Converting Fractions to Decimals - Learn Fast with Easy Formulas & Conversion Chart

Step 4: Final Answer

1 ÷ 6 = 0.1666... = 0.16̅

1. 5/16 into a decimal

Solution: 

Step 1: Write it as a division

A fraction means numerator ÷ denominator. So, 5 ÷ 16

Step 2: Set up the long division

          0.3125

     __________

16 | 5.0000

   - 4.8      (16 × 0.3 = 4.8)

     ----

      20

   - 16       (16 × 1 = 16)

     ----

       40

   - 32       (16 × 2 = 32)

     ----

        80

     - 80       (16 × 5 = 80)

      ----

       0

Step 3: Divide step by step

• 16 goes into 50 three times → remainder 2
• Bring down 0 → now 20 → 16 × 1 = 16 → remainder 4
• Bring down 0 → now 40 → 16 × 2 = 32 → remainder 8
• Bring down 0 → now 80 → 16 × 5 = 80 → remainder 0

Step 4: Final Answer

5 ÷ 16 ​= 0.3125 (Proper and Terminating Fraction)

1. 7/16 as a decimal

Solution:

Step 1: Write it as a division

 7 ÷ 16

Step 2: Now divide

         0.4375

     __________

16 | 7.0000

      - 6.4       (16 × 0.4 = 6.4)

       ----

      60

    - 48        (16 × 3 = 48)

     ----

      120

   - 112       (16 × 7 = 112)

     ----

        80

    - 80        (16 × 5 = 80)

      ----

        0

Step 3: Divide step by step

• 16 goes into 70 four times → remainder 6
• Bring down 0 → now 60 → 16 × 3 = 48 → remainder 12
• Bring down 0 → now 120 → 16 × 7 = 112 → remainder 8
• Bring down 0 → now 80 → 16 × 5 = 80 → remainder 0

Step 4: Final Answer

7/16 = 0.4375

1. Convert 1/16 to a decimal

Solution:

Step 1: Write it as a division

A fraction means numerator ÷ denominator. So, 1 ÷ 16

Step 2: Set up the long division

         0.0625

     __________

16 | 1.0000

   - 0.96       (16 × 0.06 = 0.96)

     ----

      0.040

   - 0.032      (16 × 0.002 = 0.032)

     ----

      0.008

   - 0.008      (16 × 0.0005 = 0.008)

     ----

        0

Step 3: Divide step by step

• 16 goes into 100 six times → remainder 4
• Bring down 0 → now 40 → 16 × 2 = 32 → remainder 8
• Bring down 0 → now 80 → 16 × 5 = 80 → remainder 0

Step 4: Final Answer

1 ÷ 16 = 0.0625

1. 3/8 into a decimal

Solution: 

Step 1: Write it as a division

A fraction means numerator ÷ denominator. So, 3 ÷ 8

Step 2: Set up the long division

        0.375

     __________

8 | 3.000

  - 2.4       (8 × 0.3 = 2.4)

    ----

     60

  - 56        (8 × 7 = 56)

    ----

      40

  - 40        (8 × 5 = 40)

    ----

       0

Step 3: Divide step by step

• 8 goes into 30 three times → remainder 6
• Bring down 0, now 60 → 8 × 7 = 56 → remainder 4
• Bring down 0, now 40 → 8 × 5 = 40 → remainder 0

Step 4: Final Answer

3 ÷ 8 = 0.375

1. 9/16 into a decimal

Step 1: Write as division

                                       9 ÷ 16

Step 2: Set up the long division

       0.5625

    ________

16 | 9.0000

   - 8.0      (16 × 0.5 = 8)

     ----

      10

   - 9.6      (16 × 0.6 = 9.6)

     ----

       40

     - 32       (16 × 0.2 = 32)

     ----

        80

      - 80       (16 × 0.5 = 80)

     ----

         0

Step 3: Divide step by step

• 16 into 9 → 0, remainder 9 (write 0.).
• Bring down 0 → 90. 16 × 5 = 80 → write 5 → remainder 10.
• Bring down 0 → 100. 16 × 6 = 96 → write 6 → remainder 4.
• Bring down 0 → 40. 16 × 2 = 32 → write 2 → remainder 8.
• Bring down 0 → 80. 16 × 5 = 80 → write 5 → remainder 0 (stop).

Step 4: Final Answer

9/16 = 0.5625 (Proper & Terminating)

Converting Improper Fractions

Improper fractions have numerators larger than denominators, giving results greater than 1 when converted.

Step 1: Write it as a division

                      4÷3

Step 2: Set up the long division

         1.333...

  __________

 3 | 4.000000

  - 3  (3 × 1 = 3)

  ----

   10

  - 9  (3 × 3 = 9)

  ----

   10 

Step 3: Divide Step by Step

• 3 into 4 → 1, remainder 1 (write 1.).
• Bring down 0 → 10. 3 × 3 = 9, remainder 1.
• Bring down another 0 → 10 again. 3 × 3 = 9, remainder 1.
• This pattern continues as 1.3333…

Step 4: Final Answer

4 ÷ 3 = 1.333...

1. 5/2 as a decimal

Solution: 

Step 1: Write it as a division

A fraction means numerator ÷ denominator. So, 5 ÷ 2

Step 2: Set up the long division

       2.5

     ______

2 | 5.0

  - 4      (2 × 2 = 4)

    ----

     10

  - 10     (2 × 5 = 10)

    ----

      0

Step 3: Divide step by step

• 2 goes into 5 two times, remainder 1
• Bring down 0, now it’s 10
• 2 goes into 10 five times, remainder 0

Step 4: Final Answer

5 ÷ 2 = 2.5 

6/5 as a decimal

Step 1: Write as division

                                       6 ÷ 5

Step 2: Set up the long division

     1.2

   ______

5 | 6.0

   - 5.0  (5 × 1 = 5)

   -----

     10

   - 10   (5 × 2 = 10)

   -----

      0

Step 3: Divide step by step

• 5 goes into 6 → 1 time, remainder 1
• Bring down 0 → 10 ÷ 5 = 2, remainder 0

Step 3: Final Answer

6/5 = 1.2 (Improper & Terminating)

Converting Mixed Numbers (Whole + Fraction)

To convert mixed numbers:

Step 1: Convert the fraction part into a decimal.

Step 2: Add it to the whole number.

1. 3 3/4 as a decimal

Solution: 

Step 1: Convert to improper fraction

                                                      3 3/4 = 15/4

Step 2: Write as division

                                                        15÷4

Step 3: Long division

       3.75

     _______

4 | 15.00

  - 12

    --

    30

  - 28

    --

    20

  - 20

    --

     0

Step 3: Divide step by step

• 4 × 3 = 12 → remainder 3
• Bring down 0 → 30 ÷ 4 = 7, remainder 2
• Bring down 0 → 20 ÷ 4 = 5, remainder 0

Step 4: Final Answer

3 3/4 = 3.75

1. 3 3/8 as a decimal

Solution: 

Step 1: Convert to improper fraction

                                                     3 3/8 = 27​/8

Step 2: Write as division

                                                        27÷8

Step 3: Long division

       3.375

     _______

8 | 27.000

  - 24

    --

   30

  - 24

    --

    60

  - 56

    --

    40

  - 40

    --

     0

Step 3: Divide step by step

• 8 × 3 = 24 → remainder 3
• Bring down 0 → 30 ÷ 8 = 3, remainder 6
• Bring down 0 → 60 ÷ 8 = 7, remainder 4
• Bring down 0 → 40 ÷ 8 = 5, remainder 0

Step 3: Final Answer

3 3/8 in decimal = 3.375 ( terminating decimal)

1. 2 5/8 as a decimal

Solution: 

Step 1: Convert to improper fraction

                                                       2 5/8 = (2×8 + 5)/8 = 21/8

Step 2: Write as division

                                                          21 ÷ 8

Step 3: Long division

     2.625

   ______

8 | 21.000

   - 16

     ---

      50

   - 48

     ---

      20

   - 16

     ---

     40

   - 40

     ---

       0

Step 3: Divide step by step

• 8 × 2 = 16 → remainder 5
• Bring down 0 → 50 ÷ 8 = 6, remainder 2
• Bring down 0 → 20 ÷ 8 = 2, remainder 4
• Bring down 0 → 40 ÷ 8 = 5, remainder 0

Step 4: Final Answer

21 ÷ 8 = 2.625

Using Long Division for Complex Fractions

For fractions that don’t divide evenly, use long division to get repeating or non-terminating decimals.

Example: Which is the decimal expansion of 7/22?

          0.3181...

    ______________

22 | 7.000000000

     -  66         ← (22 × 3 = 66)

      ----

         40

     -   22         ← (22 × 1 = 22)

      ----

         180

     -   176        ← (22 × 8 = 176)

      ----

           4

Now we’re back to the same remainder (4) we had earlier, so the digits 3181 will keep repeating.

Therefore, 7 ÷ 22 = 0.31818181… or simply 0.318̅ (the bar means the digits 18 repeat endlessly).

Common Fractions and Their Decimal Equivalents

Here’s a quick reference fraction decimal chart to help you remember common fractions and their decimal forms. These conversions make solving math problems, percentages and measurements much easier.

Fraction Decimal Chart

   - 1.0

     ---

      0

 Step 3: Divide step by step

• 2 doesn’t go into 1, so we write 0. and make it 10
• 2 × 5 = 10 → subtract → remainder 0
• No remainder means the division ends here.

Step 4: Final Answer

1 ÷ 2 = 0.5

It’s a terminating decimal because the division ends with no remainder.

1. What is a 1/4 as a decimal?

Solution: 

Step 1: Write it as a division

A fraction means we divide the top number (numerator) by the bottom number (denominator).

So, 1 ÷ 4

Step 2: Set up the long division

       0.25

    _________

4 | 1.00

   - 0.8   (4 × 0.2 = 0.8)

     ----

     0.20

   - 0.20  (4 × 0.05 = 0.20)

     ----

      0

Step 3: Final Answer

1 ÷ 4 = 0.25

1. What is 3/5 as a decimal

Solution: 

Step 1: Write it as a division

A fraction means numerator ÷ denominator. So, 3 ÷ 5

Step 2: Set up the long division

        0.6

    _______

5 | 3.0

   - 3.0       (5 × 6 = 30)

     ---

      0

 Step 3: Divide step by step

• 5 goes into 3 → 0, remainder 3
• Add 0 → 30 ÷ 5 = 6, remainder 0

Step 3: Final Answer

3 ÷ 5 = 0.6

1. 4/5 as a decimal

Solution:

Let’s convert 4/5 into a decimal step by step:

Step 1: Write the formula

Decimal = Denominator / Numerator​

Step 2: Divide

        0.8

    _______

5 | 4.0

   - 4.0   (5 × 0.8 = 4.0)

     ---

      0

Step 3: Final Answer

4 ÷ 5 = 0.8

1. 2 1/2 as a decimal

Solution:

Step 1: Change to improper fraction

                                           2 1/2 = 5​/2

Step 2: Write as division

                                               5÷2

Step 3: Long division

       2.5

     ______

2 | 5.0

  - 4

    --

   10

  -10

    --

    0

Step 3: Final Answer

2 1/2 = 2.5 

1. 3/5 as a decimal

Solution:

Step 1: Write as division

                                         3 ÷ 5

Step 2: Set up long division

     0.6

   ______

5 | 3.0

   - 3.0   (5 × 0.6 = 3.0)

   -----

     0

Step 3: Final Answer

3 ÷ 5 = 0.6

Non-Terminating Decimals

A non-terminating decimal is a decimal number with an infinite number of digits after the decimal point. But there are two types of non-terminating decimals:

1. Repeating (Recurring):

The digits repeat in a pattern.

Example: 1/9 = 0.111... → the 1s keep repeating.

1. Non-repeating (Irrational):

The digits go on forever without any pattern.

Example: π = 3.141592653... → the numbers never repeat in any pattern.

Examples:

1. 1/9 as a decimal

Solution:

Step 1: Write it as a division

A fraction means numerator ÷ denominator. So, 1 ÷ 9

Step 2: Set up the long division

         0.111...

     __________

9 | 1.000000

   - 0.9        (9 × 0.1 = 0.9)

     ----

      10

      - 9          (9 × 1 = 9)

     ----

       10

       - 9

      ----

       10

..…and it keeps repeating the same pattern.

Step 3: Divide step by step

• 9 goes into 10 one time → remainder 1
• Bring down 0 → still 10 → 9 × 1 = 9 → remainder 1
• This repeats again and again...

Step 4: Final Answer

1 ÷ 9 = 0.111...

It’s a proper and non-terminating (repeating) decimal.

1. 1/12 as a decimal

Solution:

Step 1: Write it as a division

                                             1÷12

Step 2: Set up long division

       0.0833…

     __________

12 | 1.00000

   - 0.96      (12 × 0.08 = 0.96)

     ----

      0.040

   - 0.036     (12 × 0.003 = 0.036)

     ----

      0.004 → continues repeating 3

Step 3: Final Answer

1/12 = 0.0833… (repeating)  non-terminating repeating decimal.

1. 8/9 as a decimal

Solution:

Step 1: Write as division

                                         8 ÷ 9

Step 2: Set up long division

     0.888…

   ______

9 | 8.000

   - 8.1  (9 × 0.8 = 7.2)

   -----

     8 (keeps repeating)

Step 3: Final Answer

8/9 = 0.888... (Non-Terminating, Repeating)

1. 1 2/3 as a decimal

Solution:

Step 1: Convert to improper fraction

                                        1 2/3 = (1×3 + 2)/3 = 5/3

Step 2: Write as division 

                                                5 ÷ 3

Step 3:Set up long division

     1.666...

   ______

3 | 5.000

   - 4.8

     ----

      20

   - 18

     ----

       20 (repeats)

Step 4: Final Answer

 5 ÷ 3 = 1.666...

1. 2/7 as a decimal

Step 1: Write as division

                                           2 ÷ 7

Step 2: Set up long division

   0.285714...

   ______

7 | 2.000000

   - 1.4

     ----

      60

   - 56

     ----

       40

   - 35

     ----

      50

   - 49

     ----

      10 

Step 3: Final Answer

2 ÷ 7 = 0.285714...

Decimal Operations (Practice Worksheets Section)

Once you understand converting fractions to decimals, the next step is to practice how decimals work in real calculations. This section includes simple worksheets and examples for adding, subtracting, multiplying, dividing and rounding decimals perfect for students who want extra practice.

Adding and Subtracting Decimals Worksheets

When adding or subtracting decimals, always line up the decimal points vertically. This ensures you’re working with the correct place values (tenths, hundredths, etc.).

Example:

  4.75  

+ 2.30  

———  

  7.05  

Tip: Add zeros if needed to make the decimal places equal before adding or subtracting.

Multiplying Decimals Worksheets

To multiply decimals:

1. Ignore the decimal points and multiply normally.
2. Count the total number of decimal places in both numbers.
3. Place the decimal point in the answer accordingly.

Example:

2.5 × 1.6 = 25 × 16 = 400, then move the decimal two places → 4.00

Answer: 4.0

Dividing Decimals Worksheet

When dividing decimals:

1. Move the decimal point in the divisor to make it a whole number.
2. Move the decimal point in the dividend the same number of places.
3. Divide as usual.

Example:

6.4 ÷ 0.8 → Move both decimals one place → 64 ÷ 8 = 8

Answer: 8

Quiz Practice: Try questions like

1. 3.6 ÷ 0.9 = ?
2. 4.2 ÷ 0.7 = ?

Rounding Decimals Worksheet

Rounding decimals helps simplify numbers for easier calculations.

Rules:

1. If the next digit is 5 or more, round up.
2. If it’s 4 or less, round down.

Examples:

4.76 → 4.8 (round up)

5.23 → 5.2 (round down)

Tip: Understanding prefixes with decimals (like 0.0 or 1.0) helps programmers avoid rounding errors in financial or scientific calculations.

1. <h3>In Finance and Daily Life

Decimals are a big part of our everyday routines whether you’re checking prices, splitting bills, or calculating discounts.

Examples:

• $2.50 = two and a half dollars
• 7.75% sales tax = 7¾ percent
• 0.5 liters = half a liter

Fraction-to-Decimal Conversion Tools

Learning fractions and decimals is much easier when you have fast tools ready. Below are online converters and printable charts you can use instantly or embed in your blog.

Online Calculators

Use these free converters to turn any fraction into a decimal instantly.

1. RapidTables Fraction to Decimal Converter - simple and clean interface.
2. Omni Calculator Fraction to Decimal Tool - handles more complex fractions too.