Converting between Fractions, Decimals, and Percents Worksheets - Free Printable

Problem: Converting Fractions, Decimals, and Percents

#### Part A: Convert the following.

1. Convert $\frac{2}{5}$ to Decimal, Percent
- Decimal: To convert a fraction to a decimal, divide the numerator by the denominator.
\[
\frac{2}{5} = 2 \div 5 = 0.4
\]
- Percent: To convert a decimal to a percent, multiply by 100.
\[
0.4 \times 100 = 40\%
\]

Answer:
- Decimal: $0.4$
- Percent: $40\%$

2. Convert $0.5$ to Fraction, Percent
- Fraction: To convert a decimal to a fraction, write the decimal as a fraction with a denominator of 10 (or higher powers of 10 based on the number of decimal places), then simplify.
\[
0.5 = \frac{5}{10} = \frac{1}{2}
\]
- Percent: To convert a decimal to a percent, multiply by 100.
\[
0.5 \times 100 = 50\%
\]

Answer:
- Fraction: $\frac{1}{2}$
- Percent: $50\%$

3. Convert $35\%$ to Decimal, Fraction
- Decimal: To convert a percent to a decimal, divide by 100.
\[
35\% = \frac{35}{100} = 0.35
\]
- Fraction: To convert a percent to a fraction, write it as a fraction over 100, then simplify.
\[
35\% = \frac{35}{100} = \frac{7}{20}
\]

Answer:
- Decimal: $0.35$
- Fraction: $\frac{7}{20}$

4. Convert $\frac{3}{12}$ to Percent, Decimal
- Percent: First, simplify the fraction.
\[
\frac{3}{12} = \frac{1}{4}
\]
Then, convert the simplified fraction to a decimal.
\[
\frac{1}{4} = 1 \div 4 = 0.25
\]
Finally, convert the decimal to a percent.
\[
0.25 \times 100 = 25\%
\]
- Decimal: As calculated above, the decimal is $0.25$.

Answer:
- Percent: $25\%$
- Decimal: $0.25$

---

#### Part B: Complete the table.

| Fractions | Decimals | Percents |
|-----------|----------|----------|
| 1) | $0.3$ | |
| 2) | | |
| 3) | | $2\%$ |
| 4) | $1.8$ | |

1. Row 1: Decimal $0.3$
- Fraction: Write $0.3$ as a fraction.
\[
0.3 = \frac{3}{10}
\]
- Percent: Convert $0.3$ to a percent.
\[
0.3 \times 100 = 30\%
\]

Completed Row:
- Fractions: $\frac{3}{10}$
- Decimals: $0.3$
- Percents: $30\%$

2. Row 2: Fraction $\frac{7}{4}$
- Decimal: Divide the numerator by the denominator.
\[
\frac{7}{4} = 7 \div 4 = 1.75
\]
- Percent: Convert $1.75$ to a percent.
\[
1.75 \times 100 = 175\%
\]

Completed Row:
- Fractions: $\frac{7}{4}$
- Decimals: $1.75$
- Percents: $175\%$

3. Row 3: Percent $2\%$
- Decimal: Convert $2\%$ to a decimal.
\[
2\% = \frac{2}{100} = 0.02
\]
- Fraction: Write $2\%$ as a fraction.
\[
2\% = \frac{2}{100} = \frac{1}{50}
\]

Completed Row:
- Fractions: $\frac{1}{50}$
- Decimals: $0.02$
- Percents: $2\%$

4. Row 4: Decimal $1.8$
- Fraction: Write $1.8$ as a fraction.
\[
1.8 = \frac{18}{10} = \frac{9}{5}
\]
- Percent: Convert $1.8$ to a percent.
\[
1.8 \times 100 = 180\%
\]

Completed Row:
- Fractions: $\frac{9}{5}$
- Decimals: $1.8$
- Percents: $180\%$

---

Final Answer:

#### Part A:
1. $\frac{2}{5}$:
- Decimal: $0.4$
- Percent: $40\%$

2. $0.5$:
- Fraction: $\frac{1}{2}$
- Percent: $50\%$

3. $35\%$:
- Decimal: $0.35$
- Fraction: $\frac{7}{20}$

4. $\frac{3}{12}$:
- Percent: $25\%$
- Decimal: $0.25$

#### Part B:
| Fractions | Decimals | Percents |
|-----------|----------|----------|
| 1) $\frac{3}{10}$ | $0.3$ | $30\%$ |
| 2) $\frac{7}{4}$ | $1.75$ | $175\%$ |
| 3) $\frac{1}{50}$ | $0.02$ | $2\%$ |
| 4) $\frac{9}{5}$ | $1.8$ | $180\%$ |

Boxed Final Answer:
\[
\boxed{
\begin{array}{c|c|c}
\text{Fractions} & \text{Decimals} & \text{Percents} \\
\hline
\frac{3}{10} & 0.3 & 30\% \\
\frac{7}{4} & 1.75 & 175\% \\
\frac{1}{50} & 0.02 & 2\% \\
\frac{9}{5} & 1.8 & 180\% \\
\end{array}
}
\]