Terminating Decimals and Non-Terminating Decimals
When we want to convert a fraction into a decimal form, we generally divide the numerator by the denominator till the remainder becomes zero. In some cases, we obtain zero as remainder but in other cases, the non-zero remainder is obtained.
Let us convert the following fractions into the decimal form.
1. 15/20 2. 1/8
We observe that on division, remainder zero is obtained. Such fractions which gives zero as a remainder on division are called terminating decimals.
Now, let us take some more examples and convert them into decimals.
1. 10/9 2. 13/6
Thus, we observe that on division, we get non-zero remainder infinitely. Such decimal are called non-terminating decimals.
If in a non-terminating decimal, a digit or a group of digits is repeating again and again, then the decimal is called the non-terminating repeating (recurring) decimal.
Converting a Terminating Decimal to a Vulgar Fraction
To convert a terminating decimal into a vulgar fraction, we put 1 in the denominator and add as many zeroes as the number of digits after decimal.
Example: Convert the following decimals into fractions.
a. 0.7 b. 6.75
Solution:
a. 0.7 = 7/10 b. 6.75 = 675/100
Converting a Non-terminating Repeating Decimal to a Vulgar Fraction
To convert a non-terminating repeating (recurring) decimal into a vulgar fraction, look at the following example.
Example: Convert the following decimals into vulgar fractions.
a. 0.777777….. b. 0.262626…...
Solution:
a. Let x = 0.777777….. (1)
Multiply equation (1) by 10, we get
10x = 7.777777…… (2)
Subtracting equation (1) from (2), we get
9x = 7
x = 7/9
b. Let x = 0.262626…... (1)
Multiply equation (1) by 100, we get
100x = 26.262626…… (2)
Subtracting equation (1) from (2), we get
99x = 26
x = 26/99
Related Topics: