Fraction to Decimal Calculator

Published on: April 7, 2024

Final Answer: Free • Full Steps: Free

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 numerator by the denominator. When the numerator 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 denominator outside and the numerator inside.
Look at the first digit of the number being divided. If the denominator is too big to fit into it, take one more digit, and keep taking digits until it does fit. Ask how many times the denominator fits, and write that number above the bar, over the last digit you used. If it will not fit once you have started, write 0 above the bar for that place. Multiply the denominator by the number you wrote, then take the result away. Bring down the next digit and start again. When the digits run out and something is still left over, put a decimal point in the answer and keep bringing down zeros instead. Stop when nothing is left over, or after 3 places if the digits keep repeating forever.

See Example 1 Hide Example 1

Problem

\(\frac{9}{16}\)

Approach

Step-by-step method

Set up the long-division box, with the denominator outside and the numerator inside.
Look at the first digit of the number being divided. If the denominator is too big to fit into it, take one more digit, and keep taking digits until it does fit. Ask how many times the denominator fits, and write that number above the bar, over the last digit you used. If it will not fit once you have started, write 0 above the bar for that place. Multiply the denominator by the number you wrote, then take the result away. Bring down the next digit and start again. When the digits run out and something is still left over, put a decimal point in the answer and keep bringing down zeros instead. Stop when nothing is left over, or after 3 places if the digits keep repeating forever.

Step 1

Step 1 - Set up the long-division box: the denominator goes outside, the numerator goes inside, and the decimal answer is written above the bar.

In this problem: We divide \(9\) by \(16\).


16	9

Step 2

Step 2 - Work from left to right. If the denominator does not fit yet, take one more digit until it does. Write how many times it fits above the bar, 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 \(16\) does not fit into \(9\). So the integer part starts with 0. Then we place a decimal point and bring down 0s to get the decimal digits.


16	9

Step 2a

Step 2a - Divide, multiply, and subtract.

In this problem: \(16\) cannot go into \(9\), so we write \(0\). Multiply: \(16 \times 0 = 0\). Subtract: \(9 - 0 = 9\).

	0
16	9
-	0
	9

Step 2b

Step 2b - Bring down 0 after the decimal.

In this problem: We bring down \(0\) to make \(90\).

	0.
16	9.	0
-	0
	9	0

Step 2c

Step 2c - Divide, multiply, and subtract.

In this problem: We look at \(90\). \(16\) fits \(5\) times. Multiply: \(16 \times 5 = 80\). Subtract: \(90 - 80 = 10\).

	0.	5
16	9.	0
-	0
	9	0
-	8	0
	1	0

Problem

\(90 - 80\)

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.

	9	0
−	8	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: \(9 - 8 = 1\) → write \(1\) under the tens column.

	9	0
−	8	0

	1	0

Final Answer

\(10\)

Step 2d

Step 2d - Bring down 0 after the decimal.

In this problem: We bring down \(0\) to make \(100\).

	0.	5
16	9.	0	0
-	0
	9	0
-	8	0
	1	0	0

Step 2e

Step 2e - Divide, multiply, and subtract.

In this problem: We look at \(100\). \(16\) fits \(6\) times. Multiply: \(16 \times 6 = 96\). Subtract: \(100 - 96 = 4\).

	0.	5	6
16	9.	0	0
-	0
	9	0
-	8	0
	1	0	0
-		9	6
			4

Problem

\(100 - 96\)

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 borrow because \(0\) in the ones column is smaller than \(6\). The columns just to the left are \(0\), so we borrow from the nearest column that is not zero, the hundreds column, and pass it along one column at a time. Take 1 from the hundreds column, so \(1\) becomes \(0\), and add 10 to the tens column, so \(0\) becomes \(10\).

	0	10
	1	0	0
−		9	6

Step 2

Step 2 - 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: Take 1 from the tens column, so \(10\) becomes \(9\), and add 10 to the ones column, so \(0\) becomes \(10\).

		9
	0	10	10
	1	0	0
−		9	6

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: \(10 - 6 = 4\) → write \(4\) under the ones column.

		9
	0	10	10
	1	0	0
−		9	6

			4

Step 4

Step 4 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.

In this problem: \(9 - 9 = 0\) → this is a leading zero, so nothing is written under the tens column.

		9
	0	10	10
	1	0	0
−		9	6

		0	4

Step 5

Step 5 - 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 hundreds column.

		9
	0	10	10
	1	0	0
−		9	6

			4

Final Answer

\(4\)

Step 2f

Step 2f - Bring down 0 after the decimal.

In this problem: We bring down \(0\) to make \(40\).

	0.	5	6
16	9.	0	0	0
-	0
	9	0
-	8	0
	1	0	0
-		9	6
			4	0

Step 2g

Step 2g - Divide, multiply, and subtract.

In this problem: We look at \(40\). \(16\) fits \(2\) times. Multiply: \(16 \times 2 = 32\). Subtract: \(40 - 32 = 8\).

	0.	5	6	2
16	9.	0	0	0
-	0
	9	0
-	8	0
	1	0	0
-		9	6
			4	0
-			3	2
				8

Problem

\(40 - 32\)

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

In this problem: We need to borrow because \(0\) in the ones column is smaller than \(2\). Take 1 from the tens column, so \(4\) becomes \(3\), and add 10 to the ones column, so \(0\) becomes \(10\).

	3	10
	4	0
−	3	2

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: \(10 - 2 = 8\) → write \(8\) under the ones column.

	3	10
	4	0
−	3	2

		8

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: \(3 - 3 = 0\) → this is a leading zero, so nothing is written under the tens column.

	3	10
	4	0
−	3	2

		8

Final Answer

\(8\)

Step 2h

Step 2h - Bring down 0 after the decimal.

In this problem: We bring down \(0\) to make \(80\).

	0.	5	6	2
16	9.	0	0	0	0
-	0
	9	0
-	8	0
	1	0	0
-		9	6
			4	0
-			3	2
				8	0

Step 2i

Step 2i - Divide, multiply, and subtract.

In this problem: We look at \(80\). \(16\) fits \(5\) times. Multiply: \(16 \times 5 = 80\). Subtract: \(80 - 80 = 0\).

	0.	5	6	2	5
16	9.	0	0	0	0
-	0
	9	0
-	8	0
	1	0	0
-		9	6
			4	0
-			3	2
				8	0
-				8	0
					0

Problem

\(80 - 80\)

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.

	8	0
−	8	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: \(8 - 8 = 0\) → this is a leading zero, so nothing is written under the tens column.

	8	0
−	8	0

		0

Final Answer

\(0\)

Final Answer

\(\frac{9}{16} = 0.5625\)

See Example 2 Hide Example 2

Problem

\(\frac{2}{7}\)

Approach

Step-by-step method

Set up the long-division box, with the denominator outside and the numerator inside.
Look at the first digit of the number being divided. If the denominator is too big to fit into it, take one more digit, and keep taking digits until it does fit. Ask how many times the denominator fits, and write that number above the bar, over the last digit you used. If it will not fit once you have started, write 0 above the bar for that place. Multiply the denominator by the number you wrote, then take the result away. Bring down the next digit and start again. When the digits run out and something is still left over, put a decimal point in the answer and keep bringing down zeros instead. Stop when nothing is left over, or after 3 places if the digits keep repeating forever.

Step 1

Step 1 - Set up the long-division box: the denominator goes outside, the numerator goes inside, and the decimal answer is written above the bar.

In this problem: We divide \(2\) by \(7\).


7	2

Step 2

In this problem: We start from the left, but \(7\) does not fit into \(2\). So the integer part starts with 0. Then we place a decimal point and bring down 0s to get the decimal digits.


7	2

Step 2a

Step 2a - Divide, multiply, and subtract.

In this problem: \(7\) cannot go into \(2\), so we write \(0\). Multiply: \(7 \times 0 = 0\). Subtract: \(2 - 0 = 2\).

	0
7	2
-	0
	2

Step 2b

Step 2b - Bring down 0 after the decimal.

In this problem: We bring down \(0\) to make \(20\).

	0.
7	2.	0
-	0
	2	0

Step 2c

Step 2c - Divide, multiply, and subtract.

In this problem: We look at \(20\). \(7\) fits \(2\) times. Multiply: \(7 \times 2 = 14\). Subtract: \(20 - 14 = 6\).

	0.	2
7	2.	0
-	0
	2	0
-	1	4
		6

Problem

\(20 - 14\)

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

In this problem: We need to borrow because \(0\) in the ones column is smaller than \(4\). Take 1 from the tens column, so \(2\) becomes \(1\), and add 10 to the ones column, so \(0\) becomes \(10\).

	1	10
	2	0
−	1	4

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: \(10 - 4 = 6\) → write \(6\) under the ones column.

	1	10
	2	0
−	1	4

		6

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: \(1 - 1 = 0\) → this is a leading zero, so nothing is written under the tens column.

	1	10
	2	0
−	1	4

		6

Final Answer

\(6\)

Step 2d

Step 2d - Bring down 0 after the decimal.

In this problem: We bring down \(0\) to make \(60\).

	0.	2
7	2.	0	0
-	0
	2	0
-	1	4
		6	0

Step 2e

Step 2e - Divide, multiply, and subtract.

In this problem: We look at \(60\). \(7\) fits \(8\) times. Multiply: \(7 \times 8 = 56\). Subtract: \(60 - 56 = 4\).

	0.	2	8
7	2.	0	0
-	0
	2	0
-	1	4
		6	0
-		5	6
			4

Problem

\(60 - 56\)

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

In this problem: We need to borrow because \(0\) in the ones column is smaller than \(6\). Take 1 from the tens column, so \(6\) becomes \(5\), and add 10 to the ones column, so \(0\) becomes \(10\).

	5	10
	6	0
−	5	6

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: \(10 - 6 = 4\) → write \(4\) under the ones column.

	5	10
	6	0
−	5	6

		4

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: \(5 - 5 = 0\) → this is a leading zero, so nothing is written under the tens column.

	5	10
	6	0
−	5	6

		4

Final Answer

\(4\)

Step 2f

Step 2f - Bring down 0 after the decimal.

In this problem: We bring down \(0\) to make \(40\).

	0.	2	8
7	2.	0	0	0
-	0
	2	0
-	1	4
		6	0
-		5	6
			4	0

Step 2g

Step 2g - Divide, multiply, and subtract.

In this problem: We look at \(40\). \(7\) fits \(5\) times. Multiply: \(7 \times 5 = 35\). Subtract: \(40 - 35 = 5\).

	0.	2	8	5
7	2.	0	0	0
-	0
	2	0
-	1	4
		6	0
-		5	6
			4	0
-			3	5
				5

Problem

\(40 - 35\)

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

In this problem: We need to borrow because \(0\) in the ones column is smaller than \(5\). Take 1 from the tens column, so \(4\) becomes \(3\), and add 10 to the ones column, so \(0\) becomes \(10\).

	3	10
	4	0
−	3	5

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: \(10 - 5 = 5\) → write \(5\) under the ones column.

	3	10
	4	0
−	3	5

		5

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: \(3 - 3 = 0\) → this is a leading zero, so nothing is written under the tens column.

	3	10
	4	0
−	3	5

		5

Final Answer

\(5\)

Final Answer

\(\frac{2}{7} = 0.285\)

Example Problems

Click one to load it into the box and solve it.