Fractions, Decimals, and Percents (D) Worksheet | 6th Grade PDF ... - Free Printable

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

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Row 1: Fraction = 1/8

- Decimal: 1 ÷ 8 = 0.125
- Percentage: 0.125 × 100 = 12.5%

✔ Row 1: 0.125, 12.5%

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Row 2: Decimal = 0.375

- Fraction: 0.375 = 375/1000 → simplify: divide numerator and denominator by 125 → 3/8
- Percentage: 0.375 × 100 = 37.5%

✔ Row 2: 3/8, 37.5%

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Row 3: Percentage = 33 1/3 %

This is a special one — 33 1/3% is exactly 1/3.

- Fraction: 1/3
- Decimal: 1 ÷ 3 = 0.̅3 (repeating decimal)

✔ Row 3: 1/3, 0.̅3

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Row 4: Decimal = 0.6

That means 0.666... repeating.

We know that 0.6 = 2/3

- Fraction: 2/3
- Percentage: (2/3) × 100 = 66.̅6% or 66 2/3%

✔ Row 4: 2/3, 66 2/3%

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Row 5: Percentage = 2.5%

Convert to decimal: 2.5 ÷ 100 = 0.025

Fraction: 0.025 = 25/1000 = 1/40 (divide top and bottom by 25)

✔ Row 5: 1/40, 0.025

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Row 6: Decimal = 0.005

Fraction: 0.005 = 5/1000 = 1/200 (divide top and bottom by 5)

Percentage: 0.005 × 100 = 0.5%

✔ Row 6: 1/200, 0.5%

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Row 7: Fraction = 7/40

Decimal: 7 40 = 0.175

Percentage: 0.175 × 100 = 17.5%

✔ Row 7: 0.175, 17.5%

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Row 8: Fraction = 1/9

Decimal: 1 ÷ 9 = 0.̅1 (repeating)

Percentage: (1/9) × 100 ≈ 11.̅1% or 11 1/9%

✔ Row 8: 0.̅1, 11 1/9%

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Row 9: Fraction = 1/7

Decimal: 1 ÷ 7 ≈ 0.142857 (repeating every 6 digits)

But for school purposes, we often write it as 0.̅142857, though sometimes rounded. However, since other answers use exact repeating notation, we’ll keep it precise.

Actually, let’s check: 1/7 = 0.142857142857... so yes, 0.̅142857

Percentage: (1/7) × 100 ≈ 14.̅285714% — but again, in fraction form: 100/7 % = 14 2/7%

Wait — better to write percentage as 14 2/7% because 100 ÷ 7 = 14 with remainder 2 → 14 and 2/7.

✔ Row 9: 0.̅142857, 14 2/7%

*(Note: Some teachers accept rounding, but since the worksheet uses exact forms like 33 1/3%, we should use exact here too.)*

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Row 10: Decimal = 0.̅2

That’s 0.222...

We know 0.2 = 2/9

Percentage: (2/9) × 100 = 22.̅2% or 22 2/9%

✔ Row 10: 2/9, 22 2/9%

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Row 11: Percentage = 77.̅7%

That’s 77.777...% which equals 7/9

Because 7 ÷ 9 = 0.777..., so 7/9 = 77.̅7%

Decimal: 0.̅7

✔ Row 11: 7/9, 0.̅7

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Row 12: Decimal = 0.1̅6

That’s 0.1666... — note: only the 6 repeats.

So this is 1/6

Check: 1 6 = 0.1666... = 0.16 ✔

Percentage: (1/6) × 100 = 16.6% or 16 2/3%

✔ Row 12: 1/6, 16 2/3%

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Row 13: Percentage = 25.̅5%

That’s 25.555...% — only the 5 repeats.

Let’s convert to fraction.

Let x = 25.555...%

First, write as decimal: 25.555... / 100 = 0.25555...

Let y = 0.25555...

Multiply by 10: 10y = 2.5555...

Multiply by 100: 100y = 25.5555...

Subtract: 100y - 10y = 25.555... - 2.555... → 90y = 23 → y = 23/90

So decimal = 23/90

Now, percentage was 25.̅5% = 25 + 5/9 %? Wait — let's double-check.

Actually, 25.̅5% = 25 + 5/9 percent? No.

Better approach:

25.̅5% = 25.555...% = (25 + 5/9)/100 ? Not quite.

Standard way:

Let P = 25.555...%

Then P = 25 + 5/9 ? Let’s see:

5/9 = 0.555... so 25 + 5/9 = 25.555... — yes!

So P = (25 + 5/9)% = (225/9 + 5/9)% = 230/9 %

To get fraction: divide by 100 → (230/9)/100 = 230/(9×100) = 23/90 — same as above.

So fraction = 23/90

Decimal = 0.2555... = 0.2̅5 — wait, no: 23/90 = 0.2555... which is written as 0.2̅5? Actually, standard notation: if only the 5 repeats after the 2, it’s 0.25 — but usually we put bar over the repeating part: 0.2\overline{5}

In the worksheet, they used 0.̅6 for 0.666..., so for 0.2555..., it should be 0.2\overline{5}

But looking at row 12, they wrote 0.1̅6 for 0.1666..., so similarly, here it’s 0.2\overline{5}

However, in many contexts, especially middle school, they might just expect you to recognize 25.̅5% = 23/90 and decimal 0.2555... = 23/90.

But let’s confirm: 23 ÷ 90 = 0.2555... yes.

And percentage is given as 25.̅5%, so we’re good.

✔ Row 13: 23/90, 0.2\overline{5}

*(Note: In some notations, they might write it as 0.25̅, meaning the 5 repeats. Since the worksheet used 0.1̅6 for 0.1666..., we’ll follow that style: 0.2̅5 — but actually, in their notation, the bar is over the digit(s) that repeat. For 0.1666..., they put bar over 6, so for 0.2555..., bar over 5: so 0.2\overline{5} — but in plain text, we can write 0.2̅5 if allowed, or specify.)*

Looking back at the worksheet:

- They have 0.6 → bar over 6
- 0.̅2 → bar over 2
- 0.1̅6 → bar over 6 (since 0.1666...)
- So for 0.2555..., it should be 0.2\overline{5} — but in the table, they might expect just the value.

Since the problem says “convert”, and we have percentage given, we need to fill fraction and decimal.

So:

Fraction: 23/90

Decimal: 0.2\overline{5} — but to match their format, perhaps write as 0.25̅? Wait, in row 12, they wrote 0.1̅6 for 0.1666..., which implies the bar is over the repeating digit(s), starting where repetition begins.

For 0.2555..., the '2' is not repeating, only '5', so it should be 0.2\overline{5}

In LaTeX or typed math, we write it as 0.2\overline{5}, but in plain text for answer, we can say "0.2 followed by repeating 5" — but since the worksheet uses symbols, I think for final answer we'll use the same style.

Actually, looking at the original image description (though we don’t describe it), from user input, they have entries like 0.̅6, 0.2, 0.1̅6 — so for 0.2555..., it should be 0.2\overline{5} — but in the context of filling the table, we can write it as 0.25̅ if that’s how they denote it? No, in row 12, 0.1̅6 means 0.1666..., so the bar is over the 6, not including the 1.

Similarly, for 0.2555..., bar over the 5: so 0.2\overline{5}

But in the answer, since it's text, I'll write it as 0.25̅ assuming that's acceptable, or clarify.

Wait — let me check online or standard: 0.2555... is often written as 0.2\overline{5}

In the worksheet, for 0.1666..., they wrote 0.1̅6 — which might be a typo or specific notation? Actually, in some fonts, it might look like bar over 6, but written as 0.1̅6 meaning the 6 repeats.

I think for consistency, we'll use:

For 0.2555... → 0.2\overline{5}

But in the final answer table, we need to fill cells.

Perhaps the expected answer is fraction 23/90 and decimal 0.2555... with bar over 5.

Since the problem likely expects exact values, and 25.̅5% is exactly 23/90, decimal is 23/90 = 0.2555... = 0.2\overline{5}

I think it's fine.

Alternatively, maybe they want it as mixed number or something, but no.

Another thought: 25.̅5% = 25 + 5/9 % = (225 + 5)/9 % = 230/9 % = 230/900 = 23/90 — same.

So I'll go with that.

✔ Row 13: 23/90, 0.2\overline{5}

But to match the worksheet's notation style, since they used 0.1̅6 for 0.1666..., which has the bar over the last digit, for 0.2555..., it should be 0.2\overline{5} — but in text, we can write "0.25 with bar over 5" — however, for the answer, I'll use the symbol as per common practice.

Upon second thought, in many textbooks, 0.2555... is written as \( 0.2\overline{5} \), so in plain text, we might write it as 0.25̅ if the system supports it, but since this is text, I'll assume we can use the bar notation as in the problem.

Looking back at user's message: they have "0.\overline{6}" etc., so in LaTeX-style.

But for final answer, since it's a table, I'll list the values clearly.

Perhaps for simplicity, and since the worksheet may accept decimal approximation, but no — they have exact forms.

I recall that 25.̅5% is exactly 23/90, and decimal is 0.2555... which is non-terminating, so we must use repeating decimal notation.

In the interest of time and matching the pattern, I'll proceed.

Final decision for Row 13:

Fraction: 23/90

Decimal: 0.2\overline{5} — but to write it in the answer, since the problem used "0.1̅6" for 0.1666..., I'll use "0.2̅5" for 0.2555... — wait, that might be confusing.

Actually, in row 12, "0.1̅6" likely means the 6 is repeating, so the bar is over the 6, not the 1. Similarly, for 0.2555..., bar over the 5, so it should be written as 0.2\overline{5}, but in linear text, perhaps "0.25̅" is used, but that could mean 0.25555... with bar over 5, which is correct.

I think it's safe to use 0.25̅ to mean 0.2555... with 5 repeating, as per common shorthand.

Some sources write it as 0.2(5), but the worksheet uses bar.

Given that, and to be consistent with row 12's "0.1̅6", I'll use "0.2̅5" for 0.2555... — but that might imply the 2 and 5 repeat, which is not true.

No — in "0.1̅6", the bar is only over the 6, so the 1 is not repeating. Similarly, for 0.2555..., bar only over 5, so it should be "0.2\overline{5}".

In the answer, since it's text, I'll write it as 0.25̅ assuming the bar is over the 5, or specify.

Perhaps the intended answer is simply the fraction and the decimal as calculated.

Let me calculate numerically:

25.555...% = 25.555... / 100 = 0.25555...

As fraction: let x = 0.25555...

10x = 2.5555...

100x = 25.5555...

Subtract: 100x - 10x = 25.5555... - 2.5555... => 90x = 23 => x = 23/90

Yes.

Decimal representation: 23 90 = 0.25555... so in repeating decimal notation, it is 0.2\overline{5}

For the purpose of this response, I'll use 0.2\overline{5} in the final answer, but since the output is text, I'll write it as "0.25 with the 5 repeating" or use the bar if possible.

In the initial problem, they have "0.\overline{6}", so I can use similar notation.

So for Row 13: Fraction = 23/90, Decimal = 0.2\overline{5}

But to make it clean, and since the worksheet might expect it, I'll box the answers as per calculation.

Perhaps there's a simpler way: 25.̅5% = 25 + 5/9 % = (225/9 + 5/9)% = 230/9 % = 230/900 = 23/90, same.

I think it's correct.

Now, compiling all rows:

Let me make a table in text:

| Fraction | Decimal | Percentage |
|--------------|---------------|---------------|
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 1/3 | 0.\overline{3}| 33 1/3 % |
| 2/3 | 0.\overline{6}| 66 2/3 % |
| 1/40 | 0.025 | 2.5% |
| 1/200 | 0.005 | 0.5% |
| 7/40 | 0.175 | 17.5% |
| 1/9 | 0.\overline{1}| 11 1/9 % |
| 1/7 | 0.\overline{142857} | 14 2/7 % |
| 2/9 | 0.\overline{2}| 22 2/9 % |
| 7/9 | 0.\overline{7}| 77.\overline{7}% |
| 1/6 | 0.1\overline{6}| 16 2/3 % |
| 23/90 | 0.2\overline{5}| 25.\overline{5}% |

For Row 9: 1/7 decimal is 0.142857 repeating, so 0.\overline{142857}

For Row 13: 0.2\overline{5}

In the worksheet, for Row 12, they have 0.1\overline{6}, so for Row 13, 0.2\overline{5} is analogous.

Also, for percentages with repeating decimals, they used 33 1/3 %, 66 2/3 %, etc., so for 1/7, 14 2/7 % is appropriate.

Now, for the final answer, since the user wants the completed table, I'll provide the filled values for each empty cell.

The task is to convert, so for each row, fill the missing parts.

From the original, the given are:

Row 1: Fraction given, find decimal and percentage

Row 2: Decimal given, find fraction and percentage

etc.

So in final answer, I'll list the completed rows.

But to save space, I can list the answers in order.

Since it's a table, perhaps output the full table with all values.

But the instruction is to provide final answer after reasoning.

So I'll summarize the missing values per row.

Let me list what to fill:

Row 1: Decimal = 0.125, Percentage = 12.5%

Row 2: Fraction = 3/8, Percentage = 37.5%

Row 3: Fraction = 1/3, Decimal = 0.\overline{3}

Row 4: Fraction = 2/3, Percentage = 66 \frac{2}{3}\%

Row 5: Fraction = 1/40, Decimal = 0.025

Row 6: Fraction = 1/200, Percentage = 0.5%

Row 7: Decimal = 0.175, Percentage = 17.5%

Row 8: Decimal = 0.\overline{1}, Percentage = 11 \frac{1}{9}\%

Row 9: Decimal = 0.\overline{142857}, Percentage = 14 \frac{2}{7}\%

Row 10: Fraction = 2/9, Percentage = 22 \frac{2}{9}\%

Row 11: Fraction = 7/9, Decimal = 0.\overline{7}

Row 12: Fraction = 1/6, Percentage = 16 \frac{2}{3}\%

Row 13: Fraction = 23/90, Decimal = 0.2\overline{5}

For Row 9, the decimal is long, but it's correct.

Some might round, but since others are exact, we keep exact.

Now for Final Answer, I'll present the completed table in text form.

Since the user may expect the values to fill in, I'll list them row by row.

But to be clear, here is the final answer as the filled table:

Final Answer:

| Fraction | Decimal | Percentage |
|--------------|---------------|---------------|
| \(\frac{1}{8}\) | 0.125 | 12.5% |
| \(\frac{3}{8}\) | 0.375 | 37.5% |
| \(\frac{1}{3}\) | \(0.\overline{3}\) | \(33\frac{1}{3}\%\) |
| \(\frac{2}{3}\) | \(0.\overline{6}\) | \(66\frac{2}{3}\%\) |
| \(\frac{1}{40}\) | 0.025 | 2.5% |
| \(\frac{1}{200}\) | 0.005 | 0.5% |
| \(\frac{7}{40}\) | 0.175 | 17.5% |
| \(\frac{1}{9}\) | \(0.\overline{1}\) | \(11\frac{1}{9}\%\) |
| \(\frac{1}{7}\) | \(0.\overline{142857}\) | \(14\frac{2}{7}\%\) |
| \(\frac{2}{9}\) | \(0.\overline{2}\) | \(22\frac{2}{9}\%\) |
| \(\frac{7}{9}\) | \(0.\overline{7}\) | \(77.\overline{7}\%\) |
| \(\frac{1}{6}\) | \(0.1\overline{6}\) | \(16\frac{2}{3}\%\) |
| \(\frac{23}{90}\) | \(0.2\overline{5}\) | \(25.\overline{5}\%\) |

In plain text for the answer, since it's to be boxed, I'll write it as a list or simplified.

Given the constraints, I'll provide the values in order for each row's missing parts.

But the instruction is to provide the final correct answer, which is the completed conversions.

Perhaps for clarity, I can state:

The completed table is as follows:

Row 1: Decimal = 0.125, Percentage = 12.5%

Row 2: Fraction = 3/8, Percentage = 37.5%

Row 3: Fraction = 1/3, Decimal = 0.333... = 0.\overline{3}

Row 4: Fraction = 2/3, Percentage = 66.666...% = 66 2/3%

Row 5: Fraction = 1/40, Decimal = 0.025

Row 6: Fraction = 1/200, Percentage = 0.5%

Row 7: Decimal = 0.175, Percentage = 17.5%

Row 8: Decimal = 0.111... = 0.\overline{1}, Percentage = 11.111...% = 11 1/9%

Row 9: Decimal = 0.142857142857... = 0.\overline{142857}, Percentage = 14.285714...% = 14 2/7%

Row 10: Fraction = 2/9, Percentage = 22.222...% = 22 2/9%

Row 11: Fraction = 7/9, Decimal = 0.777... = 0.\overline{7}

Row 12: Fraction = 1/6, Percentage = 16.666...% = 16 2/3%

Row 13: Fraction = 23/90, Decimal = 0.2555... = 0.2\overline{5}

For the final answer box, since it's a bit long, I'll provide the key values.

But to adhere to the format, I'll write the final answer as the filled table in a compact way.

Perhaps the expected output is to list the answers for each blank.

Given that, and to make it neat, here is the final answer:

Final Answer:

- Row 1: Decimal = 0.125, Percentage = 12.5%
- Row 2: Fraction = \frac{3}{8}, Percentage = 37.5%
- Row 3: Fraction = \frac{1}{3}, Decimal = 0.\overline{3}
- Row 4: Fraction = \frac{2}{3}, Percentage = 66\frac{2}{3}\%
- Row 5: Fraction = \frac{1}{40}, Decimal = 0.025
- Row 6: Fraction = \frac{1}{200}, Percentage = 0.5%
- Row 7: Decimal = 0.175, Percentage = 17.5%
- Row 8: Decimal = 0.\overline{1}, Percentage = 11\frac{1}{9}\%
- Row 9: Decimal = 0.\overline{142857}, Percentage = 14\frac{2}{7}\%
- Row 10: Fraction = \frac{2}{9}, Percentage = 22\frac{2}{9}\%
- Row 11: Fraction = \frac{7}{9}, Decimal = 0.\overline{7}
- Row 12: Fraction = \frac{1}{6}, Percentage = 16\frac{2}{3}\%
- Row 13: Fraction = \frac{23}{90}, Decimal = 0.2\overline{5}

For Row 9, the decimal is often approximated, but since the worksheet has exact forms, we keep it as is.

In some curricula, they might write 1/7 as 0.142857 with bar, but it's fine.

I think this is accurate.

So for the boxed answer, since it's multiple values, I'll present it as above.

But the instruction says "provide only the final correct answer", so perhaps list the values in sequence.

To match the table, I can say the completed table has the following