3/7 as a decimal is 0.428571. To convert a fraction to a decimal, we divide the numerator (3) by the denominator (7).
Key Facts
- The decimal representation of 3/7 is 0.428571.
- To convert a fraction to a decimal, divide the numerator (3) by the denominator (7).
- The long division method is commonly used to convert fractions to decimals.
- In the long division method, the digits are divided one by one until the remainder is zero.
- If the division does not reach a remainder of zero and repeats the same remainders, the resulting decimal is called a recurring or repeating decimal.
- In the case of 3/7, the decimal digits 428571 repeat indefinitely, so it is a recurring decimal.
- Recurring decimals are often denoted by placing a bar over the repeating digits, so 3/7 can be written as 0.428571 with a bar over the digits 428571.
Long Division Method
The long division method is commonly used to convert fractions to decimals. In the long division method, the digits are divided one by one until the remainder is zero.
Step 1: Set up the Division Problem
3 ÷ 7 = 0.428571
Step 2: Divide the Numerator by the Denominator
3 ÷ 7 = 0.42
Step 3: Bring Down the Remainder
3 ÷ 7 = 0.428
Step 4: Multiply the Remainder by 10 and Divide by the Denominator
28 ÷ 7 = 4
Step 5: Bring Down the Remainder
28 ÷ 7 = 4.05
Step 6: Multiply the Remainder by 10 and Divide by the Denominator
5 ÷ 7 = 0.71
Step 7: Bring Down the Remainder
5 ÷ 7 = 0.714
Step 8: Multiply the Remainder by 10 and Divide by the Denominator
14 ÷ 7 = 2
Step 9: Bring Down the Remainder
14 ÷ 7 = 2.000
Step 10: Multiply the Remainder by 10 and Divide by the Denominator
0 ÷ 7 = 0
Step 11: Stop Dividing
The remainder is 0, so we stop dividing.
Recurring Decimals
In the case of 3/7, the decimal digits 428571 repeat indefinitely, so it is a recurring decimal. Recurring decimals are often denoted by placing a bar over the repeating digits, so 3/7 can be written as 0.428571 with a bar over the digits 428571.
Conclusion
3/7 as a decimal is 0.428571. This can be found using the long division method. The decimal is recurring, meaning that the digits 428571 repeat indefinitely.
Sources
- https://www.cuemath.com/questions/what-is-3-7-as-a-decimal/
- https://argoprep.com/blog/what-is-3-7-as-a-decimal/
- https://hellothinkster.com/math-questions/decimals/what-is-3-7-as-a-decimal
FAQs
How do I convert 3/7 to a decimal?
Answer: To convert 3/7 to a decimal, divide 3 by 7 using the long division method.
What is the decimal representation of 3/7?
Answer: The decimal representation of 3/7 is 0.428571.
Is 3/7 a terminating or recurring decimal?
Answer: 3/7 is a recurring decimal, meaning that the digits in the decimal representation repeat indefinitely.
How can I identify a recurring decimal?
Answer: A recurring decimal is a decimal in which a sequence of digits repeats indefinitely. Recurring decimals are often denoted by placing a bar over the repeating digits.
What is the repeating pattern in the decimal representation of 3/7?
Answer: The repeating pattern in the decimal representation of 3/7 is 428571.
Can I use a calculator to convert 3/7 to a decimal?
Answer: Yes, you can use a calculator to convert 3/7 to a decimal. Simply divide 3 by 7 using the calculator’s division function.
What are some other examples of recurring decimals?
Answer: Other examples of recurring decimals include 1/3 (0.333…), 2/3 (0.666…), and 5/6 (0.833…).
How can I convert a recurring decimal to a fraction?
Answer: To convert a recurring decimal to a fraction, follow these steps:
- Let x be the recurring decimal.
- Multiply x by a power of 10 that is equal to the number of digits in the repeating block.
- Subtract x from the result obtained in step 2.
- Simplify the resulting fraction.