Write the numbers in scientific notation.

Question

Write the numbers in scientific notation.

1.

673.5

673.5= ? x 10 ^a a= ?

2.

0.034

0.034=? x 10^b b=?

Answer 1

.034 = 3.4 x 10^-2

673.5 = 6.735 x 10^2

as you move the decimal to the left 1 digit, add 1 to the exponent of 10

until you change the number to a single digit

as you move the decimal to the right 1 digit, decrease the exponent by 1

.034 = .034 x 10^0, where 10^0 = 0. any number to the 0 power = 0 (except 0^0 which is undefined)

.034 = .34 x 10^-1 where 10^-1 = 1/10 = .1

.034 = 3.4 x 10^-2 where 10^-2 = 1/100 = .01

,034 = 3.4 x .01

Answer 2

In scientific notation, it is written in a form where a number between 1 and 10 is multiplied by an exponent of 10.

For 673.5, the decimal has to be moved 2 places to left to get a number between 1 and 10 . Hence

673.5 = 6.735 * 10². Therefore a = 2

For 0.034, the decimal has to be moved 2 places to right to get a number between 1 and 10 , Hence

0.034 = 3.4 * 10^-2. Therefore b = -2