Question

Which one of the following is greater:
$(1)$$$5.0$$\left( 2 \right)$$$$0.5$$\left( 3 \right)$$0.005$$\left( 4 \right)$$0.05$$

Answer 1

Hint : We have to find which of the following is greater . We solve this by decimal concept and by making the denominator equal for each value by removing the decimal points and simultaneously multiplying the numerator by for each decimal value removed . Then comparing the numerator we find the greater number .

Complete step-by-step answer :
Given : $4$decimal values5.0$$$$,{\text{ }}0.5{\text{ }},{\text{ }}0.005{\text{ }},{\text{ }}0.05
Let us consider that
a$$$$ = {\text{ }}5.0
b$$$$ = {\text{ }}0.5
c$$$$ = {\text{ }}0.005
d$$$$ = {\text{ }}0.05
Now , removing the decimal of a{\text{ }},$$$$b{\text{ }}, c,$$$$d and obtaining fractional values
To convert the decimal values to fractional values, we can count the number of values after the decimal point. The number of values upto a non-zero number after the decimal point is equal to the number of zeros to be added in the denominator of the fractional value
Then ,
a{\text{ }} = $$$$\;\left( {\dfrac{{50}}{{10}}} \right)
$b{\text{ }} =$ $\left( {\dfrac{5}{{10}}} \right)$
$c{\text{ }} =$ $\left( {\dfrac{5}{{1000}}} \right)$
$d{\text{ }} =$ $\left( {\dfrac{5}{{100}}} \right)$
As we have $1000$ in the denominator of $c$ we will make value of denominator $= {\text{ }}1000$ in $a{\text{ }},{\text{ }}b$ and $d$
Now , taking L.C.M. and making the denominators of a{\text{ }},$$$$b{\text{ }}, $c{\text{ }},{\text{ }}d$ equal , we get
$a{\text{ }} =$ $\left( {\dfrac{{50}}{{10}}{\text{ }}} \right){\text{ }} \times {\text{ }}\left( {\dfrac{{100}}{{100}}{\text{ }}} \right)$
Then ,
$a{\text{ }} =$ $\left( {\dfrac{{5000}}{{1000}}} \right)$
Similarly for $b$and $d$
$b{\text{ }} =$ $\left( {\dfrac{5}{{10}}} \right){\text{ }} \times {\text{ }}\left( {\dfrac{{100}}{{100}}} \right)$
Then ,
$b{\text{ }} =$ $\left( {\dfrac{{500}}{{1000}}} \right)$
$d{\text{ }} =$ $\left( {\dfrac{5}{{100}}} \right){\text{ }} \times {\text{ }}\left( {\dfrac{{10}}{{10}}} \right)$
Then ,
$d{\text{ }} =$ $\left( {\dfrac{{50}}{{1000}}} \right)$
Now comparing the values ,
( As the denominator for each value is equal the greatest number can be calculated by the number which has the greatest value in the numerator )
The numerators of $a{\text{ }},{\text{ }}b{\text{ }},{\text{ }}c$ and $d$ are 5000{\text{ }},{\text{ }}500$$$$,{\text{ }}5{\text{ }},{\text{ }}50 respectively .
( As 5000{\text{ }} > $$$$500{\text{ }} > $$$$50{\text{ }} > {\text{ }}5)
a{\text{ }} > {\text{ }}b$$$$ > {\text{ }}d $> {\text{ }}c$
Hence , $a$ has the greatest value
Thus , the correct option is $\left( 1 \right)$
So, the correct answer is “Option 1”.

Note: Any number can be represented in the form of a decimal number . Also , any decimal number can be represented in the form of fraction by just removing the decimal points , decimal points are always reduced from the left side to the right of the decimal point
For an example 5.005{\text{ }} = $$$$\left( {\dfrac{{50.05}}{{10}}} \right){\text{ }} = \left( {\dfrac{{500.5}}{{100}}} \right){\text{ }} = $$$$\left( {\dfrac{{5005}}{{1000}}} \right)