Decimals, fractions, and percentages worksheet with conversion and comparison exercises.

Let’s solve this step by step.

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Part 1: Complete the table

We need to convert between decimals, fractions, and percentages.

Remember:
- To turn a decimal into a fraction: write it over 100 (if two decimal places) and simplify if needed.
- To turn a decimal into a percentage: multiply by 100 and add %.
- To turn a fraction like x/100 into a decimal: just write 0.x (with two digits).
- To turn a fraction like x/100 into a percentage: it’s just x%.

Let’s fill in each row:

Row 1: Decimal = 0.05
- Fraction: 0.05 = 5/100 → simplify? 5÷5=1, 100÷5=20 → 1/20
But since other fractions are over 100, maybe keep as 5/100? Let’s check the example: they wrote 0.01 as 1/100. So probably we should use denominator 100 unless told otherwise. But 5/100 can be simplified — but let’s see what the worksheet expects. Looking at later rows, they have 23/100 and 7/100 — so likely they want unsimplified form with denominator 100 for consistency. Wait — actually, 0.05 is 5 hundredths → 5/100. We can leave it like that or simplify. But since the example used 1/100 for 0.01, and didn’t simplify, I’ll use 5/100. Actually, wait — 5/100 simplifies to 1/20, but maybe the worksheet wants simplest form? Hmm. Let me think again.

Actually, looking at the instruction: “Remember that 0.01 can be written as a fraction (1/100)” — so they’re showing the direct conversion without simplifying. So for 0.05, it’s 5/100. But 5/100 reduces to 1/20. However, in the table below, they have 23/100 and 7/100 — which are already in simplest form. So perhaps we should reduce when possible? But 5/100 reduces to 1/20. Let me check standard practice.

Actually, in many school worksheets, they accept either, but since the example shows 1/100 for 0.01, and 0.05 is 5 times that, it’s 5/100. But to be safe, let’s do both and see. Wait — no, let’s look at the next part. In the ordering section, they have 7/100, 23/100, 9/100 — all over 100. So probably for the table, they expect fractions with denominator 100 where applicable.

So:

0.05 = 5/100
Percentage: 0.05 × 100 = 5% → 5%

But 5/100 can be simplified to 1/20. However, since the worksheet uses 1/100 for 0.01, and doesn't simplify, I'll go with 5/100. But let me confirm with another row.

Wait — row 3 has fraction 23/100 — that’s already reduced. Row 4 has 7/100 — also reduced. So for 0.05, if we write 5/100, it’s not reduced, but maybe that’s okay? Or should we reduce?

I think best practice is to reduce fractions. So 5/100 = 1/20. But then the pattern breaks because others are over 100. This is confusing.

Alternative approach: since the percentage column will be easy, and decimal is given, let's compute percentage first.

For any decimal, percentage = decimal × 100.

So:

Row 1: 0.05 → 5%
Fraction: 0.05 = 5/100 = 1/20 — but to match the style, perhaps write 5/100? I think I should follow the example. The example says 0.01 = 1/100, so 0.05 = 5/100. Even though it simplifies, they might want it as is. Let's proceed with 5/100 for now.

Actually, let's look at the answer key logic. In many such worksheets, they expect the fraction in simplest form. For example, 0.5 would be 1/2, not 5/10. So for 0.05, it should be 1/20.

But then why do they have 23/100 and 7/100? Because those are already simplest.

So for 0.05: fraction is 1/20, percentage is 5%.

Similarly, 0.32: fraction is 32/100 = 8/25, percentage is 32%.

This makes sense.

Let me decide: I will reduce fractions to simplest form, as that is standard mathematical practice.

So:

Row 1: Decimal = 0.05
- Fraction: 0.05 = 5/100 = 1/20
- Percentage: 5%

Row 2: Decimal = 0.32
- Fraction: 32/100 = 8/25 (divide numerator and denominator by 4)
- Percentage: 32%

Row 3: Fraction = 23/100
- Decimal: 23 ÷ 100 = 0.23
- Percentage: 23%

Row 4: Fraction = 7/100
- Decimal: 0.07
- Percentage: 7%

Row 5: Percentage = 41%
- Decimal: 41 ÷ 100 = 0.41
- Fraction: 41/100 (already simplest)

Row 6: Percentage = 8%
- Decimal: 0.08
- Fraction: 8/100 = 2/25 (simplify by dividing by 4)

Okay, that seems consistent.

Now, let's write the table:

| Decimal | Fraction | Percentage |
|---------|----------|------------|
| 0.05 | 1/20 | 5% |
| 0.32 | 8/25 | 32% |
| 0.23 | 23/100 | 23% |
| 0.07 | 7/100 | 7% |
| 0.41 | 41/100 | 41% |
| 0.08 | 2/25 | 8% |

Wait, for row 6, fraction is 8/100 = 2/25, yes.

But let me double-check row 2: 0.32 = 32/100 = 8/25? 32÷4=8, 100÷4=25, yes.

Row 1: 0.05 = 5/100 = 1/20, yes.

Now, Part 2: Rewrite each set of 3 in order, starting with the smallest.

We need to compare numbers in different forms. Best to convert all to decimals for easy comparison.

Set 1: 7/100, 12%, 0.09

Convert to decimals:
- 7/100 = 0.07
- 12% = 12/100 = 0.12
- 0.09 = 0.09

So: 0.07, 0.09, 0.12 → order: 7/100, 0.09, 12%

Set 2: 23/100, 3%, 0.3

Convert:
- 23/100 = 0.23
- 3% = 0.03
- 0.3 = 0.30

So: 0.03, 0.23, 0.30 → order: 3%, 23/100, 0.3

Set 3: 9/100, 10%, 0.01

Convert:
- 9/100 = 0.09
- 10% = 0.10
- 0.01 = 0.01

So: 0.01, 0.09, 0.10 → order: 0.01, 9/100, 10%

Part 3: Put correct sign (<, >, or =)

Compare the values. Convert to same form, usually decimal.

4. 0.77 vs 70%

70% = 0.70

0.77 > 0.70 → so >

5. 30% vs 3/100

30% = 0.30

3/100 = 0.03

0.30 > 0.03 → so >

6. 42/100 vs 0.3

42/100 = 0.42

0.3 = 0.30

0.42 > 0.30 → so >

7. 0.62 vs 7%

7% = 0.07

0.62 > 0.07 → so >

8. 29% vs 35/100

29% = 0.29

35/100 = 0.35

0.29 < 0.35 → so <

9. 35/100 vs 0.4

35/100 = 0.35

0.4 = 0.40

0.35 < 0.40 → so <

Now, let's compile all answers.

First, the table:

Decimal | Fraction | Percentage
--- | --- | ---
0.05 | 1/20 | 5%
0.32 | 8/25 | 32%
0.23 | 23/100 | 23%
0.07 | 7/100 | 7%
0.41 | 41/100 | 41%
0.08 | 2/25 | 8%

Ordering:

1. 7/100, 0.09, 12%
2. 3%, 23/100, 0.3
3. 0.01, 9/100, 10%

Comparisons:

4. >
5. >
6. >
7. >
8. <
9. <

I think that's all.

Let me verify one more time.

For the table, is 0.05 really 1/20? Yes, because 1 divided by 20 is 0.05.

0.32 = 32/100 = 8/25? 8 divided by 25 is 0.32, yes.

23/100 = 0.23, yes.

7/100 = 0.07, yes.

41% = 0.41, fraction 41/100.

8% = 0.08, fraction 8/100 = 2/25.

Ordering set 1: 7/100=0.07, 0.09, 12%=0.12 → correct.

Set 2: 3%=0.03, 23/100=0.23, 0.3=0.30 → correct.

Set 3: 0.01, 9/100=0.09, 10%=0.10 → correct.

Comparisons:

4. 0.77 > 0.70 → >

5. 0.30 > 0.03 → >

6. 0.42 > 0.30 → >

7. 0.62 > 0.07 → >

8. 0.29 < 0.35 → <

9. 0.35 < 0.40 → <

All good.

Final Answer:

Table:
- Row 1: Fraction = 1/20, Percentage = 5%
- Row 2: Fraction = 8/25, Percentage = 32%
- Row 3: Decimal = 0.23, Percentage = 23%
- Row 4: Decimal = 0.07, Percentage = 7%
- Row 5: Decimal = 0.41, Fraction = 41/100
- Row 6: Decimal = 0.08, Fraction = 2/25

Ordering:
1. 7/100, 0.09, 12%
2. 3%, 23/100, 0.3
3. 0.01, 9/100, 10%

Signs:
4. >
5. >
6. >
7. >
8. <
9. <