divisor (GCD), which is 10.
$$
\frac{170 \div 10}{100 \div 10} = \frac{17}{10}
$$

Answer for (f): $\boxed{\frac{17}{10}}$

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Final Answers:

$$
\boxed{\frac{49}{50}, \frac{37}{100}, \frac{61}{100}, \frac{93}{100}, \frac{9}{10}, \frac{17}{10}}
$$