Convert fractions, decimals, and percentages with this educational worksheet.

Let’s solve each table step by step. We’ll convert between decimals, fractions, and percents using simple rules:

- To turn a decimal into a percent: multiply by 100 (move decimal point two places right).
- To turn a percent into a decimal: divide by 100 (move decimal point two places left).
- To turn a fraction into a decimal: divide numerator by denominator.
- To turn a decimal into a fraction: write it over 10, 100, 1000 etc., then simplify.
- To turn a percent into a fraction: write it over 100, then simplify.

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First Table: Decimal ↔ Percentage

We are given some decimals and some percentages — we need to fill in the blanks.

Column 1:
Decimal = 0.03 → Percent = 0.03 × 100 = 3%

Column 2:
Decimal = 0.89 → Percent = 0.89 × 100 = 89%

Column 3:
Decimal = 0.075 → Percent = 0.075 × 100 = 7.5%

Column 4:
Percent = 63% → Decimal = 63 ÷ 100 = 0.63

Column 5:
Percent = 5.8% → Decimal = 5.8 ÷ 100 = 0.058

Column 6:
Percent = 0.1% → Decimal = 0.1 ÷ 100 = 0.001

Column 7:
Percent = 6⅕% → First, 6⅕ = 6 + 1/5 = 6.2 → So 6.2% → Decimal = 6.2 ÷ 100 = 0.062

✔ First Table Complete:
Decimals: 0.03, 0.89, 0.075, 0.63, 0.058, 0.001, 0.062
Percents: 3%, 89%, 7.5%, 63%, 5.8%, 0.1%, 6⅕%

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Second Table: Fraction ↔ Percentage

Given fractions and percents — fill in missing ones.

Column 1:
Fraction = 3/4 → Decimal = 3 ÷ 4 = 0.75 → Percent = 0.75 × 100 = 75%

Column 2:
Fraction = 9/10 → Decimal = 9 ÷ 10 = 0.9 → Percent = 0.9 × 100 = 90%

Column 3:
Fraction = 43/100 → Already over 100 → Percent = 43%

Column 4:
Percent = 20% → Fraction = 20/100 = 1/5 (simplify)

Column 5:
Percent = 65% → Fraction = 65/100 = 13/20 (divide top and bottom by 5)

Column 6:
Percent = 8% → Fraction = 8/100 = 2/25 (divide by 4)

Column 7:
Percent = 1.5% → Fraction = 1.5 / 100 = 15/1000 = 3/200 (multiply num/den by 10 to eliminate decimal, then simplify)

✔ Second Table Complete:
Fractions: 3/4, 9/10, 43/100, 1/5, 13/20, 2/25, 3/200
Percents: 75%, 90%, 43%, 20%, 65%, 8%, 1.5%

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Third Table: Fraction ↔ Decimal

Given some fractions and decimals — fill in blanks.

Column 1:
Decimal = 0.3 → Fraction = 3/10 → 3/10

Column 2:
Decimal = 0.12 → Fraction = 12/100 = 3/25 (simplify by dividing by 4)

Column 3:
Decimal = 0.95 → Fraction = 95/100 = 19/20 (divide by 5)

Column 4:
Fraction = 4/5 → Decimal = 4 ÷ 5 = 0.8

Column 5:
Fraction = 9/20 → Decimal = 9 ÷ 20 = 0.45

Column 6:
Fraction = 7/40 → Decimal = 7 ÷ 40 = 0.175

Column 7:
Fraction = 33/160 → Let’s divide: 33 ÷ 160
→ 160 goes into 33 zero times → 330 ÷ 160 = 2 (320), remainder 10 → 100 ÷ 160 = 0 → 1000 ÷ 160 = 6 (960), remainder 40 → 400 ÷ 160 = 2 (320), remainder 80 → 800 ÷ 160 = 5 → so 0.20625
Wait — let me check with calculator-style division:

33 ÷ 160 = ?

Actually, 160 × 0.2 = 32 → 33 - 32 = 1 → so 0.2 + (1/160) = 0.2 + 0.00625 = 0.20625

But looking at other answers, maybe they expect exact decimal? Yes, 33/160 = 0.20625 exactly.

✔ Third Table Complete:
Fractions: 3/10, 3/25, 19/20, 4/5, 9/20, 7/40, 33/160
Decimals: 0.3, 0.12, 0.95, 0.8, 0.45, 0.175, 0.20625

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Fourth Table: Fraction ↔ Decimal (with repeating decimals)

This one has repeating decimals (indicated by bar over digits).

Recall:
- 0.0̅7̅ means 0.070707... = 7/99
- 0.1̅2̅ means 0.121212... = 12/99 = 4/33
- 0.7̅58̅ means 0.758758758... = 758/999
- 0.6̅0̅1̅ means 0.601601601... = 601/999
- 0.5̅42̅1 means 0.54215421... = 5421/9999

Also, we’re given two fractions: 5/6 and 8/33 — need their decimal forms.

Column 1:
Fraction = 5/6 → Divide 5 ÷ 6 = 0.8333... = 0.8̅3 (but wait — actually 5÷6=0.8333..., which is 0.8 followed by repeating 3 → written as 0.8̅3̅? Actually standard notation is 0.8̅3̅ only if both repeat — but here only 3 repeats → should be 0.8̅3̅? Wait no — correct way: 5/6 = 0.8333... = 0.8̅3̅ is not standard. Usually we write 0.8̅3̅ meaning 8 and 3 repeat? No — better to write as 0.8\overline{3} — but in this worksheet, they use bar over repeating part.

Looking at examples: 0.0̅7̅ → bar over 07 → so two-digit repeat.

So for 5/6: 5 ÷ 6 = 0.8333... → only the 3 repeats → so it should be written as 0.8\overline{3} — but in the format of the table, they might expect just the decimal with bar over repeating digit(s). Since 3 repeats, we write 0.8̅3̅? Wait — no, that would imply both 8 and 3 repeat. Actually, standard is to put bar only over repeating part.

In the table, they have:
- 0.0̅7̅ → bar over "07" → so two digits repeat
- 0.1̅2̅ → bar over "12"
- 0.7̅5̅8̅ → bar over "758"
- etc.

So for 5/6 = 0.8333... → only the 3 repeats → so we write 0.8\overline{3} — but how to represent in text? In the answer, we can write as 0.8̅3̅? Actually, in many worksheets, they write it as 0.8̅3̅ meaning the 3 repeats — but strictly, it should be 0.8 with bar over 3 only.

Wait — look at the last column: 0.5̅4̅21̅ — bar over all four digits → so they are indicating the entire sequence repeats.

For 5/6: 5 ÷ 6 = 0.8333... → so after 8, only 3 repeats → so it's 0.8 followed by repeating 3 → so we write 0.8\overline{3} — but since the table uses bars over multiple digits when needed, for single digit repeat, we can write 0.8̅3̅? Actually, I think in this context, they expect:

5/6 = 0.8333... → written as 0.8̅3̅ is incorrect; it should be 0.8\overline{3} — but perhaps in the answer key, they accept 0.83 with bar over 3 only. However, looking at the pattern in the table, for example, 0.0̅7̅ has bar over two digits, so for single digit, they might still use bar over that digit.

Actually, let's calculate properly:

5/6 = 0.8333... → so the repeating part is "3", starting after first decimal → so we write it as 0.8\overline{3} — but in plain text, we can write as 0.83 with bar over 3 — but since we're typing, I'll use notation like 0.8\overline{3}, but for final answer, we need to match the table's style.

Looking back at the user's image description: they have "0.0̅7̅" which likely means bar over "07", so two digits. Similarly, "0.1̅2̅" bar over "12".

For 5/6, it's 0.8333... — so only one digit repeats: 3. So we should write it as 0.8\overline{3} — but in the table format, perhaps they expect 0.8̅3̅? That would be misleading. Actually, standard mathematical notation is to put the bar only over the repeating part. So for 5/6, it's 0.8 with a bar over the 3 — so in text, we can write it as 0.8̅3̅? No — better to write as 0.8\overline{3}.

But to match the table's style, let's see what they did for others.

They have:
- 0.0̅7̅ → which is 7/99
- 0.1̅2̅ → 12/99 = 4/33
- 0.7̅5̅8̅ → 758/999
- 0.6̅01̅ → 601/999
- 0.5̅42̅1 → 5421/9999

Now, for 5/6: 5/6 = ? Let's find its decimal: 5 ÷ 6 = 0.8333... = 0.8 + 0.0333... = 0.8 + 1/30 = but better: 5/6 = 83.333.../100 — no.

Standard way: 5/6 = 0.8\overline{3}

Similarly, 8/33: 8 ÷ 33 = ? 33*0.24 = 7.92, remainder 0.08 → 80÷33=2 (66), rem 14 → 140÷33=4 (132), rem 8 → so 0.242424... = 0.\overline{24} — so bar over "24"

Yes! 8/33 = 0.242424... = 0.\overline{24}

And 5/6 = 0.8333... = 0.8\overline{3} — but in the table, they might write it as 0.8̅3̅? Or perhaps they expect the full repeating sequence.

Actually, 5/6 = 0.8333... can also be written as 0.8\overline{3}, and since only one digit repeats, we put bar over 3.

In the answer, for consistency, I'll use the same notation as the table: for single digit repeat, bar over that digit; for multi-digit, bar over all.

So:

Column 1:
Fraction = 5/6 → Decimal = 0.8\overline{3} — but in text, we can write as 0.8̅3̅? To avoid confusion, let's calculate numerically.

Perhaps the table expects the decimal representation with bar over the repeating part as shown.

For 5/6: it's commonly written as 0.8\overline{3}

For 8/33: 8 ÷ 33 = 0.242424... = 0.\overline{24}

Now, the given decimals:

Column 3:
Decimal = 0.0̅7̅ = 0.070707... = 7/99 → Fraction = 7/99

Column 4:
Decimal = 0.1̅2̅ = 0.121212... = 12/99 = 4/33 → Fraction = 4/33

Column 5:
Decimal = 0.7̅5̅8̅ = 0.758758758... = 758/999 → Fraction = 758/999 (can it be simplified? 758 and 999 — gcd? 758÷2=379, 999÷3=333, no common factors — so 758/999)

Column 6:
Decimal = 0.6̅01̅ = 0.601601601... = 601/999 → Fraction = 601/999 (601 is prime? probably, so leave as is)

Column 7:
Decimal = 0.5̅4̅21̅ = 0.54215421... = 5421/9999 → Simplify: divide numerator and denominator by 3: 5421÷3=1807, 9999÷3=3333; again 1807÷13? 13*139=1807? 13*130=1690, 13*9=117, total 1807 — yes, 13*139=1807. 3333÷3=1111, 1111÷11=101 — so 5421/9999 = 1807/3333 = 139/256.38? Better to check gcd.

Actually, 5421 and 9999.

Find gcd(5421,9999).

9999 ÷ 5421 = 1 time, remainder 9999-5421=4578

5421 ÷ 4578 = 1, remainder 5421-4578=843

4578 ÷ 843 = 5 times (843*5=4215), remainder 4578-4215=363

843 ÷ 363 = 2 times (726), remainder 117

363 ÷ 117 = 3 times (351), remainder 12

117 ÷ 12 = 9 times (108), remainder 9

12 ÷ 9 = 1, rem 3

9 ÷ 3 = 3, rem 0 → gcd is 3.

So 5421÷3=1807, 9999÷3=3333

Now gcd(1807,3333)

3333 ÷ 1807 = 1, rem 1526

1807 ÷ 1526 = 1, rem 281

1526 ÷ 281 = 5 times (1405), rem 121

281 ÷ 121 = 2 times (242), rem 39

121 ÷ 39 = 3 times (117), rem 4

39 ÷ 4 = 9 times (36), rem 3

4 ÷ 3 = 1, rem 1

3 ÷ 1 = 3, rem 0 → gcd 1

So 5421/9999 = 1807/3333

But 1807 and 3333 — earlier I thought 1807=13*139, 3333=3*11*101 — no common factors, so fraction is 1807/3333.

However, in many contexts, they leave it as 5421/9999 or simplify to lowest terms. But since the problem doesn't specify, and other fractions are simplified, we should simplify.

But 1807/3333 is already simplified? From above, gcd is 1, yes.

But let's confirm: 1807 ÷ 13 = 139, as 13*139=1807. 3333 ÷ 13? 13*256=3328, 3333-3328=5, not divisible. So yes, 1807/3333 is simplified.

But perhaps for this level, they might expect 5421/9999, but I think simplified is better.

Looking back at the table, for 0.1̅2̅ they have 4/33, which is simplified from 12/99, so yes, simplify.

So 0.5̅42̅1̅ = 5421/9999 = 1807/3333

But 1807/3333 can be left as is.

Now, back to the given fractions:

Column 1:
Fraction = 5/6 → Decimal = 5 ÷ 6 = 0.8333... = 0.8\overline{3} — in the table's notation, since only 3 repeats, we write it as 0.8̅3̅? To match, perhaps they want the bar over the repeating digit. In text, I'll write it as 0.8\overline{3}, but for final answer, we need to output as per table.

Perhaps in the answer, for 5/6, decimal is 0.833... with bar over 3, so 0.8\overline{3}

Similarly, for 8/33: 8 ÷ 33 = 0.242424... = 0.\overline{24}

Now, let's list all:

Column 1:
Fraction = 5/6 → Decimal = 0.8\overline{3} (or 0.833... with bar on 3)

Column 2:
Fraction = 8/33 → Decimal = 0.\overline{24} (since 8/33 = 0.242424...)

Column 3:
Decimal = 0.0̅7̅ = 0.070707... = 7/99 → Fraction = 7/99

Column 4:
Decimal = 0.1̅2̅ = 0.121212... = 12/99 = 4/33 → Fraction = 4/33

Column 5:
Decimal = 0.7̅58̅ = 0.758758... = 758/999 → Fraction = 758/999 (already simplified)

Column 6:
Decimal = 0.6̅0̅1̅ = 0.601601... = 601/999 → Fraction = 601/999 (simplified)

Column 7:
Decimal = 0.5̅42̅1̅ = 0.54215421... = 5421/9999 = 1807/3333 → Fraction = 1807/3333

But let's double-check 8/33: 8 ÷ 33.

33 * 0.24 = 7.92, 8 - 7.92 = 0.08, then 0.08 / 33 = 8/3300 = 2/825, but better long division:

33 into 80 (after decimal) is 2, 66, remainder 14

140 ÷ 33 = 4, 132, remainder 8

80 ÷ 33 = 2, etc — so yes, 0.242424... = 0.\overline{24}

Similarly, 5/6: 6 into 50 is 8, 48, remainder 2; 20 ÷ 6 = 3, 18, remainder 2; so 0.8333... = 0.8\overline{3}

Now for the decimals given, we have fractions.

So fourth table:

Fractions: 5/6, 8/33, 7/99, 4/33, 758/999, 601/999, 1807/3333

Decimals: 0.8\overline{3}, 0.\overline{24}, 0.0̅7̅, 0.1̅2̅, 0.7̅5̅8̅, 0.6̅0̅1̅, 0.5̅4̅21̅

But to write in the box, we need to output the values.

Perhaps for the decimal of 5/6, they expect "0.83" with bar over 3, but in text, we can write as 0.8\overline{3}

Since the user's image has "0.0̅7̅" etc., in the answer, we can use similar notation.

For final answer, I'll write the decimals as:

For 5/6: 0.8\overline{3} — but to match the format, perhaps "0.83" with bar on 3, but since it's text, I'll use 0.8\overline{3}

Similarly, for 8/33: 0.\overline{24}

And for the fractions from decimals, as calculated.

Now, let's compile all answers.

First, let's make sure we have all cells filled.

Fourth table has 7 columns.

Given:
- Col1: Fraction 5/6, Decimal blank
- Col2: Fraction 8/33, Decimal blank
- Col3: Fraction blank, Decimal 0.0̅7̅
- Col4: Fraction blank, Decimal 0.1̅2̅
- Col5: Fraction blank, Decimal 0.7̅58̅
- Col6: Fraction blank, Decimal 0.6̅0̅1̅
- Col7: Fraction blank, Decimal 0.5̅4̅2̅1̅

So we need to fill:

Col1 Decimal: 5/6 = 0.8333... = 0.8\overline{3}

Col2 Decimal: 8/33 = 0.242424... = 0.\overline{24}

Col3 Fraction: 0.0̅7̅ = 7/99 → 7/99

Col4 Fraction: 0.1̅2̅ = 12/99 = 4/33 → 4/33

Col5 Fraction: 0.7̅5̅8̅ = 758/999 → 758/999

Col6 Fraction: 0.6̅0̅1̅ = 601/999 → 601/999

Col7 Fraction: 0.5̅4̅2̅1̅ = 5421/9999 = 1807/3333 → 1807/3333

Is 1807/3333 reducible? As before, gcd is 1, so yes.

Some might write it as 5421/9999, but simplified is better.

Now, for the decimal representations, in the answer, we need to write them as per the table's style.

Since the table uses bar over the repeating digits, for 0.8\overline{3}, it should be written with bar over the 3 only. In text, we can denote it as 0.8\overline{3}, but for the final answer box, perhaps list the values.

To avoid confusion, I'll write the decimals as:

- For 5/6: 0.833... with 3 repeating → in boxed answer, perhaps "0.8\overline{3}" but since it's text, I'll use the notation from the problem.

Looking at the user's input: "0.0̅7̅" which likely means the bar is over "07", so for single digit, it might be "0.8̅3" but that's ambiguous.

In many online platforms, they use \overline{} for LaTeX, but here we can write as:

For 5/6 decimal: 0.83 with bar over 3 — so in text, "0.8\overline{3}"

Similarly, for 8/33: "0.\overline{24}"

And for the others, as given.

For the final answer, I'll provide the completed tables.

Let me summarize all answers clearly.

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Final Answer:

First Table (Decimal and Percentage):
- Decimals: 0.03, 0.89, 0.075, 0.63, 0.058, 0.001, 0.062
- Percentages: 3%, 89%, 7.5%, 63%, 5.8%, 0.1%, 6⅕%

Second Table (Fraction and Percentage):
- Fractions: 3/4, 9/10, 43/100, 1/5, 13/20, 2/25, 3/200
- Percentages: 75%, 90%, 43%, 20%, 65%, 8%, 1.5%

Third Table (Fraction and Decimal):
- Fractions: 3/10, 3/25, 19/20, 4/5, 9/20, 7/40, 33/160
- Decimals: 0.3, 0.12, 0.95, 0.8, 0.45, 0.175, 0.20625

Fourth Table (Fraction and Decimal with repeating):
- Fractions: 5/6, 8/33, 7/99, 4/33, 758/999, 601/999, 1807/3333
- Decimals: 0.8\overline{3}, 0.\overline{24}, 0.0̅7̅, 0.1̅2̅, 0.7̅5̅8̅, 0.6̅0̅1̅, 0.5̅4̅2̅1̅

Note: For the repeating decimals, the bar indicates the repeating part. For example, 0.8\overline{3} means 0.8333..., and 0.\overline{24} means 0.242424....

In the fourth table, the decimal for 5/6 is 0.8333... which is written as 0.8 with a bar over the 3, and for 8/33 is 0.242424... written as 0. with bar over 24.

For the fraction 1807/3333, it is already in simplest form.

All calculations have been verified.