Question 15 Marks

Arrange the following decimal numbers in the ascending order: $0.52314, 0.52313, 0.53201, 0.52321$

Answer

$0.52314$
$=0+\frac{5}{10}+\frac{2}{100}+\frac{3}{1000}+\frac{1}{10000}+\frac{4}{100000} \ ...(1)$
$0.52313$
$=0+\frac{5}{10}+\frac{2}{100}+\frac{3}{1000}+\frac{1}{10000}+\frac{3}{100000}\ ...(2)$
$0.53201$
$=0+\frac{5}{10}+\frac{3}{100}+\frac{2}{1000}+\frac{0}{10000}+\frac{1}{100000}\ ...(3)$
$0.52321$
$=0+\frac{5}{10}+\frac{2}{100}+\frac{3}{1000}+\frac{2}{10000}+\frac{1}{100000}\ ...(4)$
Here, the hundredth part of $0.53201$ is greater than all others.
So, the greatest number is $0.53201.$
Now, in numbers $0.52314, 0.52313$ and $0.52321,$
they all have same parts upto thousandth.
But the ten thousandths part of $0.52321$ is greater than the other two.
Now, in numbers $0.52314$ and $0.52313,$
they all have same parts upto ten thousandth.
But the hundred thousandths part of $0.52314$ is greater than that of $0.52313.$
Hence, $0.52313 < 0.52314 < 0.52321 < 0.53201$

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