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Need fast!!!

Fill in the table with the corresponding value of each of the powers of 10. (Hint: Start with values you know, such as 101 and 102. Use your knowledge of exponents to calculate the other values.)

Need fast!!! Fill in the table with the corresponding value of each of the powers-example-1
User MuffinTheMan
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2 Answers

14 votes
14 votes
10^-3= 1/1000
10^-2= 1/100
10^-1= 1/10
10^1= 10
10^2= 100
10^3= 1000
10^4= 10000
10^5= 100000
User Cerniuk
by
3.1k points
26 votes
26 votes

Answer:

Question 1 Part a = 100 = 10 • 10 = 10^2

part b = 1,000 = 10 • 10 • 10 = 10^3

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 10^2. So, 100 times 100 can be written as an expression:

100 • 100

10^2 • 10^2.

part c = The following was found in the previous task:

100 • 100 = 10,000 = 10^4.

This equation is true:

100 • 100 = 10^2 • 10^2.

The fact that 100 • 100 equals both expressions means that this equation is also true:

10^2 • 10^2 = 10^4.

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:

The one in bold is your answer

All sample answers :)

User Racerror
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