Question

How do you write these numbers from least to greatest: 0.63, 0.6, 0.633, 0.603, 0.06?

Answer 1

Hint: We will write all the given numbers by expanding their decimal form to required number of places i.e. to that place where the number is already given. Then we compare all the decimal numbers accordingly. Write the numbers in increasing order of the numbers i.e. from least to greatest.
* A group of numbers is said to be in an increasing order if the successor (or the next term) is always greater than the previous term.

Complete step-by-step answer:
We are given 5 numbers: 0.63, 0.6, 0.633, 0.603 and 0.06
We see that the number 0.633 and 0.603 are the numbers having the decimal expansion up to three decimal places; 0.06, 0.63 are the numbers with decimal expansion up to two decimal places and 0.6 is the number with decimal expansion up to one decimal place.
Since they all have different decimal expansions, so we cannot compare them.
We will write all the numbers having decimal expansion up to same number of places i.e. three in this case as it is the highest number of place up to which a number is expanded.
We are already given 0.633 and 0.603 up to three decimal places,
We can write 0.63 as 0.630; 0.6 as 0.600; 0.06 as 0.060
Now we have same number of digits after the decimal place, so we can compare them easily.
We write the numbers: 0.630, 0.600, 0.633, 0.603 and 0.060 in increasing order
 \[0.06 < 0.600 < 0.603 < 0.630 < 0.633\]
So, we substitute the values of numbers back to original numbers in the order.
\[0.06 < 0.6 < 0.603 < 0.63 < 0.633\]
\[\therefore \]The numbers 0.63, 0.6, 0.633, 0.603, 0.06 arranged in order from least to greatest is written as

\[0.06 < 0.6 < 0.603 < 0.63 < 0.633\]

Note:
Many students make the mistake of writing the numbers in order wrong as they think more the digits after the decimal place means more the number is smaller, but keep in mind we can expand the decimal part by fixing required numbers of zeroes.