Fraction to Decimal Calculator
This Fraction to Decimal Calculator helps you turn a fraction into a decimal and shows the working clearly using long division. A fraction is a division waiting to happen, so divide the top number by the bottom number. When the top runs out, put a decimal point in the answer and keep bringing down zeros. Stop when nothing is left over, or when the same digits start repeating. Following the same pattern every time is what makes converting fractions easy to picture, check, and repeat on your own with any fraction.
Step-by-step method
- Set up the long-division box, with the bottom number outside and the top number inside.
- Do a division of large numbers: divide, multiply, subtract, bring down, and repeat.
- When the digits run out and something is still left over, put a decimal point in the answer and keep bringing down zeros. Stop when nothing is left over. If the digits keep repeating forever, stop after a few places.
See Example 1 Hide Example 1
Problem
Approach
Step-by-step method
- Set up the long-division box, with the bottom number outside and the top number inside.
- Do a division of large numbers: divide, multiply, subtract, bring down, and repeat.
- When the digits run out and something is still left over, put a decimal point in the answer and keep bringing down zeros. Stop when nothing is left over. If the digits keep repeating forever, stop after a few places.
Step 1
Step 1 - Set up the long-division box: the bottom number goes outside, the top number goes inside, and the decimal answer is written on top.
In this problem: We divide \(4\) by \(3\).
| 3 | 4 |
Step 2
Step 2 - Work from left to right. If the bottom number does not fit yet, take one more digit until it does. Write how many times it fits on top, multiply, then take that away to get what is left over. Bring down the next digit and go again. When the digits run out, put a decimal point in the answer and keep bringing down zeros.
In this problem: We start with the first digit \(4\) because it is big enough to divide by \(3\). Then we repeat: divide, multiply, subtract, bring down. After we run out of digits, we bring down 0s to get the decimal digits.
| 3 | 4 |
Step 2a
Step 2a - Divide, multiply, and subtract.
In this problem: We look at \(4\). \(3\) fits \(1\) time. Multiply: \(3 \times 1 = 3\). Subtract: \(4 - 3 = 1\).
| 1 | |
| 3 | 4 |
| - | 3 |
| 1 |
Problem
Approach
Step-by-step method
- Write the two numbers in columns, aligned on the right (ones under ones). Put the − sign to the left of the bottom number, and draw a line underneath.
- Starting from the rightmost column, subtract column-by-column moving right to left. If you cannot subtract in a column, borrow from the column to the left, then subtract. This repeats once for every column, moving right to left.
Step 1
Step 1 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(4 - 3 = 1\) → write \(1\) under the ones column.
| 4 | |
| − | 3 |
| 1 | |
Final Answer
Step 2b
Step 2b - Bring down 0 after the decimal.
In this problem: We bring down \(0\) to make \(10\).
| 1. | ||
| 3 | 4. | 0 |
| - | 3 | |
| 1 | 0 |
Step 2c
Step 2c - Divide, multiply, and subtract.
In this problem: We look at \(10\). \(3\) fits \(3\) times. Multiply: \(3 \times 3 = 9\). Subtract: \(10 - 9 = 1\).
| 1. | 3 | |
| 3 | 4. | 0 |
| - | 3 | |
| 1 | 0 | |
| - | 9 | |
| 1 |
Problem
Approach
Step-by-step method
- Write the two numbers in columns, aligned on the right (ones under ones). Put the − sign to the left of the bottom number, and draw a line underneath.
- Starting from the rightmost column, subtract column-by-column moving right to left. If you cannot subtract in a column, borrow from the column to the left, then subtract. This repeats once for every column, moving right to left.
Step 1
Step 1 - When the top digit in a column is too small to subtract from, borrow from the nearest column to its left that is not zero. Take one away from that digit and add ten to the column on its right, passing the borrow along one column at a time until it reaches the column you are working on.
In this problem: We need to <span class="borrow-text">borrow</span> because \(0\) in the ones column is smaller than \(9\).<br>Take 1 from the tens column, so \(1\) becomes \(0\), and add 10 to the ones column, so \(0\) becomes \(10\).
| 0 | 10 | |
| − | 9 | |
Step 2
Step 2 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(10 - 9 = 1\) → write \(1\) under the ones column.
| 0 | 10 | |
| − | 9 | |
| 1 | ||
Step 3
Step 3 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(0 - 0 = 0\) → this is a leading zero, so nothing is written under the tens column.
| 0 | 10 | |
| − | 9 | |
| 1 | ||
Final Answer
Step 2d
Step 2d - Bring down 0 after the decimal.
In this problem: We bring down \(0\) to make \(10\).
| 1. | 3 | ||
| 3 | 4. | 0 | 0 |
| - | 3 | ||
| 1 | 0 | ||
| - | 9 | ||
| 1 | 0 |
Step 2e
Step 2e - Divide, multiply, and subtract.
In this problem: We look at \(10\). \(3\) fits \(3\) times. Multiply: \(3 \times 3 = 9\). Subtract: \(10 - 9 = 1\).
| 1. | 3 | 3 | |
| 3 | 4. | 0 | 0 |
| - | 3 | ||
| 1 | 0 | ||
| - | 9 | ||
| 1 | 0 | ||
| - | 9 | ||
| 1 |
Problem
Approach
Step-by-step method
- Write the two numbers in columns, aligned on the right (ones under ones). Put the − sign to the left of the bottom number, and draw a line underneath.
- Starting from the rightmost column, subtract column-by-column moving right to left. If you cannot subtract in a column, borrow from the column to the left, then subtract. This repeats once for every column, moving right to left.
Step 1
Step 1 - When the top digit in a column is too small to subtract from, borrow from the nearest column to its left that is not zero. Take one away from that digit and add ten to the column on its right, passing the borrow along one column at a time until it reaches the column you are working on.
In this problem: We need to <span class="borrow-text">borrow</span> because \(0\) in the ones column is smaller than \(9\).<br>Take 1 from the tens column, so \(1\) becomes \(0\), and add 10 to the ones column, so \(0\) becomes \(10\).
| 0 | 10 | |
| − | 9 | |
Step 2
Step 2 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(10 - 9 = 1\) → write \(1\) under the ones column.
| 0 | 10 | |
| − | 9 | |
| 1 | ||
Step 3
Step 3 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(0 - 0 = 0\) → this is a leading zero, so nothing is written under the tens column.
| 0 | 10 | |
| − | 9 | |
| 1 | ||
Final Answer
Step 2f
Step 2f - Bring down 0 after the decimal.
In this problem: We bring down \(0\) to make \(10\).
| 1. | 3 | 3 | ||
| 3 | 4. | 0 | 0 | 0 |
| - | 3 | |||
| 1 | 0 | |||
| - | 9 | |||
| 1 | 0 | |||
| - | 9 | |||
| 1 | 0 |
Step 2g
Step 2g - Divide, multiply, and subtract.
In this problem: We look at \(10\). \(3\) fits \(3\) times. Multiply: \(3 \times 3 = 9\). Subtract: \(10 - 9 = 1\).
| 1. | 3 | 3 | 3 | |
| 3 | 4. | 0 | 0 | 0 |
| - | 3 | |||
| 1 | 0 | |||
| - | 9 | |||
| 1 | 0 | |||
| - | 9 | |||
| 1 | 0 | |||
| - | 9 | |||
| 1 |
Problem
Approach
Step-by-step method
- Write the two numbers in columns, aligned on the right (ones under ones). Put the − sign to the left of the bottom number, and draw a line underneath.
- Starting from the rightmost column, subtract column-by-column moving right to left. If you cannot subtract in a column, borrow from the column to the left, then subtract. This repeats once for every column, moving right to left.
Step 1
Step 1 - When the top digit in a column is too small to subtract from, borrow from the nearest column to its left that is not zero. Take one away from that digit and add ten to the column on its right, passing the borrow along one column at a time until it reaches the column you are working on.
In this problem: We need to <span class="borrow-text">borrow</span> because \(0\) in the ones column is smaller than \(9\).<br>Take 1 from the tens column, so \(1\) becomes \(0\), and add 10 to the ones column, so \(0\) becomes \(10\).
| 0 | 10 | |
| − | 9 | |
Step 2
Step 2 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(10 - 9 = 1\) → write \(1\) under the ones column.
| 0 | 10 | |
| − | 9 | |
| 1 | ||
Step 3
Step 3 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(0 - 0 = 0\) → this is a leading zero, so nothing is written under the tens column.
| 0 | 10 | |
| − | 9 | |
| 1 | ||
Final Answer
Final Answer
See Example 2 Hide Example 2
Problem
Approach
Step-by-step method
- Set up the long-division box, with the bottom number outside and the top number inside.
- Do a division of large numbers: divide, multiply, subtract, bring down, and repeat.
- When the digits run out and something is still left over, put a decimal point in the answer and keep bringing down zeros. Stop when nothing is left over. If the digits keep repeating forever, stop after a few places.
Step 1
Step 1 - Set up the long-division box: the bottom number goes outside, the top number goes inside, and the decimal answer is written on top.
In this problem: We divide \(3\) by \(4\).
| 4 | 3 |
Step 2
Step 2 - Work from left to right. If the bottom number does not fit yet, take one more digit until it does. Write how many times it fits on top, multiply, then take that away to get what is left over. Bring down the next digit and go again. When the digits run out, put a decimal point in the answer and keep bringing down zeros.
In this problem: We start from the left, but \(4\) does not fit into \(3\). So the integer part starts with 0. Then we place a decimal point and bring down 0s to get the decimal digits.
| 4 | 3 |
Step 2a
Step 2a - Divide, multiply, and subtract.
In this problem: \(4\) cannot go into \(3\), so we write \(0\). Multiply: \(4 \times 0 = 0\). Subtract: \(3 - 0 = 3\).
| 0 | |
| 4 | 3 |
| - | 0 |
| 3 |
Step 2b
Step 2b - Bring down 0 after the decimal.
In this problem: We bring down \(0\) to make \(30\).
| 0. | ||
| 4 | 3. | 0 |
| - | 0 | |
| 3 | 0 |
Step 2c
Step 2c - Divide, multiply, and subtract.
In this problem: We look at \(30\). \(4\) fits \(7\) times. Multiply: \(4 \times 7 = 28\). Subtract: \(30 - 28 = 2\).
| 0. | 7 | |
| 4 | 3. | 0 |
| - | 0 | |
| 3 | 0 | |
| - | 2 | 8 |
| 2 |
Problem
Approach
Step-by-step method
- Write the two numbers in columns, aligned on the right (ones under ones). Put the − sign to the left of the bottom number, and draw a line underneath.
- Starting from the rightmost column, subtract column-by-column moving right to left. If you cannot subtract in a column, borrow from the column to the left, then subtract. This repeats once for every column, moving right to left.
Step 1
Step 1 - When the top digit in a column is too small to subtract from, borrow from the nearest column to its left that is not zero. Take one away from that digit and add ten to the column on its right, passing the borrow along one column at a time until it reaches the column you are working on.
In this problem: We need to <span class="borrow-text">borrow</span> because \(0\) in the ones column is smaller than \(8\).<br>Take 1 from the tens column, so \(3\) becomes \(2\), and add 10 to the ones column, so \(0\) becomes \(10\).
| 2 | 10 | |
| − | 2 | 8 |
Step 2
Step 2 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(10 - 8 = 2\) → write \(2\) under the ones column.
| 2 | 10 | |
| − | 2 | 8 |
| 2 | ||
Step 3
Step 3 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(2 - 2 = 0\) → this is a leading zero, so nothing is written under the tens column.
| 2 | 10 | |
| − | 2 | 8 |
| 2 | ||
Final Answer
Step 2d
Step 2d - Bring down 0 after the decimal.
In this problem: We bring down \(0\) to make \(20\).
| 0. | 7 | ||
| 4 | 3. | 0 | 0 |
| - | 0 | ||
| 3 | 0 | ||
| - | 2 | 8 | |
| 2 | 0 |
Step 2e
Step 2e - Divide, multiply, and subtract.
In this problem: We look at \(20\). \(4\) fits \(5\) times. Multiply: \(4 \times 5 = 20\). Subtract: \(20 - 20 = 0\).
| 0. | 7 | 5 | |
| 4 | 3. | 0 | 0 |
| - | 0 | ||
| 3 | 0 | ||
| - | 2 | 8 | |
| 2 | 0 | ||
| - | 2 | 0 | |
| 0 |
Problem
Approach
Step-by-step method
- Write the two numbers in columns, aligned on the right (ones under ones). Put the − sign to the left of the bottom number, and draw a line underneath.
- Starting from the rightmost column, subtract column-by-column moving right to left. If you cannot subtract in a column, borrow from the column to the left, then subtract. This repeats once for every column, moving right to left.
Step 1
Step 1 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(0 - 0 = 0\) → write \(0\) under the ones column.
| 2 | 0 | |
| − | 2 | 0 |
| 0 | ||
Step 2
Step 2 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(2 - 2 = 0\) → this is a leading zero, so nothing is written under the tens column.
| 2 | 0 | |
| − | 2 | 0 |
| 0 | ||
Final Answer
Final Answer
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