How do I express a decimal in scientific notation? I know how to do it with whole numbers, but don't know what the rules are when the number is something like .00075.
the decimal is always placed after the first signigicant digit, in your case 7.5, then count the number of decimal places it was moved. That becomes your exponent of 10
if you had to move to the right, the exponent is negative, if you moved to the left, the exponent is positive.
so .0075 = 7.5 x 10-4
34567.21 = 3.456721 x 104
To express a decimal number in scientific notation, follow these steps:
1. Identify the non-zero digits in the decimal number. In the case of .00075, the non-zero digits are 7 and 5.
2. Count the number of decimal places between the non-zero digits and the original decimal point. In this case, there are 3 decimal places between 7 and 5, since the original decimal point is after 5.
3. Write down the non-zero digits as the coefficient, followed by a decimal point. For .00075, the coefficient is 75. Place the decimal point after the first non-zero digit, which gives you 7.5.
4. Determine the exponent by the count of decimal places from step 2. Since there are 3 decimal places, the exponent is -3.
5. Put the coefficient and the exponent together to express the decimal number in scientific notation. In this case, .00075 would be written as 7.5 × 10^(-3).
So, to express a decimal like .00075 in scientific notation, you would write it as 7.5 × 10^(-3).