Answer :
Final answer:
The number 3700 x 10⁻³ cm in standard notation is 3.700 cm, with only two significant digits, 3 and 7. In scientific notation, only non-zero digits and any zeros between them are significant unless otherwise indicated.
Explanation:
The number provided is 3700 x 10⁻³ cm. To write this in standard notation, we perform the multiplication by moving the decimal point three places to the left (because of the exponent -3), resulting in 3.700 cm. Then, we consider the significant figures.
The provided number has two uncertain zeros; since they are to the right of the non-zero digits and are not followed by a decimal point, these are not significant. Therefore, the significant digits in this number are 3 and 7, making for two significant figures in total.
It's also useful to note the general rule regarding significant figures in scientific notation: any trailing zeros after nonzero digits and before the decimal point are not considered significant unless specified otherwise.
For instance, 5.00 x 10² cm indicates three significant figures, while 500 cm would typically represent only one significant figure unless additional context is given.
