How do you divide and multiply in scientific notation?

Answer 1

Suppose p = a*10^x and

q = b*10^y are two numbers in scientific notation.

Then p*q = (a*b)*10^(x+y)

where, 1 <= |a|,|b| < 10 implies that 1 <= |a*b| < 100.

If a*b is greater than or equal to 10, let a*b = 10*c

then in scientific notation, p*q = c*10^(x+y+1).

Also p/q = (a/b)*10^(x-y)

where, 1 <= |a|,|b| < 10 implies that 0 < |a/b| <= 1.

If a/b is less than 1, let a/b = c/10

then in scientific notation, p/q = c*10^(x-y-1).

Answer 2

Scientific notation is a way of representing numbers, usually very large or very small, in the form a*10^b where 1 ≤ |a| < 10 is a decimal number and b is an integer (negative or positive). a is called the mantissa and b is called the exponent. To convert a number to scientific notation: · If the number has no decimal point, then add one at the end. · Then move the decimal point to just after the first digit while counting the number of places you have moved it. · The mantissa of the new number, formed after moving the decimal point is a. · If the original number is negative, then so is a. · The number of places to the left that the decimal point was moved is b. If it was moved to the right, then b is negative.

Answer 3

Suppose p = a*10^x and q = b*10^y are two numbers in scientific notation. Then p*q = (a*b)*10^(x+y) where, 1 <= |a|,|b| < 10 implies that 1 <= |a*b| < 100. If a*b is greater than or equal to 10, let a*b = 10*c then in scientific notation, p*q = c*10^(x+y+1). Also p/q = (a/b)*10^(x-y) where, 1 <= |a|,|b| < 10 implies that 0 < |a/b| <= 1. If a/b is less than 1, let a/b = c/10 then in scientific notation, p/q = c*10^(x-y-1).