Ordering numbers in standard form

Numbers written in standard form can be ordered by first looking at the power of 10, which tells you the size of the numbers. If two or more numbers have the same power of 10, use the first part of the number to decide the order.

Example

Write these numbers in ascending order:

7 \times 10^{-2}, 3.2 \times 10^2,  4.1 \times 10^4, 3.81 \times 10^{-5}, 5.6 \times 10^3, 2 \times 10^4

The numbers 4.1 \times 10^4 and 2 \times 10^4 have the same power of 10, so looking at the number at the front, we can see that 2 \times 10^4 is less than 4.1 \times 10^4.

Using the powers of 10 we can write the other numbers in order, smallest to biggest:

3.81 \times 10^{-5}, 7 \times 10^{-2}, 3.2 \times 10^2, 5.6 \times 10^3, 2 \times 10^4, 4.1 \times 10^4

Question

Write these numbers in ascending order:

6.3 \times 10^{-4}, 8.2 \times 10^5, 7.1 \times 10^{-2}, 9.01 \times 10^2, 7 \times 10^3, 6.4 \times 10^2

9.01 \times 10^2 and 6.4 \times 10^2 have the same power of 10, so looking at the number at the front, we can see that 6.4 \times 10^2 is less than 9.01 \times 10^2.

Using the powers of 10 we can write the other numbers in order, smallest to biggest:

6.3 \times 10^{-4}, 7.1 \times 10^{-2}, 6.4 \times 10^2, 9.01 \times 10^2, 7 \times 10^3, 8.2 \times 10^5