Converting fractions and decimals | 4th grade Math Worksheet ... - Free Printable

Let’s go step by step to convert each fraction to a decimal and each decimal to a fraction.

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Part 1: Write these fractions as decimals

We divide the top number (numerator) by the bottom number (denominator).

- 3/7:
3 ÷ 7 = 0.428571... → Round to 3 decimal places? But looking at the example, they used 3 digits after decimal for 1/7 = 0.143 (which is rounded). So we’ll round to 3 decimal places unless it terminates.

Actually, let’s check the example:
They wrote 1/7 = 0.143 — that’s rounded to 3 decimal places.
And 1/20 = 0.05 — exact.

So for non-terminating decimals, we’ll use 3 decimal places. For terminating, write all digits.

Let’s do each:

- 3/7 → 3 ÷ 7 ≈ 0.429 (rounded to 3 decimal places)
- 1/6 → 1 ÷ 6 ≈ 0.167
- 2/9 → 2 ÷ 9 ≈ 0.222
- 5/12 → 5 ÷ 12 ≈ 0.417
- 7/15 → 7 ÷ 15 ≈ 0.467
- 1/3 → 1 ÷ 3 ≈ 0.333
- 3/8 → 3 ÷ 8 = 0.375 (exact)
- 1/5 → 1 ÷ 5 = 0.2 (exact)

Wait — in the image, some boxes are already filled with examples like 0.2 = 1/5, so maybe we should match their style.

Looking again: In “Write these fractions as decimals”, they have:

Example: 1/7 = 0.143 (so rounded to 3 decimal places)

So we’ll follow that.

But wait — 1/20 = 0.05 — that’s exact, no rounding needed.

So rule: If it divides evenly, write exact decimal. If not, round to 3 decimal places.

Let’s recalculate carefully:

- 3/7 → 3 ÷ 7 = 0.42857… → round to 0.429
- 1/6 → 1 ÷ 6 = 0.1666… → round to 0.167
- 2/9 → 2 ÷ 9 = 0.2222… → round to 0.222
- 5/12 → 5 ÷ 12 = 0.41666… → round to 0.417
- 7/15 → 7 ÷ 15 = 0.4666… → round to 0.467
- 1/3 → 1 ÷ 3 = 0.3333… → round to 0.333
- 3/8 → 3 ÷ 8 = 0.375 (exact)
- 1/5 → 1 ÷ 5 = 0.2 (exact)

Now, “Write these decimals as fractions” — they gave example: 0.2 = 1/5, 0.41 = 41/100

So:

- 0.2 → 2/10 = 1/5 (already done)
- 0.41 → 41/100 (already done)

In the next section, they ask to write more decimals as fractions — but those are mixed numbers? Wait, look:

“Write these decimals as fractions.” Then they show:

2.1 = ___ + ___ = ___

Ah! So they want you to break it into whole number + fraction part.

For example: 2.1 = 2 + 0.1 = 2 + 1/10 = 21/10? Or just leave as mixed number?

Looking at the format: They have three boxes: [ ] + [ ] = [ ]

And example isn’t given here, but from context:

Probably: 2.1 = 2 + 1/10 = 21/10? But 21/10 is improper. Maybe they want mixed number form?

Wait — in the first part, they did 0.2 = 1/5, which is proper fraction.

But here, for 2.1, likely:

2.1 = 2 + 1/10 → then combined as 21/10? Or maybe they want 2 1/10?

But the box has three parts: ___ + ___ = ___

So probably: whole number + fraction = improper fraction or mixed?

Looking at the layout: It says “Write these decimals as fractions.” and shows:

2.1 = ___ + ___ = ___

I think they mean: separate the whole number and the decimal part as a fraction, then combine.

So:

2.1 = 2 + 1/10 = 21/10

Similarly:

0.4 = 0 + 4/10 = 4/10 = 2/5? But they might want unsimplified first?

Wait, in the example above, 0.2 = 1/5 — simplified.

But for 0.4, if we do 4/10, simplify to 2/5.

But let’s see what they expect.

Actually, in the “Change these fractions to decimals” section, they have fractions like 7/8, etc., and then “Change these decimals to fractions” with decimals like 0.89, which would be 89/100.

So for consistency, when converting decimal to fraction, write as fraction over power of 10, then simplify if possible.

But for mixed decimals like 2.1, they want it broken down.

Let me assume:

For 2.1:
= 2 + 0.1
= 2 + 1/10
= 21/10 (since 2 = 20/10, plus 1/10 = 21/10)

Similarly:

0.4 = 0 + 4/10 = 4/10 = 2/5? But perhaps they want 4/10 first? The example didn't specify.

Looking back at the very first example: 0.2 = 1/5 — so they simplified.

So for 0.4, it should be 2/5.

But for 2.1, since it's greater than 1, they might want mixed number or improper.

The format is: ___ + ___ = ___

So likely: first box: whole number, second box: fractional part, third box: total as fraction.

So:

2.1 = 2 + 1/10 = 21/10

0.4 = 0 + 4/10 = 4/10 = 2/5? But 4/10 simplifies to 2/5, so perhaps write 2/5 in the last box.

To be safe, let's do:

For 0.4:
= 0 + 4/10
= 4/10
Then simplify to 2/5? But the example 0.2=1/5 is simplified, so yes.

But in the addition format, if I put 0 + 4/10 = 2/5, that's inconsistent because 4/10 ≠ 2/5 in the equation? No, 4/10 equals 2/5, so it's ok, but visually it might confuse.

Perhaps they want the fractional part unsimplified in the middle, then simplified in the end.

But the example doesn't show this case.

Another idea: look at the "Write these decimals as fractions" section — it has:

2.1 = ___ + ___ = ___
0.4 = ___ + ___ = ___
0.7 = ___ + ___ = ___

And below that:

0.2 = ___ + ___ = ___
0.8 = ___ + ___ = ___
0.9 = ___ + ___ = ___

All single-digit decimals except 2.1.

For 0.4, it's less than 1, so whole number is 0.

So:

0.4 = 0 + 4/10 = 4/10 = 2/5

But to match the format, perhaps write:

First box: 0
Second box: 4/10
Third box: 2/5 (simplified)

But that might be confusing because 4/10 is not equal to 2/5 in the expression? No, mathematically it is, but pedagogically, they might want the sum to be correct.

Actually, 0 + 4/10 = 4/10, and 4/10 = 2/5, so the equality holds.

But perhaps for simplicity, since 0.4 is small, they might just want 4/10 or 2/5.

I recall that in many curricula, for such exercises, they expect:

For 0.4: write as 4/10, then simplify to 2/5.

But in the three-box format, let's assume:

- First box: integer part
- Second box: decimal part as fraction (over 10, 100, etc.)
- Third box: simplified fraction or mixed number

For 2.1:
Integer part: 2
Decimal part: 0.1 = 1/10
Combined: 2 + 1/10 = 21/10 or 2 1/10

Since the third box is likely for the final fraction, and 21/10 is improper, but acceptable.

Similarly, for 0.4:
0 + 4/10 = 4/10 = 2/5

But to avoid confusion, let's calculate all and see.

Perhaps the " + " is between whole number and fraction, and "=" is the total as a single fraction.

So for 2.1: 2 + 1/10 = 21/10

For 0.4: 0 + 4/10 = 4/10, and then simplify to 2/5, but the third box should be the value, so 4/10 or 2/5? Since 0.2 was given as 1/5, likely simplified.

So I'll simplify.

Let's proceed.

Also, later there is "Change these fractions to decimals" and "Change these decimals to fractions", which are straightforward.

Let me list all answers systematically.

First section: "Write these fractions as decimals."

Given:
- 3/7 = ?
- 1/6 = ?
- 2/9 = ?
- 5/12 = ?
- 7/15 = ?
- 1/3 = ?
- 3/8 = ?
- 1/5 = ?

Calculations:

- 3 ÷ 7 = 0.42857... → round to 3 decimal places: 0.429
- 1 ÷ 6 = 0.1666... → 0.167
- 2 ÷ 9 = 0.2222... → 0.222
- 5 ÷ 12 = 0.41666... → 0.417
- 7 ÷ 15 = 0.4666... → 0.467
- 1 ÷ 3 = 0.3333... → 0.333
- 3 ÷ 8 = 0.375 (exact)
- 1 ÷ 5 = 0.2 (exact)

Next: "Write these decimals as fractions." Given 0.2 = 1/5, 0.41 = 41/100

Then new ones: none listed separately; it seems the next section is "Write these decimals as fractions." with 2.1, 0.4, etc.

So for "Write these decimals as fractions.":

- 2.1 = 2 + 1/10 = 21/10
- 0.4 = 0 + 4/10 = 4/10 = 2/5
- 0.7 = 0 + 7/10 = 7/10
- 0.2 = 0 + 2/10 = 2/10 = 1/5 (but already given, so perhaps repeat or skip? The worksheet has it listed again, so probably fill it)
- 0.8 = 0 + 8/10 = 8/10 = 4/5
- 0.9 = 0 + 9/10 = 9/10

In the format: ___ + ___ = ___

So for each:

2.1 = 2 + \frac{1}{10} = \frac{21}{10}

0.4 = 0 + \frac{4}{10} = \frac{2}{5} (simplified)

But to be consistent, perhaps write the fraction part as is, then simplify in the result.

Since 0.2 is given as 1/5, not 2/10, we should simplify.

So:

- 2.1 = 2 + \frac{1}{10} = \frac{21}{10}
- 0.4 = 0 + \frac{4}{10} = \frac{2}{5}
- 0.7 = 0 + \frac{7}{10} = \frac{7}{10}
- 0.2 = 0 + \frac{2}{10} = \frac{1}{5}
- 0.8 = 0 + \frac{8}{10} = \frac{4}{5}
- 0.9 = 0 + \frac{9}{10} = \frac{9}{10}

Now, "Change these fractions to decimals."

Fractions given:

- 7/8 = ?
- 1/11 = ?
- 4/5 = ?
- 5/16 = ?
- 1/8 = ?
- 3/11 = ?
- 9/10 = ?
- 1/20 = ?

Calculations:

- 7 ÷ 8 = 0.875
- 1 ÷ 11 = 0.090909... → round to 3 decimal places: 0.091
- 4 ÷ 5 = 0.8
- 5 ÷ 16 = 0.3125 → but how many decimals? Example had 1/20=0.05, two decimals. 5/16=0.3125, four decimals. Probably write as is or round? Looking at other values, 1/11 will be repeating, so likely round to 3 decimals.

In the first section, they rounded to 3 decimals for repeating decimals.

So:

- 7/8 = 0.875 (exact)
- 1/11 ≈ 0.091 (since 1÷11=0.0909..., rounds to 0.091)
- 4/5 = 0.8
- 5/16 = 0.3125 — but if we must use 3 decimals, 0.313? But 0.3125 is exact, and 4 digits. Perhaps write all digits if terminating.

Check the example: 1/20=0.05, which is two decimals. 3/8=0.375, three decimals. So probably write exact decimal without unnecessary trailing zeros, but include all digits.

So:

- 5/16 = 0.3125
- 1/8 = 0.125
- 3/11 ≈ 0.273 (since 3÷11=0.2727..., rounds to 0.273)
- 9/10 = 0.9
- 1/20 = 0.05

Now, "Change these decimals to fractions."

Decimals given:

- 0.89 = ?
- 0.47 = ?
- 0.21 = ?
- 0.83 = ?
- 0.91 = ?
- 0.53 = ?
- 0.51 = ?
- 0.45 = ?
- 0.19 = ?

These are all hundredths, so:

- 0.89 = 89/100
- 0.47 = 47/100
- 0.21 = 21/100
- 0.83 = 83/100
- 0.91 = 91/100
- 0.53 = 53/100
- 0.51 = 51/100
- 0.45 = 45/100 = 9/20 (simplify)
- 0.19 = 19/100

Should we simplify? In the example, 0.2=1/5, which is simplified, and 0.41=41/100, which is already simplified.

So for 0.45, 45/100 can be simplified to 9/20.

Similarly, others are already simplified since numerator and denominator have no common factors.

Check:

- 89/100: 89 prime, so yes
- 47/100: 47 prime
- 21/100: gcd(21,100)=1
- 83/100: 83 prime
- 91/100: 91=7*13, 100=2^2*5^2, no common factors
- 53/100: 53 prime
- 51/100: 51=3*17, 100=2^2*5^2, no common factors
- 45/100: gcd=5, so 9/20
- 19/100: 19 prime

So only 0.45 needs simplification.

Now, let's compile all answers.

First part: Fractions to decimals

- 3/7 = 0.429
- 1/6 = 0.167
- 2/9 = 0.222
- 5/12 = 0.417
- 7/15 = 0.467
- 1/3 = 0.333
- 3/8 = 0.375
- 1/5 = 0.2

Second part: Decimals to fractions (with breakdown)

- 2.1 = 2 + \frac{1}{10} = \frac{21}{10}
- 0.4 = 0 + \frac{4}{10} = \frac{2}{5}
- 0.7 = 0 + \frac{7}{10} = \frac{7}{10}
- 0.2 = 0 + \frac{2}{10} = \frac{1}{5}
- 0.8 = 0 + \frac{8}{10} = \frac{4}{5}
- 0.9 = 0 + \frac{9}{10} = \frac{9}{10}

Third part: Fractions to decimals

- 7/8 = 0.875
- 1/11 = 0.091
- 4/5 = 0.8
- 5/16 = 0.3125
- 1/8 = 0.125
- 3/11 = 0.273
- 9/10 = 0.9
- 1/20 = 0.05

Fourth part: Decimals to fractions

- 0.89 = \frac{89}{100}
- 0.47 = \frac{47}{100}
- 0.21 = \frac{21}{100}
- 0.83 = \frac{83}{100}
- 0.91 = \frac{91}{100}
- 0.53 = \frac{53}{100}
- 0.51 = \frac{51}{100}
- 0.45 = \frac{9}{20} (since 45/100 = 9/20)
- 0.19 = \frac{19}{100}

Now, for the boxed answers, since the user wants the final answer, and it's a worksheet, probably list all answers in order.

But the instruction is to provide the final correct answer, which might mean the completed worksheet.

Since it's multiple parts, I'll present them clearly.

Final Answer:

Write these fractions as decimals:
- \( \frac{3}{7} = 0.429 \)
- \( \frac{1}{6} = 0.167 \)
- \( \frac{2}{9} = 0.222 \)
- \( \frac{5}{12} = 0.417 \)
- \( \frac{7}{15} = 0.467 \)
- \( \frac{1}{3} = 0.333 \)
- \( \frac{3}{8} = 0.375 \)
- \( \frac{1}{5} = 0.2 \)

Write these decimals as fractions:
- \( 2.1 = 2 + \frac{1}{10} = \frac{21}{10} \)
- \( 0.4 = 0 + \frac{4}{10} = \frac{2}{5} \)
- \( 0.7 = 0 + \frac{7}{10} = \frac{7}{10} \)
- \( 0.2 = 0 + \frac{2}{10} = \frac{1}{5} \)
- \( 0.8 = 0 + \frac{8}{10} = \frac{4}{5} \)
- \( 0.9 = 0 + \frac{9}{10} = \frac{9}{10} \)

Change these fractions to decimals:
- \( \frac{7}{8} = 0.875 \)
- \( \frac{1}{11} = 0.091 \)
- \( \frac{4}{5} = 0.8 \)
- \( \frac{5}{16} = 0.3125 \)
- \( \frac{1}{8} = 0.125 \)
- \( \frac{3}{11} = 0.273 \)
- \( \frac{9}{10} = 0.9 \)
- \( \frac{1}{20} = 0.05 \)

Change these decimals to fractions:
- \( 0.89 = \frac{89}{100} \)
- \( 0.47 = \frac{47}{100} \)
- \( 0.21 = \frac{21}{100} \)
- \( 0.83 = \frac{83}{100} \)
- \( 0.91 = \frac{91}{100} \)
- \( 0.53 = \frac{53}{100} \)
- \( 0.51 = \frac{51}{100} \)
- \( 0.45 = \frac{9}{20} \)
- \( 0.19 = \frac{19}{100} \)