Rules in performing the four fundamental operation 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 bigger exponent (then adjust if necessary).

Example 1:

4×10^6 + 9×10^4

1) 9×10^4 = 0.9×10^5 = 0.09×10^6

2) 4 + 0.09 = 4.09

3) 4.09×10^6

Example 2:

6×10^7 + 5.5×10^7

1) No change needed (same exponent)

2) 6 + 5.5 = 11

3) 11×10^7 = 1.1×10^8

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

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Subtraction:

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

2) Add the numbers.

3) Keep the bigger exponent (adjust if necessary).

Example 1:

4×10^6 - 9×10^4

1) 9×10^4 = 0.9×10^5 = 0.09×10^6

2) 4 - 0.09 = 3.91

3) 3.91×10^6

Example 2:

6×10^7 + 5.5×10^7

1) No change needed (same exponent)

2) 6 - 5.5 = 0.5

3) 0.5×10^7 = 5×10^6

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

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Multiplication:

1) Multiply the numbers.

2) Add the exponents.

3) If necessary, adjust the exponent.

Example:

3×10^8 × 5×10^4

1) 3×5 = 15

2) 8+4 = 12

3) 15×10^12 = 1.5×10^13

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Division:

1) Divide the numbers.

2) Subtract the exponents.

3) If necessary, adjust the exponent.

Example:

2×10^9 / 5×10^4

1) 2/5 = 0.4

2) 9 - 4 = 5

3) 0.4×10^5 = 4×10^4

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