Converting Fractions, Decimals, and Percents (B) Worksheet | PDF ... - Free Printable

Let’s solve each table step by step. We’ll convert between decimals, fractions, and percentages as needed.

---

First Table: Decimal ↔ Percentage

We know:
- To go from decimal to percentage → multiply by 100 and add % sign.
- To go from percentage to decimal → divide by 100 (remove % sign).

Given:

Decimal row:
0.01 → ?% → 1%
0.58 → ?% → 58%
0.09 → ?% → 9%
? ← 6% → 0.06
? ← 0.2% → 0.002
? ← 1.5% → 0.015
? ← ½% → ½% = 0.5% → 0.005

So first table filled:

| Decimal | 0.01 | 0.58 | 0.09 | 0.06 | 0.002 | 0.015 | 0.005 |
|-----------|-------|-------|-------|-------|--------|--------|--------|
| Percentage| 1% | 58% | 9% | 6% | 0.2% | 1.5% | ½% |

---

Second Table: Fraction ↔ Percentage

Convert fraction to percent: divide numerator by denominator, then ×100.

Given:

Fraction row:
¼ → ?% → 1÷4 = 0.25 → 25%
¹/₁₀ → ?% → 1÷10 = 0.1 → 10%
³/₁₀₀ → ?% → 3÷100 = 0.03 → 3%
? ← 50% → 50/100 = ½
? ← 17% → 17/100 → ¹⁷/₁₀₀ (already simplified)
? ← 90% → 90/100 = /₁₀
? ← 1% → 1/100 → ¹/₁₀₀

So second table filled:

| Fraction | ¼ | ¹/₁₀ | ³/₁₀₀ | ½ | ¹⁷/₁₀₀ | ⁹/₁₀ | ¹/₁₀₀ |
|-----------|-------|-------|--------|-------|---------|--------|--------|
| Percentage| 25% | 10% | 3% | 50% | 17% | 90% | 1% |

---

Third Table: Fraction ↔ Percentage

Again, convert fraction to percent or vice versa.

Given:

Percentage row:
20% → ? → 20/100 = ¹/₅
80% → ? → 80/100 = ⁴/₅
15% → ? → 15/100 = ³/₂₀
³/ → ?% → 3÷5 = 0.6 → 60%
¹/₅₀ → ?% → 1÷50 = 0.02 → 2%
¹²/₂₅ → ?% → 12÷25 = 0.48 → 48%
/₂₀ → ?% → 7÷20 = 0.35 → 35%

So third table filled:

| Fraction | ¹/₅ | ⁴/₅ | ³/₂₀ | ³/₅ | ¹/₅₀ | ¹²/₂₅ | ⁷/₂₀ |
|-----------|-------|-------|--------|-------|--------|--------|--------|
| Percentage| 20% | 80% | 15% | 60% | 2% | 48% | 35% |

---

Fourth Table: Fraction → Decimal

Divide numerator by denominator.

Given fractions:

¹/₃ → 1 ÷ 3 = 0.333... → write as 0.\overline{3} (but for school level, often rounded to 0.33 or left as repeating — we’ll use exact decimal form if possible, but since it repeats, we can write 0.333... or just 0.3)

But let’s check what’s expected. Since other answers may be terminating, but these are not. Let’s compute all:

¹/₃ = 0.333... → 0.\overline{3}
²/₃ = 0.666... → 0.\overline{6}
¹/₉ = 0.111... → 0.\overline{1}
¹/ = 0.1666... → 0.1\overline{6}
⁵/₆ = 0.8333... → 0.8\overline{3}
¹/₁₁ = 0.090909... → 0.\overline{09}
³/₇ ≈ 0.428571... → this is repeating too: 0.\overline{428571}

But in many middle school worksheets, they might expect you to write the decimal approximation to 3 places or recognize repeating patterns. However, looking at the context of the worksheet ( Cazoom Maths, grade 6), they likely want exact decimal representations where possible, and for repeating decimals, perhaps written with bar notation or rounded.

Wait — let me double-check if any of these actually terminate? No, none do except maybe if misread.

Actually, let’s list them properly:

¹/ = 0.333... → 0.3̅
²/ = 0.666... → 0.6̅
¹/ = 0.111... → 0.1̅
¹/₆ = 0.1666... → 0.16̅
⁵/₆ = 0.8333... → 0.83̅
¹/₁₁ = 0.090909... → 0.09̅
³/ = 0.428571428571... → 0.428571̅

But for simplicity in filling the table, and since the worksheet doesn’t specify rounding, I think we should write the repeating decimals using bar notation over the repeating part.

However, in some curricula, they accept 3 decimal places. But given that 1/3 is exactly 0.333..., and others similar, I’ll use standard repeating decimal notation.

Alternatively, perhaps the worksheet expects us to leave them as decimals without bars? But that would be inaccurate.

Looking back at the original image — the last table has “Decimal” row empty under those fractions. In typical US 6th grade (as per 6.RP.A.3c), they learn to convert fractions to decimals, including repeating ones, and represent them appropriately.

I will write them with bar notation for accuracy.

But let me confirm calculations once more:

¹/₃ = 0.333... → correct
²/₃ = 0.666... → correct
¹/₉ = 0.111... → correct
¹/₆ = 0.1666... → yes, because 1÷6=0.1666...
⁵/₆ = 0.8333... → yes
¹/₁₁ = 0.090909... → yes, period 2
³/₇ = 0.428571 repeating → period 6

So final fourth table:

| Fraction | ¹/₃ | ²/₃ | ¹/₉ | ¹/₆ | ⁵/₆ | ¹/₁₁ | ³/₇ |
|-----------|-----------|-----------|-----------|------------|------------|------------|--------------|
| Decimal | 0.3̅ | 0.6̅ | 0.1 | 0.16̅ | 0.83̅ | 0.09̅ | 0.428571̅ |

But wait — in many printed worksheets, especially for younger students, they might prefer writing out a few digits or using ellipsis. However, since this is an answer key, precision matters.

Alternatively, perhaps they expect decimal approximations to 3 places? Let’s see the other tables — no decimals were approximate there; all were exact conversions.

For example, 0.01 was exact, 0.58 exact, etc.

In the fourth table, since all are non-terminating, we must indicate repetition.

But let me check online or standard practice for Cazoom Maths — actually, I recall that in their materials, for such problems, they often write the repeating decimal with a dot or bar.

Since we’re to provide final answer, and to keep it clean, I’ll write them using standard mathematical notation for repeating decimals.

However, in plain text, we can write:

1/3 = 0.333...
But better to use bar.

Since the output is text, I’ll use the format like "0.3..." but that’s not precise.

Actually, in the context of this problem, and since the user didn't specify format, I'll write the decimals as they are commonly represented in such worksheets: either as repeating with bar or as approximate.

Wait — let's look again at the worksheet title: “Converting Fractions, Decimals, and Percents (B)” — and it’s for 6.RP.A.3c which is about ratio and proportion, converting among forms.

In Common Core 6.RP.A.3c, students are expected to convert fractions to decimals, and understand that some repeat.

I think for accuracy, I’ll use the bar notation in the final answer.

But in text, how to represent? Usually, we write 0.\overline{3}, etc.

Yes.

So:

¹/₃ = 0.\overline{3}
²/₃ = 0.\overline{6}
¹/ = 0.\overline{1}
¹/₆ = 0.1\overline{6}
⁵/₆ = 0.8\overline{3}
¹/₁₁ = 0.\overline{09}
³/₇ = 0.\overline{428571}

Now, compiling all tables into final answer.

But the question says “Fill in the missing gaps.” So we need to present the completed tables.

Since it’s multiple tables, I’ll list each one with the filled values.

Final Answer should contain all filled-in values for each cell.

Perhaps best to write each table as a grid with answers.

But since it’s text, I’ll describe row by row.

Alternatively, since the user wants the final answer after reasoning, I’ll summarize all missing values in order.

But to be clear, let’s list the answers for each blank in sequence.

Looking at the original layout:

Table 1: Decimal and Percentage rows.

Missing in Decimal row: positions 4,5,6,7 → corresponding to percentages 6%, 0.2%, 1.5%, ½%

So:

After 0.09, next decimal is for 6% → 0.06
Then for 0.2% → 0.002
Then for 1.5% → 0.015
Then for ½% → 0.005

And in Percentage row, first three blanks: for decimals 0.01→1%, 0.58→58%, 0.09→9%

So Table 1 completed:

Decimal: 0.01, 0.58, 0.09, 0.06, 0.002, 0.015, 0.005
Percentage: 1%, 58%, 9%, 6%, 0.2%, 1.5%, ½%

Table 2: Fraction and Percentage

Fraction row given: ¼, ¹/₁₀, ³/₁₀₀, then blanks for 50%,17%,90%,1%

So fractions for those percentages:

50% = ½
17% = ¹⁷/₁₀₀
90% = ⁹/₁₀
1% = ¹/₁₀₀

Percentage row: for fractions ¼→25%, ¹/₁₀→10%, ³/₁₀₀→3%

So Table 2:

Fraction: ¼, ¹/₁₀, ³/₁₀₀, ½, ¹⁷/₁₀₀, ⁹/₁₀, ¹/₁₀₀
Percentage: 25%, 10%, 3%, 50%, 17%, 90%, 1%

Table 3: Fraction and Percentage

Percentage row given: 20%,80%,15%, then blanks for fractions ³/₅,¹/₅₀,¹²/₂₅,⁷/₂₀

So fractions for first three percentages:

20% = ¹/
80% = ⁴/
15% = ³/₂₀

Percentages for given fractions:

³/₅ = 60%
¹/₅₀ = 2%
¹²/₂₅ = 48%
⁷/₂₀ = 35%

So Table 3:

Fraction: ¹/₅, ⁴/₅, ³/₂₀, ³/₅, ¹/₅₀, ¹²/₂, ⁷/₂₀
Percentage: 20%, 80%, 15%, 60%, 2%, 48%, 35%

Table 4: Fraction to Decimal

Fractions: ¹/₃, ²/₃, ¹/₉, ¹/₆, ⁵/₆, ¹/₁₁, ³/₇

Decimals:

¹/₃ = 0.\overline{3}
²/₃ = 0.\overline{6}
¹/ = 0.\overline{1}
¹/₆ = 0.1\overline{6}
⁵/₆ = 0.8\overline{3}
¹/₁₁ = 0.\overline{09}
³/₇ = 0.\overline{428571}

Now, for the final answer, since it's a fill-in-the-blank, I'll present each table with the missing values filled.

But to match the format, perhaps list the answers in order as they appear.

Since the instruction is to provide the final answer after reasoning, and it's a bit long, I'll box the complete filled tables.

But in text, I can write:

Final Answer:

Table 1:
Decimal: 0.01, 0.58, 0.09, 0.06, 0.002, 0.015, 0.005
Percentage: 1%, 58%, 9%, 6%, 0.2%, 1.5%, \frac{1}{2}\%

Table 2:
Fraction: \frac{1}{4}, \frac{1}{10}, \frac{3}{100}, \frac{1}{2}, \frac{17}{100}, \frac{9}{10}, \frac{1}{100}
Percentage: 25%, 10%, 3%, 50%, 17%, 90%, 1%

Table 3:
Fraction: \frac{1}{5}, \frac{4}{5}, \frac{3}{20}, \frac{3}{5}, \frac{1}{50}, \frac{12}{25}, \frac{7}{20}
Percentage: 20%, 80%, 15%, 60%, 2%, 48%, 35%

Table 4:
Fraction: \frac{1}{3}, \frac{2}{3}, \frac{1}{9}, \frac{1}{6}, \frac{5}{6}, \frac{1}{11}, \frac{3}{7}
Decimal: 0.\overline{3}, 0.\overline{6}, 0.\overline{1}, 0.1\overline{6}, 0.8\overline{3}, 0.\overline{09}, 0.\overline{428571}

To make it neat, and since the user might expect simple decimal approximations, but I think for correctness, repeating decimals should be indicated.

However, upon second thought, in many elementary worksheets, for 1/3 they might write 0.333, but that's approximate. Given that the other conversions are exact, I think we should use exact forms.

But let me verify one thing: in Table 1, ½% is given, which is 0.5%, so decimal 0.005 — that's exact.

Similarly, in Table 4, all are irrational in decimal sense, but rational numbers, so repeating decimals are exact representation.

I think it's fine.

Perhaps for Table 4, since it's "Decimal" row, and no specification, but to be safe, I'll use the repeating decimal notation.

Now, for the final answer box, I'll write the completed tables as above.

But to save space, perhaps list the missing values in order.

The problem says "fill in the missing gaps", so for each blank cell, provide the value.

But there are many cells.

Perhaps the expected answer is to have the full tables.

Since this is a text response, I'll present it clearly.

Final decision: Provide each table with all values, highlighting the filled ones, but since it's final answer, just the complete version.

So here goes.