Jiaxin

**Solution: **

**Step:1** To convert a fraction into a decimal, following procedure is used.

**1.** Observe the denominator of the fraction, if the denominator is a number which can be written in the form , where are non-negative integers, then the fraction can be converted in a terminating decimal otherwise it is a non-terminating decimal.

**2.** Divide the numerator by denominator.

**3.** If the division is non-terminating or the division is too long, then the decimal expansion can be rounded up to 2 to 3 decimal places, which gives the approximate value of fraction.

**Step:2** To Similarly, to convert a decimal into fraction, following procedure is used.

**1.** Observe, after how many places from the right a decimal is placed.

**2. **Divide the number after removing the decimal from it by a number as etc number of zeros after 1 depends upon the place from the right a decimal is placed.

**3.** Convert the fraction obtained in step 2 in simplest form.. If the denominator is greater than the numerator then the fraction is proper and if the numerator is greater than denominator then the fraction is improper.

**Conversion of to a decimal:**

**1.**In the fraction , the denominator 16 can be written as .

Therefore, the decimal expansion of above fraction is a terminating decimal.

**2.** Divide the numerator 5 by 16.

**3. **The exact decimal expansion of is .

**Answer: ** is as a decimal.

** **

**Similar Problems:**

** **

**Problem 1:** Convert as a decimal.

**Solution:**

**Step:1** In the fraction , the denominator 4 can be written as .

**Step:2** Therefore, the decimal expansion of above fraction is a terminating decimal.

Divide the numerator 1 by 4.

**Answer:** is as a decimal.

** **

**Problem 2:** Convert as a fraction.

**Solution:**

**Step:1** In the fraction , the denominator 4 can be written as .

**Step:2** Therefore, the decimal expansion of above fraction is a terminating decimal.

**2.** Divide the numerator 1 by 8.

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