How do you apply 4 fundamental operations in scientific notation?

Answer 1

Addition:

1) Change the lower exponent to match (by dividing its number by 10 successively)

2) Add the numbers.

3) Keep the biger exponent (then adjust if necessary)

Example 1:

4x10^6 + 9x10^4

1) 9x10^4=0.9x10^5=0.09x10^6

2) 4+0.09=4.09

3) 4.09x10^6

Example 2: 6x10^7 + 5.5x10^7

1) No change needed (same exponent)

2) 6+5.5=11.5

3)11.5x10^7

Subtraction:

1) Change the lowe exponent to match (by dividing its number by 10 successively)

2) Subtract the numbers

3)keep the bigger exponent (adjust if necessary)

Example 1:

4x10^6 - 9x10^4

1)9x10^4= 0.9x10^5=0.09x10^6

2) 4 - 0.09 = 3.91

3) 3.91x10^6

Example 2:

6x10^7 - 5.5x10^7

1) No change needed (same exponent)

2) 6 - .5 = 0.5

3) 0.5x10^7 = 5x10^6

Notice that in exmaple 1 we didn't change the exponent in step 3, but in example 2 we did.

Multiplucation:

1) Multiply the numbers

2) Add the exponents

3) If necessary, adjus the exponent

Wxample:

3x10^8 x 5x10^4

1) 3x5= 13

2) 8+4= 12

3) 15x10^12=1.3x10^13

Division:

1) Divide the numbers.

2) Subtract the exponents.

3) If necessary, adjust the exponent.

Example:

2x10^9 / 5x10^4

1) 2/5= 0.4

2) 9-4=5

3) 0.4x10^5= 4x10^4

Answer 2

To apply the four fundamental operations (addition, subtraction, multiplication, and division) in scientific notation, you first perform the respective operation on the coefficients (numbers) while keeping the base (10) the same. Then, adjust the exponent of 10 according to the rules of each operation. For addition and subtraction, the exponents must be the same, so you adjust the coefficients accordingly. For multiplication, you multiply the coefficients and add the exponents. For division, you divide the coefficients and subtract the exponents.