When you convert a number from decimal notation to scientific notation, how do you know if the exponent will be positive or negative?

Answer 1

A positive exponent means you are multiplying the new number by 10 to return to the original number, whereas a negative exponent means you would divide by 10. The simplest way to know if the exponent will be positive or negative is to compare the original number with the new number without the exponent. If the new number is smaller than the original, then the exponent will be positive. If the new number is larger than the original, the exponent will be negative.

Let's use 435 as an example.

Number: 435

Scientific Notation: 4.35 x 10²

4.35 is less than 435, so the exponent will be positive. The positive 2 means that you are multiplying 4.35 by 10 twice to return to the original number.

Let's use .00073 as another example.

Number. 0.00073

Scientific Notation: 7.3 x 10 ^-4

7.3 is larger than 0.00073, so the exponent will be negative. This means instead of multiplying 7.3 by 10, we are dividing 7.3 by 10 four times to make the original number.

Answer 2

This may be seen best by doing 2 examples.

(1)

Convert 233.17 to exponential.

233.17 = 2.3317 x 10²

(2)

Convert 0.000235 to exponential.

0.000235 = 2.35 x 10^-4

Can you see it?

Answer 3

The exponent is positive if the decimal point is moved to the left to obtain a base number for the scientific notation and is negative if the decimal point moves to the right.

For example:

6829000=6.829x10⁶ - The decimal point had to be moved to the left by 6 positions. The exponent in the scientific notation is 6 and is positive

.000967 = 9.67x10^-4

The decimal point was moved to the right by 4 positions which makes it negative.