Question 15 Marks
Arrange the following decimal numbers in the ascending order:
0.52314, 0.52313, 0.53201, 0.52321
0.52314, 0.52313, 0.53201, 0.52321
Answer
View full question & 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
$=0+\frac{5}{10}+\frac{2}{100}+\frac{3}{1000}+\frac{1}{10000}+\frac{4}{100000} \ ...(1)$
$0.52313$
$=0+\frac{5}{10}+\frac{2}{100}+\frac{3}{1000}+\frac{1}{10000}+\frac{3}{100000}\ ...(2)$
$0.53201$
$=0+\frac{5}{10}+\frac{3}{100}+\frac{2}{1000}+\frac{0}{10000}+\frac{1}{100000}\ ...(3)$
$0.52321$
$=0+\frac{5}{10}+\frac{2}{100}+\frac{3}{1000}+\frac{2}{10000}+\frac{1}{100000}\ ...(4)$
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