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. We’ll do this carefully so you can follow along easily.

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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 = 0.42857... but since we’re likely rounding to 3 decimal places or using exact values, let’s check if it repeats. Actually, for school problems like this, sometimes they expect you to use calculator or known equivalents — but 3/7 is approximately 0.429 (rounded to 3 decimal places). However, looking at the worksheet layout, maybe they want exact decimal forms? Wait — actually, in many elementary worksheets, they might expect you to write the decimal equivalent even if it’s repeating, but here the boxes are small — perhaps they want rounded answers? Let me double-check common conversions.

Wait — actually, looking again: The first example given is 1/5 = 0.2 and 0.2 = 1/5 — so they’re showing simple ones. But 3/7 doesn’t terminate. Hmm. Maybe I made a mistake — let’s look at the actual problems:

Actually, re-examining the image description (even though I’m not supposed to describe it), the user provided text that says:

> Write these fractions as decimals:
> - 3/7 = ?
> - 1/20 = ?

And then:

> Write these fractions as decimals:
> - 0.2 = □ / □ → already filled as 1/5
> - 0.41 = □ / □ → filled as 41/100

Then later sections have more.

But wait — perhaps I should just solve what’s listed clearly.

Looking back at the original problem statement from the user’s upload (as interpreted):

The main tasks are:

#### Section A: Fractions to Decimals
- 3/7 → ?
- 1/20 → ?

#### Section B: Decimals to Fractions
- 0.2 → 1/5 (already done)
- 0.41 → 41/100 (already done)

Then next section:

#### Write these fractions as decimals:
- 3/4 = ?
- 7/10 = ?
- 1/2 = ?
- 1/5 = ?
- 3/8 = ?
- 9/10 = ?
- 2/5 = ?
- 7/20 = ?

#### Write these decimals as fractions:
- 0.1 = ?
- 0.4 = ?
- 0.7 = ?
- 0.2 = ?
- 0.8 = ?
- 0.9 = ?
- 0.5 = ?
- 0.6 = ?

Then:

#### Change these fractions to decimals:
- 1/2 = ?
- 1/4 = ?
- 1/5 = ?
- 1/8 = ?
- 1/10 = ?
- 1/20 = ?
- 3/4 = ?
- 3/5 = ?
- 3/8 = ?
- 3/10 = ?
- 3/20 = ?
- 3/25 = ?

#### Change these decimals to fractions:
- 0.19 = ?
- 0.45 = ?
- 0.21 = ?
- 0.83 = ?
- 0.91 = ?
- 0.53 = ?
- 0.33 = ?
- 0.64 = ?
- 0.15 = ?
- 0.27 = ?
- 0.51 = ?
- 0.73 = ?

Okay — now I’ll solve them one by one, carefully.

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## Step-by-step Solutions

First Set: Fractions to Decimals

1. 3/7 → 3 ÷ 7 = 0.428571... → Typically rounded to 0.429 (if 3 decimal places) — but some curricula accept repeating decimal notation. Since the box is small, probably 0.429

But wait — let’s check if any of these are meant to be exact terminating decimals. 3/7 does NOT terminate. Maybe there’s a typo? Or perhaps in context, they want approximate? Let’s hold on and see others.

Actually, looking at the second one:

2. 1/20 → 1 ÷ 20 = 0.05 → Easy! So 0.05

So maybe 3/7 is intended to be calculated as is. But let’s proceed with standard practice.

In many grade-level worksheets, if it doesn't terminate, they may still ask for rounded value. Let's assume 3 decimal places unless specified.

So:

- 3/7 ≈ 0.429
- 1/20 = 0.05

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Next Section: Fractions to Decimals (more)

These are all terminating:

- 3/4 = 3 ÷ 4 = 0.75
- 7/10 = 7 ÷ 10 = 0.7
- 1/2 = 1 ÷ 2 = 0.5
- 1/5 = 1 ÷ 5 = 0.2
- 3/8 = 3 ÷ 8 = 0.375
- 9/10 = 9 ÷ 10 = 0.9
- 2/5 = 2 ÷ 5 = 0.4
- 7/20 = 7 ÷ 20 = 0.35

All good.

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Decimals to Fractions

Remember: Decimal means “tenths”, “hundredths”, etc.

- 0.1 = 1/10
- 0.4 = 4/10 = simplify → 2/5
- 0.7 = 7/10
- 0.2 = 2/10 = 1/5
- 0.8 = 8/10 = 4/5
- 0.9 = 9/10
- 0.5 = 5/10 = 1/2
- 0.6 = 6/10 = 3/5

Note: Always simplify if possible.

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Change these fractions to decimals (again, similar set)

This seems redundant, but let’s do it:

- 1/2 = 0.5
- 1/4 = 0.25
- 1/5 = 0.2
- 1/8 = 0.125
- 1/10 = 0.1
- 1/20 = 0.05
- 3/4 = 0.75
- 3/5 = 0.6
- 3/8 = 0.375
- 3/10 = 0.3
- 3/20 = 0.15
- 3/25 = 3 ÷ 25 = 0.12

(因为 25 × 0.12 = 3)

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Change these decimals to fractions

Now, two-digit decimals → hundredths.

- 0.19 = 19/100 → cannot simplify → 19/100
- 0.45 = 45/100 = simplify → divide numerator and denominator by 5 → 9/20
- 0.21 = 21/100 → no simplification → 21/100
- 0.83 = 83/100 → prime? yes → 83/100
- 0.91 = 91/100 → 91=7×13, 100 not divisible → 91/100
- 0.53 = 53/100 → prime → 53/100
- 0.33 = 33/100 → can’t reduce → 33/100
- 0.64 = 64/100 = divide by 4 → 16/25
- 0.15 = 15/100 = divide by 5 → 3/20
- 0.27 = 27/100 → no common factors → 27/100
- 0.51 = 51/100 → 51=3×17 → no match with 100 → 51/100
- 0.73 = 73/100 → prime → 73/100

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Now, going back to the very first part: 3/7.

Since 3 ÷ 7 = 0.428571..., and if we round to three decimal places, it’s 0.429. Some teachers might accept 0.428 or 0.43 depending on instructions, but since other answers are exact, perhaps they expect the repeating form? But the box size suggests decimal approximation.

Alternatively — maybe I misread? Let me check if 3/7 was meant to be something else? No, based on typical worksheets, it’s fine.

But wait — in the initial example, they showed 1/5 = 0.2 and 0.2 = 1/5 — so they’re matching exactly. For 3/7, since it doesn’t terminate, perhaps the worksheet expects you to leave it as is? But that doesn’t make sense.

Another thought: Maybe the first "Write these fractions as decimals" includes only 3/7 and 1/20 — and 3/7 is an error? Unlikely.

Perhaps in this curriculum, they teach long division and expect students to compute it. Let’s calculate 3 ÷ 7 properly:

7 into 3.0000...

7 goes into 30 four times (28), remainder 2 → bring down 0 → 20

7 into 20 twice (14), rem 6 → bring down 0 → 60

7 into 60 eight times (56), rem 4 → bring down 0 → 40

7 into 40 five times (35), rem 5 → bring down 0 → 50

7 into 50 seven times (49), rem 1 → and so on.

So 0.428571... repeating every 6 digits.

For practical purposes in elementary math, often rounded to 3 decimal places: 0.429

I think that’s acceptable.

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## Final Compilation of Answers

Let’s list them in order as per the worksheet structure.

First Box: Fractions to Decimals

- 3/7 = 0.429 (approximate)
- 1/20 = 0.05

Second Box: Decimals to Fractions (already partially filled)

- 0.2 = 1/5 (given)
- 0.41 = 41/100 (given)

Third Section: Fractions to Decimals

- 3/4 = 0.75
- 7/10 = 0.7
- 1/2 = 0.5
- 1/5 = 0.2
- 3/8 = 0.375
- 9/10 = 0.9
- 2/5 = 0.4
- 7/20 = 0.35

Fourth Section: Decimals to Fractions

- 0.1 = 1/10
- 0.4 = 2/5
- 0.7 = 7/10
- 0.2 = 1/5
- 0.8 = 4/5
- 0.9 = 9/10
- 0.5 = 1/2
- 0.6 = 3/5

Fifth Section: Fractions to Decimals (again)

- 1/2 = 0.5
- 1/4 = 0.25
- 1/5 = 0.2
- 1/8 = 0.125
- 1/10 = 0.1
- 1/20 = 0.05
- 3/4 = 0.75
- 3/5 = 0.6
- 3/8 = 0.375
- 3/10 = 0.3
- 3/20 = 0.15
- 3/25 = 0.12

Sixth Section: Decimals to Fractions

- 0.19 = 19/100
- 0.45 = 9/20
- 0.21 = 21/100
- 0.83 = 83/100
- 0.91 = 91/100
- 0.53 = 53/100
- 0.33 = 33/100
- 0.64 = 16/25
- 0.15 = 3/20
- 0.27 = 27/100
- 0.51 = 51/100
- 0.73 = 73/100

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Final Answer:

Here are all the answers filled in:

First part:
- 3/7 = 0.429
- 1/20 = 0.05

Second part (decimals to fractions):
- 0.2 = 1/5
- 0.41 = 41/100

Third part (fractions to decimals):
- 3/4 = 0.75
- 7/10 = 0.7
- 1/2 = 0.5
- 1/5 = 0.2
- 3/8 = 0.375
- 9/10 = 0.9
- 2/5 = 0.4
- 7/20 = 0.35

Fourth part (decimals to fractions):
- 0.1 = 1/10
- 0.4 = 2/5
- 0.7 = 7/10
- 0.2 = 1/5
- 0.8 = 4/5
- 0.9 = 9/10
- 0.5 = 1/2
- 0.6 = 3/5

Fifth part (fractions to decimals):
- 1/2 = 0.5
- 1/4 = 0.25
- 1/5 = 0.2
- 1/8 = 0.125
- 1/10 = 0.1
- 1/20 = 0.05
- 3/4 = 0.75
- 3/5 = 0.6
- 3/8 = 0.375
- 3/10 = 0.3
- 3/20 = 0.15
- 3/25 = 0.12

Sixth part (decimals to fractions):
- 0.19 = 19/100
- 0.45 = 9/20
- 0.21 = 21/100
- 0.83 = 83/100
- 0.91 = 91/100
- 0.53 = 53/100
- 0.33 = 33/100
- 0.64 = 16/25
- 0.15 = 3/20
- 0.27 = 27/100
- 0.51 = 51/100
- 0.73 = 73/100

✔ All answers verified.