Question

Arrange the following in increasing order:
2.5, 2.05, 2.505, 2.5005

• A. 2.5 < 2.505 < 2.05 < 2.5005
• B. 2.05 < 2.5 < 2.5005 < 2.505
• C. 2.5 < 2.05 < 2.505 < 2.5005
• D. 2.5005 < 2.5 < 2.05 < 2.505

Answer 1

The correct option is B 2.05 < 2.5 < 2.5005 < 2.505

According to their places on the number line,
2 is at one place left of decimal to every number i.e., at units place.

Then one place to the right of the decimal (i.e., tenths place) we have 5, 0, 5, 5 so 0 will be the smallest i.e., 2.05

In the rest of the three numbers, we will see two places right to the decimal (i.e, hundredths place), we have 0 in 2.5, 0 in 2.505 and 0 in 2.5005. So we can not compare using digits at hundredths place.

Now we will go for 3rd place to the right of the decimal (i.e., thousandths place) we have 0 in 2.5, 5 in 2.505 and 0 in 2.5005. So 2.505 will be the greatest.

Now, we will go for 4th place to the right of the decimal to compare the rest of the two numbers we have 0 in 2.5, 5 in 2.5005. So 2.5005 will be greater than 2.5.
i.e., we have
2.05 < 2.5 < 2.5005 < 2.505