2.3 X 10^-10; 3.2 X 10 ^-10; 2.3 X 10^-12; 2.3 X 10^-8
The numbers arranged in ascending order are:
2.3 x 10^-12
2.3 x 10^-10
2.3 x 10^-8
3.2 x 10^-10
To arrange the given numbers in increasing order, we need to compare the exponents first.
The exponents for the given numbers are:
-10, -10, -12, -8.
The numbers with smaller exponents will be on the left side:
2.3 X 10^-12, 2.3 X 10^-10, 2.3 X 10^-10, 2.3 X 10^-8.
Rearranging these numbers in increasing order would be:
2.3 X 10^-12, 2.3 X 10^-10, 2.3 X 10^-10, 2.3 X 10^-8.
To compare these numbers, we need to put them in order from smallest to largest.
The general rule for comparing numbers in scientific notation is to compare the powers of 10 first. If the powers are different, the number with the smaller power of 10 is the smallest. If the powers are the same, then we compare the base numbers (the numbers multiplied by the powers of 10) to determine the smaller number.
Let's go step by step:
1. 2.3 X 10^-10
2. 3.2 X 10^-10
3. 2.3 X 10^-12
4. 2.3 X 10^-8
First, let's compare the powers of 10:
-10, -10, -12, -8
We can see that the highest power of 10 is -8, so the number with -8 as the exponent will be the largest. Therefore, we can already determine that 2.3 X 10^-8 is the largest number.
Next, let's compare the remaining three numbers:
-10, -10, -12
Since they have the same power of 10, we need to compare the base numbers:
- 2.3, 3.2, 2.3
Comparing the base numbers, we can see that 2.3 is the smallest among them. Therefore, the order from smallest to largest is:
2.3 X 10^-12, 2.3 X 10^-10, 3.2 X 10^-10, 2.3 X 10^-8