**Expressing rational numbers as decimals :**

A rational number is any number that can be written as a ratio in the form a/b, where a and b are integers and b is not 0. Examples of rational numbers are 6 and 0.5.

7 can be written as 7/1

0.25 can be written as 1/4

Every rational number can be written as a terminating decimal or a repeating decimal. A terminating decimal, such as 0.5, has a finite number of digits.

A repeating decimal has a block of one or more digits that repeat indefinitely.

1. Remember that the fraction bar means “divided by.” Divide the numerator by the denominator.

2. Divide until the remainder is zero or until the digits in the quotient begin to repeat.

3. Add zeros after the decimal point in the dividend as needed.

4. When a decimal has one or more digits that repeat indefinitely, write the decimal with a bar over the repeating digit(s).

**Example 1 :**

Write the fraction 1/4 as a decimal.

**Solution : **

Hence, the decimal equal to the fraction 1/4 is 0.25

**Example 2 :**

Write the fraction 1/3 as a decimal.

**Solution : **

Hence, the decimal equal to the fraction 1/3 is 0.333......

or

**Example 3 :**

Write 96/200 as a decimal.

**Solution :**

**Step 1 :**

In the fraction 96/200, the denominator 200 is a multiple of 100.

So we can change the denominator 200 as 100 by dividing both numerator and denominator by 2.

96/200 = (96÷2) / (200÷2) = 48/100

**Step 2 :**

In 48/100, since the denominator is 100, 48/100 can be easily converted to decimal.

In the numerator 48, there is no decimal point. Let us assume there is a decimal at the end of 48, that is (48.)

Since we divide 48 by 100 and there are two zeros in 100, we have to move the decimal point in (48.) two digits to the left.

So, we have

48/100 = 0.48

Hence, the decimal equal to the fraction 96/200 is 0.48

**Example 4 :**

Write 2/5 as a decimal.

**Solution :**

**Step 1 :**

In the fraction 2/5, the denominator 5 is a factor of 10. So we can change the denominator 5 as 10 by multiplying both numerator and denominator by 2.

2/5 = (2x2) / (5x2) = 4/10

**Step 2 :**

In 4/10, since the denominator is 10, 4/10 can be easily converted to decimal.

In the numerator 4, there is no decimal point. Let us assume there is a decimal point after 4, that is (4.).

Since we divide 4 by 10 and there is only one zero in 10, we have to move the decimal point in (4.) one digit to the left.

So, we have

4/10 = 0.4

Hence, the decimal equal to the fraction 2/5 is 0.4

**Example 5 :**

Write 48/5 as a decimal.

**Solution :**

**Step 1 :**

In the fraction 48/5, the denominator 5 is a factor of 10. So we can change the denominator 5 as 10 by multiplying both numerator and denominator by 2.

48/5 = (48x2) / (5x2) = 96/10

**Step 2 :**

In 96/10, since the denominator is 10, 96/10 can be easily converted to decimal.

In the numerator 96, there is no decimal point. Let us assume there is a decimal point after 96, that is (96.).

Since we divide 96 by 10 and there is only one zero in 10, we have to move the decimal point in (96.) one digit to the left.

So, we have

96/10 = 9.6

Hence, the decimal equal to the fraction 48/5 is 9.6

**Example 6 :**

Write 1/8 as a decimal.

**Solution :**

In the fraction 1/8, the denominator 8 is not a factor or multiple of 10 or 100.

And also, we can not change the denominator 8 as a multiple of 10 or 100.

So, use long division to divide the numerator by the denominator.

Hence, the decimal equal to the fraction 1/8 is 0.125

After having gone through the stuff given above, we hope that the students would have understood "Expressing rational numbers as decimals".

Apart from the stuff given above, if you want to know more about "Expressing rational numbers as decimals", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**