Understanding percentages worksheet with exercises on decimal to percentage conversion, fraction to percentage conversion, and sorting values into categories.

Let's solve the worksheet step by step and explain each part.

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Understanding Percentages Worksheet

#### Key Concept Reminder:
- "Per cent" means "out of 100".
- 50% = 50 out of 100 = 50/100 = 1/2 = 0.5

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Part 1: Convert decimals to percentages

To convert a decimal to a percentage, multiply by 100.

1. 0.5 = 0.5 × 100 = 50%
2. 0.7 = 0.7 × 100 = 70%
3. 0.9 = 0.9 × 100 = 90%
4. 0.45 = 0.45 × 100 = 45%
5. 0.61 = 0.61 × 100 = 61%
6. 0.77 = 0.77 × 100 = 77%

✔ Answers:
1. 50%
2. 70%
3. 90%
4. 45%
5. 61%
6. 77%

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Part 2: Complete the number sentences

We need to express fractions with denominator 100, then write as percentage and decimal.

#### 7.
$$
\frac{9}{10} = \frac{?}{100} = ?\% = 0.?
$$

- Multiply numerator and denominator by 10:
$$
\frac{9}{10} = \frac{90}{100}
$$
- 90/100 = 90%
- 90% = 0.9

✔ So:
$$
\frac{9}{10} = \frac{90}{100} = 90\% = 0.9
$$

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#### 8.
$$
\frac{6}{10} = \frac{?}{100} = ?\% = 0.?
$$

- Multiply numerator and denominator by 10:
$$
\frac{6}{10} = \frac{60}{100}
$$
- 60/100 = 60%
- 60% = 0.6

✔ So:
$$
\frac{6}{10} = \frac{60}{100} = 60\% = 0.6
$$

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#### 9.
$$
\frac{40}{200} = \frac{?}{100} = ?\% = 0.?
$$

- Simplify:
$$
\frac{40}{200} = \frac{1}{5} = 0.2
$$
- To write with denominator 100:
$$
\frac{40}{200} = \frac{20}{100}
$$
- 20/100 = 20%
- 20% = 0.2

✔ So:
$$
\frac{40}{200} = \frac{20}{100} = 20\% = 0.2
$$

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Part 3: Sort the values into columns

We are given:

- 0.6
- 49%
- 80%
- 40/200
- 0.99
- 25/50
- 0.5

We need to classify them as:
- Less than a half (less than 0.5)
- Equal to a half (equal to 0.5)
- More than a half (greater than 0.5)

Let’s convert all to decimals or compare directly.

1. 0.6 → 0.6 > 0.5 → More than a half
2. 49% → 49/100 = 0.49 < 0.5 → Less than a half
3. 80% → 0.8 > 0.5 → More than a half
4. 40/200 → We already did this: = 0.2 → Less than a half
5. 0.99 → > 0.5 → More than a half
6. 25/50 → = 1/2 = 0.5 → Equal to a half
7. 0.5 → = 0.5 → Equal to a half

Now sort:

#### ✔ Final Sorting:

| Less than a half | Equal to a half | More than a half |
|------------------|------------------|-------------------|
| 49% | 25/50 | 0.6 |
| 40/200 | 0.5 | 80% |
| | | 0.99 |

> Note: You can list in any order within each column.

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✔ Final Answers Summary:

#### Part 1: Decimals to Percentages
1. 50%
2. 70%
3. 90%
4. 45%
5. 61%
6. 77%

#### Part 2: Number Sentences
7. $\frac{9}{10} = \frac{90}{100} = 90\% = 0.9$
8. $\frac{6}{10} = \frac{60}{100} = 60\% = 0.6$
9. $\frac{40}{200} = \frac{20}{100} = 20\% = 0.2$

#### Part 3: Sorting
| Less than a half | Equal to a half | More than a half |
|------------------|------------------|-------------------|
| 49% | 25/50 | 0.6 |
| 40/200 | 0.5 | 80% |
| | | 0.99 |

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This completes the worksheet! Let me know if you'd like a printable version or further explanation on any step.