Answer :
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.
### 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.
