Help!!! I am not sure if I am doing the math problems correct.?

Question

a. Rewrite the expression in standard notation:
9.7 x 10^2 = 970 ( is this right ??)

b. (6.8 x 10^3) x (4.54 x 10^6) ( I really don't understand this one)
c (2.0 x 10^-1) x (8.5 x 10^5)

Please explain, so I can understand :o)

Answer 1

You did a. absolutely correctly.

As for b and c, all you do is multiply. Because of the commutative property, you can rearrange the numbers you're multiplying.

b) 6.8 x 10^3 x 4.54 x 10^6 = 6.8 x 4.54 x 10^3 x 10^6
Remember that when you multiply numbers with exponents that have the same base, you keep the same base and add the exponent. 10^3 * 10^6 = 10^(3 + 6) = 10^9
6.8 x 4.54 = 30.872
So you have 30.872 x 10^9. This is not in scientific notation, since 30 > 10. You want to change it to 3.0872 x 10^10.

c) Same thing.
2.0 x 10^-1 x 8.5 x 10^5
= 2.0 x 8.5 x 10^-1 x 10^5
= 17.0 x 10^(-1 + 5)
= 17.0 x 10^4
= 1.7 x 10^5

Answer 2

a Yes, 9.7 x 10^2 is correct. Standard notation is one digit to the left of the decimal point The remainder of digits to the right of the decimal point. followed by an "*" or a lowercase "x". which is followed by the number 10. which is then followed by the exponent needed to raise ten to the appropriate power.

b. multiply 6.8 times 4.54. The result is larger than 10 so you must move the decimal point one place to the left to achieve standard notation. That gives you something times 10^1.
Then we need to take into account the powers of ten in the original problem as well as the one just created.
Combining 10^3, 10^6 and 10^1 becomes 10^10

your answer will therefore be something x 10^10

c. work this just like b.

Answer 3

Im gonna give you the answers first
A. is right
B. 6800 x 4540000 = 308720000000 = 3.08 x 10^11
C. .2 x 850000 = 170000 = 1.7 x 10^5

This is scientific notation and to do this look at the number after the ten. In problem B the first parenthesis is (6.8 x 10^3) to do this move the decimal three places to the right 6.8 becomes 6800. Now do the same thing to the other side (4.54 x 10^6) move the decimal 6 places to the right. It becomes 4540000. Multiply the two numbers it becomes 308720000000 now put it back into scientific notation. Move the decimal place to the left until u get to the first number and count spots. there are 12 spots so it is 3.08 x 10^12. to determine how many spaces u go look at the porblem which ever one has more decimal places is how many you go 4.54 = 2 decimal place 6.8 = 1 decimal places. 2>1 so it has 2 decimal places and you get the answer of 3.08 x 10^12.
the final answer C. negitive means move to the left. 2 x 10^-1 becomes .2. Do the same thing in problem B to 8.5 x 10^5. you get 850000. to get the answer multiply t he two 85000 x .2 = 170000

Answer 4

a. 9.7 x 10^2
9.7 x 100
970 correct

b. (6.8x10^3) x (4.54 x 10^6)
(6.8 x 1000)x (4.54 x 1000000)
6800x 4540000
30872000000

c (2.0 x 10^-1) x (8.5 x 10^5
(2.0 x -10) x (8.5 x 100000)
-20 x 850000
-17000000

Answer 5

a is correct

For b, you can simply multiply the two values together and add the exponents of 10.

(6.8 x 10^3) x (4.54 x 10^6)
30.872 x 10^9
3.0872 x 10^10

And the same thing for c

Answer 6

Standard form is a number from 1 to just under 10 multiplied by a power of ten. That means that in the first example you started with the standard form and converted it to a number written in the ordinary way and correctly.
To do the others, multiply the first part of each with a calculator and add the powers of ten. Remember that if the first part comes to 10 or more you must take out another power of ten.

Answer 7

a.) Correct

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b.)
(6.8 * 10^3)(4.54 * 10^6)
(6.8 * 4.54)(10^(3 + 6))
30.872 * 10^9
(3.0872 * 10^1) * 10^9
3.0872 * 10^(1 + 9)
3.0872 * 10^10
Standard Notation = 30,872,000,000

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c.)
(2.0 * 10^-1)(8.5 * 10^5)
(2 * 8.5) * 10^(-1 + 5)
17 * 10^4
(1.7 * 10^1) * 10^4
1.7 * 10^(1 + 4)
1.7 * 10^5
Standard Notation = 170,000

Answer 8

a.9.7*10^2 is in scientificnotation.in expanded form it will be 970

b.6.8*4.54*10^9
=30.872*10^9
=3.0872*10^10 or in expanded form 30872000000

c.2.0*8.5*10^4
=1.7^10^5 or in expanded form 170000

Answer 9

a. This is correct. 970 is 9.7 times 10^2 (100).