Math worksheet on converting decimals, fractions, and percentages with exercises for ordering and comparison.

Here is the step-by-step solution to complete your worksheet.

Part 1: Complete the Table

To fill in the table, we need to convert between decimals, fractions, and percentages.
* Decimal to Fraction: Write the decimal over 100 (e.g., $0.05 = \frac{5}{100}$) and simplify if possible.
* Decimal to Percentage: Multiply by 100 and add the % sign (move the decimal point two places to the right).
* Fraction to Decimal: Divide the top number by the bottom number. Since these are all over 100, just move the decimal point two places to the left.
* Percentage to Decimal: Divide by 100 (move the decimal point two places to the left).

Row 1: 0.05
* Fraction: $\frac{5}{100}$. Simplify by dividing top and bottom by 5: $\frac{1}{20}$.
* Percentage: $0.05 \times 100 = 5\%$

Row 2: 0.32
* Fraction: $\frac{32}{100}$. Simplify by dividing top and bottom by 4: $\frac{8}{25}$.
* Percentage: $0.32 \times 100 = 32\%$

Row 3: $\frac{23}{100}$
* Decimal: Move decimal 2 places left: $0.23$
* Percentage: The denominator is 100, so it is $23\%$

Row 4: $\frac{7}{100}$
* Decimal: Move decimal 2 places left: $0.07$
* Percentage: The denominator is 100, so it is $7\%$

Row 5: 41%
* Decimal: Move decimal 2 places left: $0.41$
* Fraction: $\frac{41}{100}$ (This cannot be simplified further because 41 is a prime number).

Row 6: 8%
* Decimal: Move decimal 2 places left: $0.08$
* Fraction: $\frac{8}{100}$. Simplify by dividing top and bottom by 4: $\frac{2}{25}$.

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Part 2: Rewrite in Order (Smallest to Largest)

To compare these easily, let's convert everything to decimals first.

Set 1: $\frac{7}{100}$, $12\%$, $0.09$
* $\frac{7}{100} = 0.07$
* $12\% = 0.12$
* $0.09 = 0.09$
* Order: $0.07 < 0.09 < 0.12$
* Answer: $\frac{7}{100}, \quad 0.09, \quad 12\%$

Set 2: $\frac{23}{100}$, $3\%$, $0.3$
* $\frac{23}{100} = 0.23$
* $3\% = 0.03$
* $0.3 = 0.30$
* Order: $0.03 < 0.23 < 0.30$
* Answer: $3\%, \quad \frac{23}{100}, \quad 0.3$

Set 3: $\frac{9}{100}$, $10\%$, $0.01$
* $\frac{9}{100} = 0.09$
* $10\% = 0.10$
* $0.01 = 0.01$
* Order: $0.01 < 0.09 < 0.10$
* Answer: $0.01, \quad \frac{9}{100}, \quad 10\%$

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Part 3: Put in the Correct Sign (<, >, or =)

4. $0.77 \bigcirc 70\%$
* Convert $70\%$ to decimal: $0.70$
* Compare: $0.77 > 0.70$
* Sign: $>$

5. $30\% \bigcirc \frac{3}{100}$
* Convert $30\%$ to fraction: $\frac{30}{100}$
* Compare: $\frac{30}{100} > \frac{3}{100}$
* Sign: $>$

6. $\frac{42}{100} \bigcirc 0.3$
* Convert $\frac{42}{100}$ to decimal: $0.42$
* Convert $0.3$ to two decimal places for easier comparison: $0.30$
* Compare: $0.42 > 0.30$
* Sign: $>$

7. $0.62 \bigcirc 7\%$
* Convert $7\%$ to decimal: $0.07$
* Compare: $0.62 > 0.07$
* Sign: $>$

8. $29\% \bigcirc \frac{35}{100}$
* Convert $29\%$ to fraction: $\frac{29}{100}$
* Compare: $\frac{29}{100} < \frac{35}{100}$
* Sign: $<$

9. $\frac{35}{100} \bigcirc 0.4$
* Convert $\frac{35}{100}$ to decimal: $0.35$
* Convert $0.4$ to two decimal places: $0.40$
* Compare: $0.35 < 0.40$
* Sign: $<$

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Final Answer:

Table Completion:

| Decimal | Fraction | Percentage |
| :--- | :--- | :--- |
| 0.05 | $\frac{1}{20}$ | 5% |
| 0.32 | $\frac{8}{25}$ | 32% |
| 0.23 | $\frac{23}{100}$ | 23% |
| 0.07 | $\frac{7}{100}$ | 7% |
| 0.41 | $\frac{41}{100}$ | 41% |
| 0.08 | $\frac{2}{25}$ | 8% |

Ordering Sets (Smallest to Largest):

1. $\frac{7}{100}, \quad 0.09, \quad 12\%$
2. $3\%, \quad \frac{23}{100}, \quad 0.3$
3. $0.01, \quad \frac{9}{100}, \quad 10\%$

Comparison Signs:

4. $0.77 \mathbf{>} 70\%$
5. $30\% \mathbf{>} \frac{3}{100}$
6. $\frac{42}{100} \mathbf{>} 0.3$
7. $0.62 \mathbf{>} 7\%$
8. $29\% \mathbf{<} \frac{35}{100}$
9. $\frac{35}{100} \mathbf{<} 0.4$