Question

Write the decimal expansion of ${\displaystyle \frac{1}{7}}$. Hence, write the decimal expansion of ${\displaystyle \frac{2}{7}},{\displaystyle \frac{3}{7}},{\displaystyle \frac{4}{7}},{\displaystyle \frac{5}{7}}$ and ${\displaystyle \frac{6}{7}}$.

Answer 1

Hint: In this question we will find the decimal expansion of ${\displaystyle \frac{1}{7}}$. Then we have to find the decimal expansion of ${\displaystyle \frac{2}{7}},{\displaystyle \frac{3}{7}},{\displaystyle \frac{4}{7}},{\displaystyle \frac{5}{7}}$ and ${\displaystyle \frac{6}{7}}$but we don’t need to divide them instead we will simply multiply it with the value of ${\displaystyle \frac{1}{7}}$. For instance ${\displaystyle \frac{2}{7}}=2\left({\displaystyle \frac{1}{7}}\right)$ Here we put the value of ${\displaystyle \frac{1}{7}}$and multiply it with 2 then we will get the value of ${\displaystyle \frac{2}{7}}$. In the same way we will find the other values of the given fraction.

Complete step-by-step answer:
Decimal expansion of ${\displaystyle \frac{1}{7}}$= 0.142857
Now, we have to write the decimal expansion of ${\displaystyle \frac{2}{7}},{\displaystyle \frac{3}{7}},{\displaystyle \frac{4}{7}},{\displaystyle \frac{5}{7}}$ and ${\displaystyle \frac{6}{7}}$.
${\displaystyle \frac{2}{7}}$= $2\left({\displaystyle \frac{1}{7}}\right)=2(0.142857)=0.285714$
${\displaystyle \frac{3}{7}}$$=3\left({\displaystyle \frac{1}{7}}\right)=3(0.142857)=0.428571$
${\displaystyle \frac{4}{7}}=4\left({\displaystyle \frac{1}{7}}\right)=4(0.142857)=0.571428$
${\displaystyle \frac{5}{7}}=5\left({\displaystyle \frac{1}{7}}\right)=5(0.142857)=0.714285$
${\displaystyle \frac{6}{7}}=6\left({\displaystyle \frac{1}{7}}\right)=6(0.142857)=0.857142$

Note: A fraction represents a part of a whole. It looks easier than decimal. It has two parts that are numerator and denominator. The number which is on top is called numerator and the number in the bottom is called denominator. There are different types of fractions as follows: Proper Fraction – If a numerator is less than a denominator, then it will be a proper fraction. Improper Fraction – If a numerator is greater than denominator then it is called Improper Fraction. Mixed fraction – A fraction which consists of a whole number with a proper fraction, is called Mixed Fraction. Unit Fraction – A fraction in which the value of the numerator is 1 is called Unit Fraction. Like Fractions – Those fractions which have the same denominators, then those fractions are Like Fractions. Unlike Fractions –The Fractions with different denominators, known as Unlike Fractions.
Alternatively, we can find the decimal expression of a number by doing a simple division for each number.