Chapter 1, Problem 23P

(a)

To determine

The number of scientific figures in $0.00574\text{kg}$, and the standard notation of the $0.00574\text{kg}$.

Answer to Problem 23P

The number of scientific figures in $0.00574\text{kg}$ is $\underset{\_}{3}$, and the standard notation of the $0.00574\text{kg}$ is $\underset{\_}{5.74\times {10}^{-3}\text{kg}}$.

Explanation of Solution

In scientific notation, any number is written as a number between one and ten times an integer power of ten. The significant figures are all the digits that are known accurately plus the one estimated digit.

The rules for identifying the significant figures are, the nonzero digits are always significant, final or ending zeros written to the right of the decimal point are significant, zeros written to the right of the decimal point for the purpose of spacing the decimal point are not significant, zeros written to the left of the decimal point may be significant, and zeros written between significant figures are significant.

According to the rule the first two zeros in $0.00574\text{kg}$ are not significant, so the significant number is three. To write the number in scientific notation, move the decimal point three places to the right, and compensate by multiplying by ${10}^{-3}$. That is $5.74\times {10}^{-3}\text{kg}$.

Conclusion:

Therefore, the number of scientific figures in $0.00574\text{kg}$ is $\underset{\_}{3}$, and the standard notation of the $0.00574\text{kg}$ is $\underset{\_}{5.74\times {10}^{-3}\text{kg}}$.

(b)

To determine

The number of scientific figures in $2\text{m}$, and the standard notation of the $2\text{m}$.

Answer to Problem 23P

The number of scientific figures in $2\text{m}$ is $\underset{\_}{1}$, and the standard notation of the $2\text{m}$ is $\underset{\_}{2\text{m}}$.

Explanation of Solution

According to the rule the number two is significant, so the significant number is one. The number in scientific notation is same as given. That is $2\text{m}$.

Conclusion:

Therefore, the number of scientific figures in $2\text{m}$ is $\underset{\_}{1}$, and the standard notation of the $2\text{m}$ is $\underset{\_}{2\text{m}}$.

(c)

To determine

The number of scientific figures in $0.450\times {10}^{-2}\text{m}$, and the standard notation of the $0.450\times {10}^{-2}\text{m}$.

Answer to Problem 23P

The number of scientific figures in $0.450\times {10}^{-2}\text{m}$ is $\underset{\_}{3}$, and the standard notation of the $0.450\times {10}^{-2}\text{m}$ is $\underset{\_}{4.50\times {10}^{-3}\text{m}}$.

Explanation of Solution

According to the rule the three zeros after the decimal point in $0.450\times {10}^{-2}\text{m}$ are significant, so the significant number is three. To write the number in scientific notation, move the decimal point one places to the right, and compensate by multiplying by ${10}^{-1}$. That is $4.50\times {10}^{-3}\text{m}$.

Conclusion:

Therefore, the number of scientific figures in $0.450\times {10}^{-2}\text{m}$ is $\underset{\_}{3}$, and the standard notation of the $0.450\times {10}^{-2}\text{m}$ is $\underset{\_}{4.50\times {10}^{-3}\text{m}}$.

(d)

To determine

The number of scientific figures in $45.0\text{kg}$, and the standard notation of the $45.0\text{kg}$.

Answer to Problem 23P

The number of scientific figures in $45.0\text{kg}$ is $\underset{\_}{3}$, and the standard notation of the $45.0\text{kg}$ is $\underset{\_}{4.50\times {10}^1\text{kg}}$.

Explanation of Solution

According to the rule the two numbers after the decimal point in $45.0\text{kg}$ are significant, so the significant number is three. To write the number in scientific notation, move the decimal point one places to the left, and compensate by multiplying by ${10}^1$. That is $4.50\times {10}^1\text{kg}$.

Conclusion:

Therefore, the number of scientific figures in $45.0\text{kg}$ is $\underset{\_}{3}$, and the standard notation of the $45.0\text{kg}$ is $\underset{\_}{4.50\times {10}^1\text{kg}}$.

(e)

To determine

The number of scientific figures in $10.09\times {10}^4\text{s}$, and the standard notation of the $10.09\times {10}^4\text{s}$.

Answer to Problem 23P

The number of scientific figures in $10.09\times {10}^4\text{s}$ is $\underset{\_}{4}$, and the standard notation of the $10.09\times {10}^4\text{s}$ is $\underset{\_}{1.009\times {10}^5\text{s}}$.

Explanation of Solution

According to the rule the two numbers after the decimal point and before the decimal point in $10.09\times {10}^4\text{s}$ are significant, so the significant number is four. To write the number in scientific notation, move the decimal point one places to the left, and compensate by multiplying by ${10}^1$. That is $1.009\times {10}^5\text{s}$.

Conclusion:

Therefore, the number of scientific figures in $10.09\times {10}^4\text{s}$ is $\underset{\_}{4}$, and the standard notation of the $10.09\times {10}^4\text{s}$ is $\underset{\_}{1.009\times {10}^5\text{s}}$.

(f)

To determine

The number of scientific figures in $0.09500\times {10}^5\text{mL}$, and the standard notation of the $0.09500\times {10}^5\text{mL}$.

Answer to Problem 23P

The number of scientific figures in $0.09500\times {10}^5\text{mL}$ is $\underset{\_}{4}$, and the standard notation of the $0.09500\times {10}^5\text{mL}$ is $\underset{\_}{9.500\times {10}^3\text{mL}}$.

Explanation of Solution

According to the rule the zero just after the decimal point in $0.09500\times {10}^5\text{mL}$ is not significant, so the significant number is four. To write the number in scientific notation, move the decimal point two places to the right, and compensate by multiplying by ${10}^{-2}$. That is $\underset{\_}{9.500\times {10}^3\text{mL}}$.

Conclusion:

Therefore, the number of scientific figures in $0.09500\times {10}^5\text{mL}$ is $\underset{\_}{4}$, and the standard notation of the $0.09500\times {10}^5\text{mL}$ is $\underset{\_}{9.500\times {10}^3\text{mL}}$.