The Correct Answer and Explanation is:
Based on the task of ordering the provided decimal numbers from least to greatest, here is the correct answer:
1.a: a. 0.000000001
2.a: b. 0.000000009
3.a: c. 0.000000038
4.a: d. 0.000000080
5.a: e. 0.000000085
6.a: f. 0.00000049
7.a: g. 0.0000005
8.a: h. 0.0000009
9.a: i. 0.00000099
The task shown in the image requires ordering a series of nine very small decimal numbers from the smallest to the largest value. To accomplish this, we must use a systematic method for comparing decimal numbers.
The most effective strategy is to first examine the number of zeros that appear immediately after the decimal point before the first non-zero digit. A number with more leading zeros is inherently smaller. In this list, we have numbers with eight, seven, and six leading zeros. The numbers with eight zeros will be the smallest, followed by those with seven, and then those with six.
First, we compare the numbers with eight leading zeros: 0.000000001 (a) and 0.000000009 (b). Since 1 is less than 9, 0.000000001 is the smallest number overall, and 0.000000009 is the second smallest.
Next, we look at the numbers with seven leading zeros: 0.000000038 (c), 0.000000080 (d), and 0.000000085 (e). We compare them based on the digits that follow the zeros. Since 38 is less than 80, and 80 is less than 85, their order is c, d, then e. These are the third, fourth, and fifth smallest numbers.
Finally, we order the numbers with six leading zeros: 0.00000049 (f), 0.0000005 (g), 0.0000009 (h), and 0.00000099 (i). Comparing the significant figures, 49 is less than 50 (for 0.5), which is less than 90 (for 0.9), which is less than 99. Therefore, their correct order is f, g, h, and i.
This establishes the complete sequence from least to greatest. It is important to note that the entry shown in the image, placing option ‘c’ in the ‘6.a’ position, is incorrect, as 0.000000038 is the third smallest value, not the sixth.
