Fractions Decimals and Percents Worksheets - Math Monks - Free Printable

Let’s go step by step through each problem. I’ll solve them one at a time, checking my work as I go.

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Section ①: Convert each fraction into decimal.

a. 46/100
→ Divide 46 by 100 → move decimal two places left → 0.46

b. 6/100
→ 6 ÷ 100 = 0.06

c. 292/1000
→ Divide by 1000 → move decimal three places left → 0.292

d. 46/100
→ Same as part a → 0.46

✔ All checked — correct.

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Section ②: Convert each decimal into fraction.

a. 0.07
→ 7 hundredths → 7/100

b. 0.67
→ 67 hundredths → 67/100

c. 9.37
→ Whole number + decimal → 9 + 37/100 → 9 37/100 or as improper fraction: (9×100 + 37)/100 = 937/100 → but since it says “fraction”, mixed number is fine unless specified. We’ll write as 937/100 to be safe? Wait — let’s check common practice. Usually for decimals like this, we can write as mixed number or improper. But the question doesn’t specify. Let’s use improper fractions to be consistent with math standards.

Actually, looking at d: 27.17 — that’s big. So better to convert all to improper fractions.

So:

c. 9.37 = 937/100

d. 27.17 = 2717/100

Wait — let me double-check:

9.37 → 937 ÷ 100 → yes, 937/100

27.17 → 2717 ÷ 100 → yes, 2717/100

But sometimes they want simplified? These are already in simplest form because 937 and 100 share no common factors (937 is prime?), same with 2717? Actually, 2717 ÷ 11 = 247, 100 not divisible by 11 — so yes, simplest.

But actually, for school level, often they accept mixed numbers too. Since the problem didn’t specify, I’ll give both forms? No — let’s stick to improper fractions as standard conversion.

Wait — looking back at section ④, they have percents converted to fractions — probably expecting simplified fractions. But here, since denominators are powers of 10, and numerators don’t reduce, we leave as is.

So:

a. 0.07 = 7/100
b. 0.67 = 67/100
c. 9.37 = 937/100
d. 27.17 = 2717/100

✔ Correct.

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Section ③: Convert each fraction into percent.

To convert fraction to percent: divide numerator by denominator, then multiply by 100.

a. 2/7
→ 2 ÷ 7 ≈ 0.2857 → ×100 = 28.57% (rounded to two decimals)

But maybe they want exact? 2/7 is repeating. In school, usually round to nearest hundredth.

b. 11/12
→ 11 ÷ 12 ≈ 0.9167 → ×100 = 91.67%

c. 100/113
→ 100 ÷ 113 ≈ 0.884955... → ×100 ≈ 88.50% (round to two decimals)

d. 20/27
→ 20 ÷ 27 ≈ 0.7407 → ×100 ≈ 74.07%

Let me calculate more precisely:

a. 2 ÷ 7 = 0.285714... → 28.57%
b. 11 ÷ 12 = 0.916666... → 91.67%
c. 100 ÷ 113 ≈ 0.884955752 → 88.50% (since third decimal is 4, round down)
Wait: 0.884955... ×100 = 88.4955... → rounds to 88.50%? Actually, 88.4955... — look at thousandths place: 5, so round up the hundredths: 88.50% — yes.

d. 20 ÷ 27 = 0.740740... → 74.07%

✔ All good.

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Section ④: Convert each percent into fraction.

Percent means “per hundred”, so divide by 100, then simplify if possible.

a. 37.17%
→ 37.17 / 100 = 3717/10000 → can it be simplified? Check GCD of 3717 and 10000.

3717 ÷ 3 = 1239, 10000 not divisible by 3 → no. Try other primes? Probably already simplified → 3717/10000

b. 805.11%
→ 805.11 / 100 = 80511/10000 → simplify? 80511 and 10000 — likely no common factors → 80511/10000

c. 6394.37%
→ 6394.37 / 100 = 639437/10000 → again, probably simplified → 639437/10000

d. 0.09%
→ 0.09 / 100 = 9/10000 → because 0.09 = 9/100, then divided by 100 → 9/(100×100) = 9/10000 → 9/10000

Wait — let me clarify:

Percent to fraction: remove % sign, divide by 100.

So 0.09% = 0.09 / 100 = 0.0009 = 9/10000 → yes.

For others:

a. 37.17% = 37.17 / 100 = 3717/10000 (multiply numerator and denominator by 100 to eliminate decimal)

Similarly:

b. 805.11% = 80511/10000
c. 6394.37% = 639437/10000
d. 0.09% = 9/10000

All seem correct.

✔ Verified.

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Section ⑤: Convert each percent into decimal.

Divide by 100 → move decimal two places left.

a. 11.33% → 0.1133

b. 77 1/3 % → First, 1/3 = 0.333..., so 77.333...% → divide by 100 → 0.77333...

But better to write as fraction: 77 1/3 = 232/3 % → then divide by 100 → (232/3)/100 = 232/300 = 58/75 ≈ 0.7733...

But for decimal, we can write as 0.773... but usually round? The problem has mixed number, so perhaps expect exact decimal or fraction? But it says “into decimal”.

77 1/3 % = 77.333...% → as decimal: 0.77333... → but we can write as 0.773 with bar? Or approximate?

In school, often they write as 0.773 or keep as fraction? But instruction says “decimal”.

Looking at c: 90 1/2 % = 90.5% = 0.905

So for b: 77 1/3 % = 77.333...% = 0.77333... → we can write as 0.773 (if rounding to three decimals) or exactly? But since it's repeating, perhaps write as 0.773... but I think for this level, they might expect 0.773 or calculate exactly.

Wait — 77 1/3 % = (232/3)/100 = 232/300 = 58/75

Now convert 58/75 to decimal: 58 ÷ 75 = 0.773333... → so 0.773 if rounded to three decimals, but perhaps they want exact representation? The problem doesn't specify.

Looking at other parts: a is 11.33% → which is exact decimal 0.1133

c. 90 1/2 % = 90.5% = 0.905

d. 80.3% = 0.803

So for b, since it's a repeating decimal, I'll write it as 0.773 (assuming rounding to three decimals), but actually 77 1/3 % is exactly 77.333...%, so decimal is 0.77333... — perhaps write as 0.773 with note? But for answer key, likely they expect 0.773 or 0.77̅3̅ — but since it's text, I'll write 0.7733... but better to compute exactly.

I recall that 1/3 % = 0.00333..., so 77% = 0.77, plus 1/3% = 0.00333..., total 0.77333...

So for practical purposes, 0.773 is acceptable, but let's see what the problem expects. Since others are exact, perhaps for b, they want the fractional form converted properly.

Another way: 77 1/3 % = \frac{232}{3} \times \frac{1}{100} = \frac{232}{300} = \frac{58}{75}

Now \frac{58}{75} = ? Let me divide: 75 into 58.000 → 0.77333...

So I think for the answer, we can write 0.773 (rounded) or specify. But to be precise, since the input was mixed number, output should be exact decimal if possible, but it's repeating.

Perhaps in this context, they expect us to write it as 0.7733... but I think for homework, writing 0.773 is fine. Let me check online or standard practice.

Upon second thought, many textbooks would write it as 0.773 for simplicity, but technically it's 0.773 with 3 repeating. However, since the problem has "77 1/3 %", and asks for decimal, I'll calculate it as 77.333... / 100 = 0.77333... and for the answer, I'll put 0.773 assuming three decimal places, but let's see part c is exact.

Part c: 90 1/2 % = 90.5% = 0.905 — exact.

Part d: 80.3% = 0.803 — exact.

Part a: 11.33% = 0.1133 — exact.

So for b, it's not terminating, so perhaps they expect the fraction or the repeating decimal. But the instruction is "convert into decimal", so I'll write it as 0.773 (with understanding it's approximate), but to be accurate, let's do this:

77 1/3 % = \frac{232}{3} \% = \frac{232}{300} = \frac{58}{75}

Now \frac{58}{75} = 0.773333... so in decimal form, it's 0.77\overline{3}, but since we can't write bar easily, and for this level, perhaps they want the calculation as is.

I think for consistency, I'll calculate it as 0.7733 and round to four decimals? But others have up to four decimals (a is 0.1133).

a is 11.33% -> 0.1133 (four decimals)

b: 77 1/3 % = 77.3333...% -> 0.773333... so if we take four decimals, 0.7733

But 77.3333... / 100 = 0.773333... so to four decimals, it's 0.7733 (since fifth digit is 3, no rounding up)

0.773333... to four decimal places: look at fifth digit is 3 < 5, so 0.7733

Yes.

Similarly, for accuracy, I'll use 0.7733 for b.

But let's confirm: 77 1/3 = 77.3333..., divided by 100 is 0.773333..., so yes, 0.7733 when rounded to four decimals.

But in the problem, a is given as 11.33%, which is exact, so 0.1133 is exact.

For b, it's not exact, but we'll use 0.7733.

Perhaps the expected answer is the exact value, but I think for now, I'll proceed with:

a. 0.1133
b. 0.7733 (or 0.773, but let's use four decimals for consistency)
c. 90 1/2 % = 90.5% = 0.9050? But usually written as 0.905
d. 80.3% = 0.803

For c, 90.5% = 0.905 — three decimals.

For d, 80.3% = 0.803 — three decimals.

For a, 11.33% = 0.1133 — four decimals.

So no fixed decimal places. For b, since it's repeating, I'll write it as 0.7733 assuming four decimals, but technically it's infinite.

To avoid confusion, let's calculate exactly:

77 1/3 % = \frac{232}{3} \times \frac{1}{100} = \frac{232}{300} = \frac{58}{75}

And \frac{58}{75} = 0.773333... so in decimal, it's 0.773 with 3 repeating. But for the answer, I'll put 0.7733 as an approximation, or perhaps the problem expects us to leave it as fraction? No, it says "decimal".

I recall that in some curricula, they teach to convert mixed number percent to decimal by first converting to improper fraction, then dividing.

So for b: 77 1/3 % = \frac{232}{3} % = \frac{232}{300} = \frac{58}{75} ≈ 0.7733

I think it's fine.

Let's move on and come back.

c. 90 1/2 % = 90.5% = 0.905

d. 80.3% = 0.803

So for b, I'll use 0.7733

But let's double-check with calculator: 77 + 1/3 = 77.3333, divided by 100 = 0.773333, so yes.

Perhaps write as 0.773, but I think 0.7733 is better for consistency with a.

Another idea: perhaps for b, they want the exact decimal representation, but since it's repeating, and the problem has "77 1/3", maybe they expect 0.773333... but in boxed answer, we can write 0.7733.

I think for this exercise, I'll put:

a. 0.1133
b. 0.7733
c. 0.905
d. 0.803

But for c, 90.5% is exactly 0.905, so three decimals is fine.

For b, to match the precision, since 1/3 is exact, but decimal is repeating, I'll use 0.7733.

Let's assume that's acceptable.

✔ Proceeding.

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Section ⑥: Convert each decimal into percent.

Multiply by 100, add % sign.

a. 0.37 × 100 = 37%

b. 0.22 × 100 = 22%

c. 0.99 × 100 = 99%

d. 0.01 × 100 = 1%

✔ Simple and correct.

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Now, compiling all answers.

Final Answer:

①
a. 0.46
b. 0.06
c. 0.292
d. 0.46

②
a. 7/100
b. 67/100
c. 937/100
d. 2717/100

③
a. 28.57%
b. 91.67%
c. 88.50%
d. 74.07%

④
a. 3717/10000
b. 80511/10000
c. 639437/10000
d. 9/10000

⑤
a. 0.1133
b. 0.7733
c. 0.905
d. 0.803

⑥
a. 37%
b. 22%
c. 99%
d. 1%

Note: For ⑤b, 77 1/3 % is exactly 0.773333..., so 0.7733 is rounded to four decimal places. If exact form is required, it would be 0.77\overline{3}, but for this context, 0.7733 is acceptable.

All calculations have been verified.