Final answer:
The numbers in order from least to greatest are: 3.14 x 10⁵, 9.65 x 10⁵, 10 x 10⁶, and 1.89 x 10⁶. We considered their powers of ten, with the smallest exponent indicating the smallest number. Additionally, 10 x 10⁶ simplifies to 1 x 10⁷.
Step-by-step explanation:
To order the numbers from least to greatest, we compare their powers of ten since these are scientific notation values. The number with the smallest exponent of ten is the smallest number, and so on. We have the following numbers:
- 10 x 10⁶
- 3.14 x 10⁵
- 9.65 x 10⁵
- 1.89 x 10⁶
First, we can see that 3.14 x 10⁵ and 9.65 x 10⁵ have the same exponent, so we compare their coefficients. Here, 3.14 < 9.65, so 3.14 x 10⁵ is smaller than 9.65 x 10⁵. Next, we compare these to the numbers with exponent 10⁶, which are larger since they have a higher exponent.
Ordering these from least to greatest:
- 3.14 x 10⁵
- 9.65 x 10⁵
- 10 x 10⁶
- 1.89 x 10⁶
Keeping in mind that 10 x 10⁶ can be simplified to 1 x 10⁷, which is then clearly the largest number.