Question

Arrange them in increasing order! \[{10^{ - 13}},{10^{ - 12}},2.4 \times {10^{ - 14}},4 \times {10^{ - 9}}\] .

Answer 1

Hint: In this problem, we have to arrange the given numbers in increasing order. Increasing order is the numbers are said to be in ascending order when they are arranged from the smallest number to the largest number. We need to compare the values and then order it in the ascending order.

Complete step-by-step answer:
In the given problem,
 \[{10^{ - 13}},{10^{ - 12}},2.4 \times {10^{ - 14}},4 \times {10^{ - 9}}\]
In this given list of numbers, first we have to find the value of all and then compare with one another to arrange them in increasing order.
By finding the values of the following numbers, we get
 \[
  {10^{ - 13}} = 0.0000000000001 \\
  {10^{ - 12}} = 0.000000000001 \\
  2.4 \times {10^{ - 14}} = 2.4 \times 0.00000000000001 = 2400000000000 \\
  4 \times {10^{ - 9}} = 4 \times 0.000000001 = 4000000000 \;
 \]
By arranging them in lower order to higher by comparing one another, we get
 \[0.0000000000001,0.000000000001,4000000000,2400000000000\]
Therefore, the increasing order of the numbers are \[0.0000000000001,0.000000000001,4000000000,2400000000000\] and will be represented as follows, \[{10^{ - 13}} < {10^{ - 12}} < 4 \times {10^{ - 9}} < 2.4 \times {10^{ - 14}}\]
So, the correct answer is “ \[{10^{ - 13}} < {10^{ - 12}} < 4 \times {10^{ - 9}} < 2.4 \times {10^{ - 14}}\] ”.

Note: In this problem, we have to arrange the numbers in the ascending order, first, we need to compare the values and then order it in the ascending order. The procedure to arrange the numbers in the smallest order to the largest order is as follows:
Step 1: The first and foremost step is to count the number of digits in the number. The number with the least number of digits is the smallest number. If the list has more numbers with the least digit, then compare the values and write down the smallest number.
Step 2: Write down the smallest number first, and then compare with all the remaining numbers with the same number of digits.
Step 3: Continue the comparison of numbers with the next level of digits, and write down the numbers in the ascending order till all the numbers are arranged in the form of ascending order.