How do you add/substract/multiply/divide in scientific notation?

Question

Thanks!

Answer 1

To add in scientific notation, you first have to put each number in the same power of ten. For example, say you have 3.2 x 10^5 + 3.2 x 10^6. Let's make them both powers of six. Then the first number becomes 0.32 x 10^6, and the second number stays the same. So we have 0.32 x 10^6 + 3.2 x 10^6. Now add 0.32 and 3.2 to get 3.52, and keep the 10^6. The final answer would be 3.52 x 10^6. To subtract is the same process, except subtracting instead of adding, of course.

Multiplying and dividing is easier. Say you have (4 x 10^6)(3 x 10^5). Multiply the 4 and 3 to get 12, then add the exponents to get 11. The final answer is 12 x 10^11. For division, you would instead divide the base numbers and subtract the exponents.

Answer 2

Definitions-

Mantissa - the value to be multiplied by the power of 10 to get the actual value, normally a value greater than or equal to one and less than 10.

Exponent - the power to raise 10 to before multiplying the mantissa

Example: In 3.14*10^6, the 3.14 is the mantissa and 6 is the exponent

To Add/subtract numbers in scientific notation, the numbers must first be converted such that their exponents are equal. Then the mantissas are added/subtracted. The exponent remains the same, unless both it and the mantissa need to be altered to bring the mantissa back into the range of between 1 and 10.

Example:

7.837 * 10^3 + 9.644 * 10^4 = ?

Since exponents are not equal, it and the mantissa must be adjusted. Dividing the first term by 10 and adding 1 to its exponent will accomplish it.

0.7837 * 10^4 + 9.644 * 10^4 = ?

Now the mantissas may be added, and the result is

0.7837 * 10^4 + 9.644 * 10^4 = 10.4277 * 10^4

If desired, the solution may be adjusted as previously mentioned -

10.4277 * 10^4 = 1.0428 * 10^5

Answer 3

all you do for multiply and divide is add or subtract the exponents while doing the math so for example:
(2 x 10^2) x (2 x 10^3)
= 4 x 10^5 (you do the math, 2x2, and add the exponents)

Division you subtract
(2 x 10^2) / (2 x 10^3)
= 4 x 10^-1 (that's a negative 1 exponent)

Sorry I can't remember addition and subtraction except to do it in long form

Answer 4

hmm... when adding and subtracting, make sure that the exponents are the same then add the figures... when multiplying and dividing, add if multiply or subtract if divide then multiply or divide the figures... it's easy!!!

Answer 5

Factor out the common powers of ten would be an easy way . . . if that's what you're asking. Say I have:

5.34*10^(5) = 5.34E5

and

6.78*10^(3) = 6.78E3

to add 5.34E5 + 6.78E3

= 10^3*(5.34E2 + 6.78)
=10^3*(534 + 6.78)
=10^3*(540.78)
=5.41E5

Answer 6

nathing