Question

Which is greater?
(a) $0.099$ or $0.19$
(b) $1.5$ or $1.50$
(c)$1.431$ or $1.490$
(d) $3.3$ or $3.300$
(e) $5.64$ or $5.603$

Answer 1

Hint: We compare two decimal numbers by comparing the place values from left to right. First, we compare the number before the decimal point. If the digits before the decimal point are equal then we compare the digits after the decimal point.

Complete step by step solution: (a)We need to compare $0.099$and $0.19$to tell which one is greater.
On comparing the digits before the decimal point we see both are the same digits. So we will compare the digits after the decimal point.
The next digits are $0$ and $1$ whose place value is $\dfrac{1}{{10}}$ .On comparing we see that $1 > 0$ .
Hence,$0.19 > 0.099$
(b) )We need to compare $1.5$ and $1.50$ to tell which one is greater.
On comparing the digits before the decimal point we see both are the same digits. So we will compare the digits after the decimal point.
The next digits are same$\left( 5 \right)$ whose place value is $\dfrac{1}{{10}}$ . First, we should know that adding extra zeroes to the right of the last digit of decimal value does not change the value of the number. So we can write $1.5$ at $1.50$
So we see that on comparing the next digit we get,$1.50 = 1.50$
Hence, $1.50 = 1.50$
(c) We need to compare $1.431$ and $1.490$.
On comparing the digits before the decimal point we see both are the same digits$\left( 1 \right)$. So we will compare the digits after the decimal point.
The next digits are same$\left( 4 \right)$ whose place value is $\dfrac{1}{{10}}$ .We will compare the digits whose place value is $\dfrac{1}{{100}}$. We see that $9 > 3$
Hence $1.490 > 1.431$
(d)Here we are given $3.3$ and $3.300$.We can add extra zeroes on the first number to make it easier to compare as it will not change the value of the number.
So we are comparing here,$3.300$ and $3.300$
Clearly both are same numbers so we can say that both are equal.
Hence,$3.3 = 3.300$
(e)We need to compare $5.64$ and $5.603$. We can add extra zeroes on the first number to make it easier to compare as it will not change the value of the number. So we can write-$5.64 = 5.640$
On comparing the digits before the decimal point we see both are the same digits$\left( 5 \right)$. So we will compare the digits after the decimal point.
The next digits are same$\left( 6 \right)$ whose place value is $\dfrac{1}{{10}}$ .We will compare the digits whose place value is $\dfrac{1}{{100}}$. We see that $4 > 0$ .
Hence, $5.64 > 5.603$

Note: Note: When we are comparing the decimal numbers we follow the following rules-
1) Compare the digits from left to right and first compare the digits before the decimal point. If they are great than or less than then the number will also e greater than or less than. But if they are equal then compare the tenths place. If they are also equal then compare the hundredths place digit. Keep on moving to the right until you can find which one is greater or until it is proved that they are equal.
2) Adding extra zeroes to the right of the last digit of a decimal number does not change its value.