Answer:
See below.
Step-by-step explanation:
Part A)
She needs to compare by division the following two numbers:
8 × 10^-6 and 4 × 10^-5
If she divides the whole parts and then divides the powers of ten, she must do both divisions in the same order.
That means either
a) divide 8 by 4, and then divide 10^-6 by 10^-5
or
b) divide 4 by 8, and then divide 10^-5 by 10^-6
Doing a), you get
8/4 = 2
10^-6 / 10^-5 = 0.1
Multiply the parts: 2 × 0.1 = 0.2
Doing b), you get
4/8 = 0.5
10^-5 / 10^-6 = 10
Multiply the parts: 0.5 × 10 = 5
Conclusion:
The smaller number, 8 × 10^-6, is 0.2 of the larger number, 4 × 10^-5,
or, stated differently,
the larger number, 4 × 10^-5, is 5 times the smaller number, 8 × 10^-6
Let's see what she did.
She divided 8 by 4.
Then she divided 10^-5 by 10^-6. This is a mistake because she reversed the order of the powers of 10 before dividing.
Let's look at the choices:
Choice d) is correct because it has both divisions in the same order and comes to the correct conclusion that the larger number is 5 times greater than the smaller number.
Answer: d)
Part B)
8 × 10^-6 = 0.000008
4 × 10^-5 = 0.00004
Larger number: 4 × 10^-5
