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Chapter 1: Problem 17

True or false? For mathematical operation performed on two measurements, the number of significant figures in the answer is the same as the least number of significant figures in either of the measurements. Explain your answer.

Short Answer

Expert verified
False. The statement is true for multiplication and division operations, but not always for addition and subtraction operations. For addition and subtraction, the result should have the same number of decimal places as the measurement with the least number of decimal places, which may result in a different number of significant figures.

Step by step solution

01

Understand the concept of significant figures

Significant figures are the digits in a measurement that are deemed to be accurate and reliable. They are important in science and engineering because they help to convey the accuracy of a number and they affect the way results should be reported.
02

Analyze the statement for addition and subtraction operations

For addition and subtraction operations, the rule is that the result should have the same number of decimal places as the measurement with the least number of decimal places. This means that the statement is not always true for addition and subtraction operations, as the number of significant figures in the answer may be different from the least number of significant figures in either of the measurements. Example: \(12.34 + 5.6 = 17.94\), but since the least number of decimal places is 1, we report the answer as \(18.0\), which has 3 significant figures, even though both original measurements have more significant figures.
03

Analyze the statement for multiplication and division operations

For multiplication and division operations, the rule is that the result should have the same number of significant figures as the measurement with the least number of significant figures. This means that the statement is true for multiplication and division operations. Example: \(12.34 \times 5.6 = 69.104\), but since the least number of significant figures is 2, we report the answer as \(69\), which has 2 significant figures, the same as the least number of significant figures in either of the measurements.
04

Conclusion

The statement is true for multiplication and division operations but not always for addition and subtraction operations. So overall, the statement is false. The number of significant figures in the answer can be different from the least number of significant figures in either of the measurements, particularly when performing addition/subtraction operations.

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Most popular questions from this chapter

You go to a convenience store to buy candy and find the owner to be rather odd. He allows you to buy pieces in multiples of four, and to buy four, you need $0.23. He only allows you to do this by using 3 pennies and 2 dimes. You have a bunch of pennies and dimes, and instead of counting them, you decide to weigh them. You have 636.3 g of pennies, and each penny weighs 3.03 g. Each dime weighs 2.29 g. Each piece of candy weighs 10.23 g. a. How many pennies do you have? b. How many dimes do you need to buy as much candy as possible? c. How much should all these dimes weigh? d. How many pieces of candy could you buy? (number of dimes from part b) e. How much would this candy weigh? f. How many pieces of candy could you buy with twice as many dimes?

The density of an irregularly shaped object was determined as follows. The mass of the object was found to be \(28.90 \mathrm{g}=\) 0.03 \(\mathrm{g} .\) A graduated cylinder was partially filled with water. The reading of the level of the water was \(6.4 \mathrm{cm}^{3} \pm 0.1 \mathrm{cm}^{3}\) The object was dropped in the cylinder, and the level of the water rose to $9.8 \mathrm{cm}^{3} \pm 0.1 \mathrm{cm}^{3} .$ What is the density of the object with appropriate error limits? (See Appendix \(1.5 . )\)

Precious metals and gems are measured in troy weights in the English system: $$\begin{aligned} 24 \text { grains } &=1 \text { pennyweight (exact) } \\ 20 \text { pennyweight } &=1 \text { troy ounce (exact) } \\ 12 \text { troy ounces } &=1 \text { troy pound (exact) } \\ 1 \operatorname{grain} &=0.0648 \mathrm{g} \\ 1 \text { carat } &=0.200 \mathrm{g} \end{aligned}$$ a. The most common English unit of mass is the pound avoirdupois. What is 1 troy pound in kilograms and in pounds? b. What is the mass of a troy ounce of gold in grams and in carats? c. The density of gold is 19.3 \(\mathrm{g} / \mathrm{cm}^{3} .\) What is the volume of a troy pound of gold?

When a marble is dropped into a beaker of water, it sinks to the bottom. Which of the following is the best explanation? a. The surface area of the marble is not large enough to be held up by the surface tension of the water. b. The mass of the marble is greater than that of the water. c. The marble weighs more than an equivalent volume of the water. d. The force from dropping the marble breaks the surface tension of the water. e. The marble has greater mass and volume than the water. Justify your choice, and for choices you did not pick, explain what is wrong about them.

Round off each of the following numbers to the indicated number of significant digits, and write the answer in standard scientific notation. a. 0.00034159 to three digits b. \(103.351 \times 10^{2}\) to four digits c. 17.9915 to five digits d. \(3.365 \times 10^{5}\) to three digits
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