Question

Which one of the following is greater?
1.23 or 1.2

Answer 1

Hint: Subtract the second number from the first number. If the result of the subtraction is greater than 0 then the first one is greater than the second one. Otherwise the second one is greater than the first one.

Complete step-by-step answer:
Here in this problem we have to compare two numbers 1.23 and 1.2
We have to find out which one is greater.

We can see that both the numbers are decimal numbers. A decimal number can be defined as a number whose whole number part and the fractional part are separated by a decimal point. The dot in a decimal number is called a decimal point. The digits after the decimal point show a value smaller than one.
For example, if we take the first number 1.23, 1 is the whole number part. After the decimal point we have 23, this is our fractional part. We can write 1.23 as:
$1.23=1+0.23=1+\dfrac{23}{100}$
So basically, $0.23=\dfrac{23}{100}$
Now the second number is 1.2
The whole number part is 1 and the decimal number part or we can say the fractional part is:
$0.2=\dfrac{2}{10}$
Again we can write $\dfrac{2}{10}$ as $\dfrac{2}{10}=\dfrac{2\times 10}{10\times
10}=\dfrac{20}{100}=0.20$
Basically we can put or drop zeros at the end of the decimal part. The number remains the same.
Now let’s subtract the two numbers:
$1.23-1.20=0.03$
So, 0.03 is greater than zero. We can say:
$\begin{align}
& 1.23-1.2>0 \\
& \Rightarrow 1.23>1.2 \\
\end{align}$
Hence, 1.23 is greater than 1.2.

Note: Alternatively we can compare the numbers using fractions.
$\dfrac{1.23}{1.2}=\dfrac{123\times 10}{12\times 100}=\dfrac{123}{120}$
Now, $\dfrac{123}{120}>1$
The numerator is bigger than the denominator. Therefore,
$\begin{align}
& \dfrac{1.23}{1.2}>1 \\
& \Rightarrow 1.23>1.2 \\
\end{align}$
Hence, 1.23 is greater than 1.2.