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Convert the fraction below into a decimalEdit the repeating and non-repeating part of the decimal:
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Q. Convert the fraction below into a decimalEdit the repeating and non-repeating part of the decimal:
- Set Up Long Division: We start by setting up the long division of divided by . Since is less than , we add a decimal point to and add a zero to make it . Now we divide by .
- Perform Division: Performing the division, goes into once ( times is ), and we subtract from , which leaves us with a remainder of .
- Repeat Indefinitely: We bring down another zero and divide by again. This process will repeat indefinitely because each time we will have a remainder of .
- Identify Repeating Decimal: Since the remainder continues to be after each division, the decimal will repeat the digit infinitely. Therefore, the decimal representation of is , with the digit repeating indefinitely.
- Edit Decimal Representation: Edit the repeating and non-repeating part of the decimal: The non-repeating part is , and the repeating part is . So we write the decimal as with a bar over the to indicate that it repeats.
