Always keep the least number of significant figures. Two types of figures can be significant: non-zero numbers and zeroes that come after the demical place. 

\(\displaystyle 32.1\) has 3 significant figures while \(\displaystyle 0.003\) also has 3.

Therefore, your answer should also have 3 significant figures.

There are two categories that count as significant figures: non-zero numbers before the decimal point and everything after the decimal point. Since the number given is \(\displaystyle \small 20000kg\), there is only one non-zero number before the decimal point.

This number could have been rounded from any variation past the first digit, and we cannot assume that it is exact. To write this number in exact terms, we must use scientific notation or a decimal.

There are two categories that count as significant figures: non-zero numbers before the decimal point and everything after the decimal point.

When performing any operation between two numbers with different significant figures, always base it off the smallest number of significant figures. In this case, \(\displaystyle 100kg\) has only one significant figure; therefore our answer should also have only one significant figure.

Your answer should have the same number of significant figures as the term with the fewest significant figures. There are only two categories that qualify as significant figures: any terms after the decimal point and non-zero digits before the decimal.

In this problem, \(\displaystyle 300\frac{m}{s}\) has the fewest number of significant figures: only one. \(\displaystyle 2.00kg\) has three significant figures, but its precision is diminished by multiplying by a less precise term.

When multiplying or dividing, the answer must have the same number of significant figures as the term with the fewest significant figures in the problem. In this question, the one term (\(\displaystyle \small 200\)) has only significant figure, and the other term (\(\displaystyle \small 230.0\)) has four. Our final answer must match the term with the fewest significant figures: one. It is important to remember that zeroes after a decimal are significant figures, and determine the precision of a value. Zeroes before a decimal, such as in \(\displaystyle \small 200\), simply serve as place holders, and are no considered significant unless there is a decimal or scientific notation to clarify the term.

\(\displaystyle 230.0 \div 200=1.15\)

Round to the ones place to get an answer with only one significant figure.

\(\displaystyle 230.0 \div 200=1.15\approx 1\)

When multiplying or dividing, the answer must have the same number of significant figures as the term with the fewest significant figures in the problem. In this question, the one term (\(\displaystyle \small 4.2\)) has two significant figures, and the other term (\(\displaystyle \small 12.3\)) has three. Our final answer must match the term with the fewest significant figures: two.

\(\displaystyle 12.3\times 4.2 = 51.66\)

Round to the tens place to get an answer with only two significant figures.

\(\displaystyle 12.3\times4.2=51.66\approx 52\)

Leading and trailing zeroes are not considered significant. To make this problem simpler, we may want to re-write the equation in scientific notation.

\(\displaystyle F=2.12kg*0.05\frac{m}{s^2}\)

\(\displaystyle F=(2.12kg)*(5*10^{-2}\frac{m}{s})\)

The first term still has three digits, all of which are significant. The second term, however, has been reduced to only one digit. Our term with the fewest significant figures determines how many significant figures should be in the solution. In this case, there would only be one significant figure in the solution.

Significant figures are used to round scientific calculations in order to preserve precision. Every initial measurement will carry some degree of uncertainty or variation. It is important to carry that uncertainty to the final calculation, instead of unintentionally assigning greater certainty to the given values.

When determining significant figures, any zeroes that precede the first non-zero digit are considered insignificant and any zeroes that follow the final non-zero digit are considered insignificant. Any and all non-zero digits are significant. Sometimes it can help to write a number in scientific notation to identify significant figures.

\(\displaystyle 6.279*10^{56}\rightarrow4\ \text{significant figures}\)

\(\displaystyle 0.0000316=3.16*10^{-5}\rightarrow3\ \text{significant figures}\)

\(\displaystyle 239.8401=2.398401*10^2\rightarrow7\ \text{significant figures}\)

\(\displaystyle 7093000.084=7.093000084*10^6\rightarrow10\ \text{significant figures}\)

\(\displaystyle 0092043.7600120=9.2043760012*10^4\rightarrow11\ \text{significant figures}\)

Significant figures are used to round scientific calculations in order to preserve precision. Every initial measurement will carry some degree of uncertainty or variation. It is important to carry that uncertainty to the final calculation, instead of unintentionally assigning greater certainty to the given values.

When determining significant figures, any zeroes that precede the first non-zero digit are considered insignificant and any zeroes that follow the final non-zero digit are considered insignificant. Any and all non-zero digits are significant. Sometimes it can help to write a number in scientific notation to identify significant figures.

\(\displaystyle 6.017*10^{-14}\rightarrow4\ \text{significant figures}\)

\(\displaystyle 0.098=9.8*10^{-2}\rightarrow2\ \text{significant figures}\)

\(\displaystyle .098=9.8*10^{-2}\rightarrow2\ \text{significant figures}\)

\(\displaystyle 0462.10=4.621*10^{2}\rightarrow4\ \text{significant figures}\)

\(\displaystyle 1260.007=1.260007*10^{3}\rightarrow7\ \text{significant figures}\)

Significant figures are used to round scientific calculations in order to preserve precision. Every initial measurement will carry some degree of uncertainty or variation. It is important to carry that uncertainty to the final calculation, instead of unintentionally assigning greater certainty to the given values.

When determining significant figures, any zeroes that precede the first non-zero digit are considered insignificant and any zeroes that follow the final non-zero digit are considered insignificant. Any and all non-zero digits are significant. Sometimes it can help to write a number in scientific notation to identify significant figures.

\(\displaystyle 505=5.05*10^2\rightarrow 3\ \text{significant figures}\)

\(\displaystyle 50.01=5.001*10^1\rightarrow 4\ \text{significant figures}\)

\(\displaystyle 150=1.5*10^2\rightarrow 2\ \text{significant figures}\)

\(\displaystyle .005=5*10^{-3}\rightarrow 1\ \text{significant figure}\)

\(\displaystyle 500=5*10^2\rightarrow 1\ \text{significant figure}\)