1 With addition change the scientific notation back to 'normal numbers' and then add accordingly
2 With subtraction change the scientific back to 'normal numbers' and then subtract accordingly
3 With division subtract the exponents and divide the decimals
4 With multiplication add the exponents and multiply the decimals
5 Note that if changes occur below 1 or greater than 9 in the decimal element of the scientific notation then appropriate adjustments must be made
Ask yourself. Would you rather write this out in long hand? 234,000,000,000,000,000,000 ----------------------------------- Or this? 2.34 X 1020 -------------- Let alone adding, subtracting, multiplying and dividing the first long number.
If you are adding or subtracting two numbers in scientific notation, you must rewrite one of the numbers to the same power of ten as the other, before performing the addition (or subtraction).
Add them
When dividing in scientific notation, you subtract the exponent of the divisor from the exponent of the dividend. This will give you the exponent of the quotient after division.
Same.
Yes, it does.
Ask yourself. Would you rather write this out in long hand? 234,000,000,000,000,000,000 ----------------------------------- Or this? 2.34 X 1020 -------------- Let alone adding, subtracting, multiplying and dividing the first long number.
- when adding or subtracting in scientific notation, you must express the numbers as the same power of 10. This will often involve changing the decimal place of the coefficient.
Add them
If you are adding or subtracting two numbers in scientific notation, you must rewrite one of the numbers to the same power of ten as the other, before performing the addition (or subtraction).
yes its really important
When dividing in scientific notation, you subtract the exponent of the divisor from the exponent of the dividend. This will give you the exponent of the quotient after division.
Same.
Subtract them.
Multiplying numbers in scientific notation is easier when the numbers are very, very large or very, very small. Multiplying 0.000000000385 x 0.0000000474 is a pain. Multiplying 3.85 x 10-10 x 4.74 x 10-8 is not.
Multiplying each factor by powers of ten
The idea is to save page space and time. Instead of writing out a 1 followed by 100 zeros for a google (which would take up a long time and a lot of space) you simply write 10^100. +++ It can, depending on the values being manipulated, also facilitate arithmetic by turning multiplying or dividing the powers into adding or subtracting the indices (the principle of the logarithm).