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Sagot :
Sure, let's break down and simplify each expression step-by-step.
### a) [tex]\(2.6 \times 10^3 + 1.8 \times 10^3\)[/tex]:
1. Convert each term to standard form:
[tex]\(2.6 \times 10^3 = 2600\)[/tex]
[tex]\(1.8 \times 10^3 = 1800\)[/tex]
2. Add the numbers:
[tex]\(2600 + 1800 = 4400\)[/tex]
So the result for (a) is [tex]\(4400\)[/tex].
### b) [tex]\(3.5 \times 10^4 + 5.7 \times 10^4\)[/tex]:
1. Convert each term to standard form:
[tex]\(3.5 \times 10^4 = 35000\)[/tex]
[tex]\(5.7 \times 10^4 = 57000\)[/tex]
2. Add the numbers:
[tex]\(35000 + 57000 = 92000\)[/tex]
So the result for (b) is [tex]\(92000\)[/tex].
### c) [tex]\(4.3 \times 10^5 + 6.7 \times 10^5\)[/tex]:
1. Convert each term to standard form:
[tex]\(4.3 \times 10^5 = 430000\)[/tex]
[tex]\(6.7 \times 10^5 = 670000\)[/tex]
2. Add the numbers:
[tex]\(430000 + 670000 = 1100000\)[/tex]
So the result for (c) is [tex]\(1100000\)[/tex].
### d) [tex]\(6.4 \times 10^9 + 9.7 \times 10^{\circ}\)[/tex]:
Here, the term [tex]\(10^{\circ}\)[/tex] should be interpreted as [tex]\(10^0 = 1\)[/tex], so:
1. Convert each term to standard form:
[tex]\(6.4 \times 10^9 = 6400000000\)[/tex]
[tex]\(9.7 \times 10^0 = 9.7\)[/tex]
2. Add the numbers:
[tex]\(6400000000 + 9.7 = 6400000009.7\)[/tex]
So the result for (d) is [tex]\(6400000009.7\)[/tex].
### e) [tex]\(3.4 \times 10^2 + 2.6 \times 10^3\)[/tex]:
1. Convert each term to standard form:
[tex]\(3.4 \times 10^2 = 340\)[/tex]
[tex]\(2.6 \times 10^3 = 2600\)[/tex]
2. Add the numbers:
[tex]\(340 + 2600 = 2940\)[/tex]
So the result for (e) is [tex]\(2940\)[/tex].
### f) [tex]\(2 \times 10^3 + 4 \times 10^2\)[/tex]:
1. Convert each term to standard form:
[tex]\(2 \times 10^3 = 2000\)[/tex]
[tex]\(4 \times 10^2 = 400\)[/tex]
2. Add the numbers:
[tex]\(2000 + 400 = 2400\)[/tex]
So the result for (f) is [tex]\(2400\)[/tex].
### g) [tex]\(6 \times 10^5 + 3 \times 10^4\)[/tex]:
1. Convert each term to standard form:
[tex]\(6 \times 10^5 = 600000\)[/tex]
[tex]\(3 \times 10^4 = 30000\)[/tex]
2. Add the numbers:
[tex]\(600000 + 30000 = 630000\)[/tex]
So the result for (g) is [tex]\(630000\)[/tex].
### h) [tex]\(1.5 \times 10^7 - 9.5 \times 10^5\)[/tex]:
1. Convert each term to standard form:
[tex]\(1.5 \times 10^7 = 15000000\)[/tex]
[tex]\(9.5 \times 10^5 = 950000\)[/tex]
2. Subtract the numbers:
[tex]\(15000000 - 950000 = 14050000\)[/tex]
So the result for (h) is [tex]\(14050000\)[/tex].
Thus, the final results are:
a) 4400
b) 92000
c) 1100000
d) 6400000009.7
e) 2940
f) 2400
g) 630000
h) 14050000
### a) [tex]\(2.6 \times 10^3 + 1.8 \times 10^3\)[/tex]:
1. Convert each term to standard form:
[tex]\(2.6 \times 10^3 = 2600\)[/tex]
[tex]\(1.8 \times 10^3 = 1800\)[/tex]
2. Add the numbers:
[tex]\(2600 + 1800 = 4400\)[/tex]
So the result for (a) is [tex]\(4400\)[/tex].
### b) [tex]\(3.5 \times 10^4 + 5.7 \times 10^4\)[/tex]:
1. Convert each term to standard form:
[tex]\(3.5 \times 10^4 = 35000\)[/tex]
[tex]\(5.7 \times 10^4 = 57000\)[/tex]
2. Add the numbers:
[tex]\(35000 + 57000 = 92000\)[/tex]
So the result for (b) is [tex]\(92000\)[/tex].
### c) [tex]\(4.3 \times 10^5 + 6.7 \times 10^5\)[/tex]:
1. Convert each term to standard form:
[tex]\(4.3 \times 10^5 = 430000\)[/tex]
[tex]\(6.7 \times 10^5 = 670000\)[/tex]
2. Add the numbers:
[tex]\(430000 + 670000 = 1100000\)[/tex]
So the result for (c) is [tex]\(1100000\)[/tex].
### d) [tex]\(6.4 \times 10^9 + 9.7 \times 10^{\circ}\)[/tex]:
Here, the term [tex]\(10^{\circ}\)[/tex] should be interpreted as [tex]\(10^0 = 1\)[/tex], so:
1. Convert each term to standard form:
[tex]\(6.4 \times 10^9 = 6400000000\)[/tex]
[tex]\(9.7 \times 10^0 = 9.7\)[/tex]
2. Add the numbers:
[tex]\(6400000000 + 9.7 = 6400000009.7\)[/tex]
So the result for (d) is [tex]\(6400000009.7\)[/tex].
### e) [tex]\(3.4 \times 10^2 + 2.6 \times 10^3\)[/tex]:
1. Convert each term to standard form:
[tex]\(3.4 \times 10^2 = 340\)[/tex]
[tex]\(2.6 \times 10^3 = 2600\)[/tex]
2. Add the numbers:
[tex]\(340 + 2600 = 2940\)[/tex]
So the result for (e) is [tex]\(2940\)[/tex].
### f) [tex]\(2 \times 10^3 + 4 \times 10^2\)[/tex]:
1. Convert each term to standard form:
[tex]\(2 \times 10^3 = 2000\)[/tex]
[tex]\(4 \times 10^2 = 400\)[/tex]
2. Add the numbers:
[tex]\(2000 + 400 = 2400\)[/tex]
So the result for (f) is [tex]\(2400\)[/tex].
### g) [tex]\(6 \times 10^5 + 3 \times 10^4\)[/tex]:
1. Convert each term to standard form:
[tex]\(6 \times 10^5 = 600000\)[/tex]
[tex]\(3 \times 10^4 = 30000\)[/tex]
2. Add the numbers:
[tex]\(600000 + 30000 = 630000\)[/tex]
So the result for (g) is [tex]\(630000\)[/tex].
### h) [tex]\(1.5 \times 10^7 - 9.5 \times 10^5\)[/tex]:
1. Convert each term to standard form:
[tex]\(1.5 \times 10^7 = 15000000\)[/tex]
[tex]\(9.5 \times 10^5 = 950000\)[/tex]
2. Subtract the numbers:
[tex]\(15000000 - 950000 = 14050000\)[/tex]
So the result for (h) is [tex]\(14050000\)[/tex].
Thus, the final results are:
a) 4400
b) 92000
c) 1100000
d) 6400000009.7
e) 2940
f) 2400
g) 630000
h) 14050000
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