Answer:
Question 1 Part a = 100 = 10 • 10 = 102
part b = 1,000 = 10 • 10 • 10 = 103
part c = Exponent of 10 Value
10^-3 0.001
10^-2 0.01
10^-1 0.1
10^1 10
10^2 100
10^3 1,000
10^4 10,000
10^5 100,000
part d = The value of 10^-3 is 0.001 , and the value of 10^-2 is 0.01. With an increase of 1 in the power value, the answer increases 10 times. To get 10^0 , increase the power of 10^-1 by 1. So, its value should be 10 times that of 10^-1, which is 0.1 x 10 = 1. The value of 10^0 is 1.
Similarly, working up the table from the bottom row, from 10^5 to 10^4 to 10^3 and so on, there is a definite pattern in the answers. As the power drops by 1, the answer is 1/10 times the previous value.
The value of 10^2 is 100 , and the value of 10^1 is 10 . So, for 10^0, the answer will be 10 x 1.10, or 1 , which is the same answer found when working downward through the numbers in the table.
Question 2 part a = Using standard multiplication, 100 • 100 equals 10,000. According to the table in question 1, part C, 10,000 equals 10 to the power of 4.
part b = According to the table, 100 equals the exponential expression 102. So, 100 times 100 can be written as an expression:
100 • 100
102 • 102.
part c = The following was found in the previous task:
100 • 100 = 10,000 = 104.
This equation is true:
100 • 100 = 102 • 102.
The fact that 100 • 100 equals both expressions means that this equation is also true:
102 • 102 = 104.
In this particular example, you can obtain the power of 4 (on base 10) by adding the two powers, 2 and 2, or by multiplying them.
Question 3 part a = 100,000 x 1/100,000 = 100,000/100,000 = 1 = 10^0
Using the standard method of multiplication, 100,000 times 1/100,000 is 1. 1 can be represented as a power of 10 by writing it as 10^0.
part b = 100,000 = 10^5, and 1/100,000 = 1/10^5 = 10^-5
So, 100,000 x 1/100,000 = 10^5 x 10^-5
You can represent 100,000 x 1/100,000 in exponential form as 10^5 x 10^-5 .
part c = In part A of this question, using the standard method of multiplication showed that 100,000 x 1/100,000 = 10^0.
In part B, the equivalent exponential expression was 100,000 x 1/100,000 = 10^5 x 10^-5.
Adding the exponents gives 10^5 + (^-5) = 10^0 = 1, which is the same answer found in part A of this question. However, multiplying the exponents gives 10^5 + (^-5) = 10^25 which is not the answer found in part A. So, adding the exponents will give the correct answer but multiplying the exponents will not.
part d = Because both terms have the same base, 10, adding the powers will give the correct equivalent expression: 10a • 10b = 10(a+b).
Explanation:
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