Answered

Find trusted answers to your questions with the help of IDNLearn.com's knowledgeable community. Ask any question and receive comprehensive, well-informed responses from our dedicated team of experts.

Carry out the operations indicated on the following exponential numbers:

a. [tex][tex]$3.24 \times 10^3 + 2.40 \times 10^3$[/tex][/tex]

b. [tex][tex]$4.76 \times 10^2 + 7.7 \times 10^1$[/tex][/tex]

c. [tex][tex]$6.75 \times 10^3 - 1.74 \times 10^3$[/tex][/tex]

d. [tex][tex]$3.74 \times 10^5 - 2 \times 10^3$[/tex][/tex]

Sagot :

GinnyAnsweridn
Certainly! Let's carefully perform each of the given operations that involve exponential numbers.

### Part (a): [tex]\( 3.24 \times 10^3 + 2.40 \times 10^3 \)[/tex]

1. Notice that both terms are in the form [tex]\( a \times 10^3 \)[/tex].
2. Adding these together involves adding the coefficients (3.24 and 2.40).
3. Therefore:
[tex]\[ 3.24 \times 10^3 + 2.40 \times 10^3 = (3.24 + 2.40) \times 10^3 = 5.64 \times 10^3 \][/tex]
4. Converting this into a standard number gives:
[tex]\[ 5.64 \times 10^3 = 5640.0 \][/tex]

### Part (b): [tex]\( 4.76 \times 10^2 + 7.7 \times 10^1 \)[/tex]

1. Express [tex]\( 7.7 \times 10^1 \)[/tex] in terms of [tex]\( 10^2 \)[/tex]:
[tex]\[ 7.7 \times 10^1 = 0.77 \times 10^2 \][/tex]
2. Now, add the coefficients (4.76 and 0.77):
[tex]\[ 4.76 \times 10^2 + 0.77 \times 10^2 = (4.76 + 0.77) \times 10^2 = 5.53 \times 10^2 \][/tex]
3. Converting this into a standard number gives:
[tex]\[ 5.53 \times 10^2 = 553.0 \][/tex]

### Part (c): [tex]\( 6.75 \times 10^3 - 1.74 \times 10^3 \)[/tex]

1. Both terms are in the form [tex]\( a \times 10^3 \)[/tex].
2. Subtracting these involves subtracting the coefficients (6.75 and 1.74):
[tex]\[ 6.75 \times 10^3 - 1.74 \times 10^3 = (6.75 - 1.74) \times 10^3 = 5.01 \times 10^3 \][/tex]
3. Converting this into a standard number gives:
[tex]\[ 5.01 \times 10^3 = 5010.0 \][/tex]

### Part (d): [tex]\( 3.74 \times 10^5 - 2 \times 10^3 \)[/tex]

1. First, express [tex]\( 2 \times 10^3 \)[/tex] in terms of [tex]\( 10^5 \)[/tex]:
[tex]\[ 2 \times 10^3 = 0.02 \times 10^5 \][/tex]
2. Now, subtract the coefficients (3.74 and 0.02):
[tex]\[ 3.74 \times 10^5 - 0.02 \times 10^5 = (3.74 - 0.02) \times 10^5 = 3.72 \times 10^5 \][/tex]
3. Converting this into a standard number gives:
[tex]\[ 3.72 \times 10^5 = 372000.0 \][/tex]

### Summary of Solutions:

a. [tex]\( 3.24 \times 10^3 + 2.40 \times 10^3 = 5640.0 \)[/tex]

b. [tex]\( 4.76 \times 10^2 + 7.7 \times 10^1 = 553.0 \)[/tex]

c. [tex]\( 6.75 \times 10^3 - 1.74 \times 10^3 = 5010.0 \)[/tex]

d. [tex]\( 3.74 \times 10^5 - 2 \times 10^3 = 372000.0 \)[/tex]

These are the results for the given operations.
Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. Thank you for visiting IDNLearn.com. For reliable answers to all your questions, please visit us again soon.