Question
Arrange in ascending order: $0.011, 1.001, 0.101, 0.110.$
✓
Answer
Given numbers are $0.011, 1.001, 0.101$ and $0.110.$
$\therefore0.011=0+\frac{0}{10}+\frac{1}{100}+\frac{1}{1000}$
$1.001=1+\frac{0}{10}+\frac{0}{100}+\frac{1}{1000}$
$0.101=0+\frac{1}{10}+\frac{0}{100}+\frac{1}{1000}$
$0.110=0+\frac{1}{10}+\frac{1}{100}+\frac{0}{1000}$
Here, the whole number part of $1.001$ is greater than $0.011, 0.101$ and $0.110.$
Now, tenths part of $0.101=\frac{1}{10}$
And tenths part of $0.110=\frac{1}{10}$
$\therefore 0.011<0.101$ and $0.011<0.110$
Again, hundredths parts of $0.101=\frac{1}{100}$
And hundredths parts of $0.110=\frac{1}{100}$
$\therefore 0.101<0.110$
Hence, the ascending order of given numbers are $0.011<0.101<0.110<1.001$
$\therefore0.011=0+\frac{0}{10}+\frac{1}{100}+\frac{1}{1000}$
$1.001=1+\frac{0}{10}+\frac{0}{100}+\frac{1}{1000}$
$0.101=0+\frac{1}{10}+\frac{0}{100}+\frac{1}{1000}$
$0.110=0+\frac{1}{10}+\frac{1}{100}+\frac{0}{1000}$
Here, the whole number part of $1.001$ is greater than $0.011, 0.101$ and $0.110.$
Now, tenths part of $0.101=\frac{1}{10}$
And tenths part of $0.110=\frac{1}{10}$
$\therefore 0.011<0.101$ and $0.011<0.110$
Again, hundredths parts of $0.101=\frac{1}{100}$
And hundredths parts of $0.110=\frac{1}{100}$
$\therefore 0.101<0.110$
Hence, the ascending order of given numbers are $0.011<0.101<0.110<1.001$
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