What are significant digits? How can you tell whether zeros are significant?

Decide whether each of the following statements makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.

Next year's federal deficit will be $\$ 675.734$ billion.

Under the standard rules for counting significant digits, which of the following numbers has the most significant digits? a. $5.0 \times 10^{-1}$ b. $5 \times 10^3$ c. $500,000$

What is the order of magnitude estimate for the number of steps you take in an average day?

Rewrite the following statements using a number in scientific notation.

My new music player has a capacity of $340$ gigabytes. (Recall that giga means billion.)

Describe several ways of putting each of the following in perspective: the size of a large university; $1 billion; the size of an atom; the Sun's remaining lifetime.

Sampling techniques can be used to estimate physical quantities. To estimate a large quantity, you might measure a representative small sample and find the total quantity by "scaling up."To estimate a small quantity, you might measure several of the small quantities together and "scale down." In each of the following, describe your estimation technique and answer the questions.

Example: How thick is a sheet of a paper?

Solution: One way to estimate the thickness of a sheet of paper is to measure the thickness of a ream ($500$ sheets) of paper. A particular ream was $7.5$ centimeters thick. Thus, a sheet of paper from this ream was $7.5 \mathrm{~cm} \div 500=0.015 \mathrm{~cm}$, or $0.15$ millimeter, thick.

How much does a sheet of paper weigh?How thick is a penny? a nickel? a dime? a quarter? Would you rather have your height stacked in pennies, nickels, dimes, or quarters? Explain.

In the following statement, express the first number as a percentage of the second number. The full-time year-round median salary for U.S. men in 2015 was $\$ 50,383$, and the full-time year-round median salary for U.S. women in $2015$ was $\$ 39,621$.

Determine whether the following claims could be true. Explain your answer.

By turning off her lights and closing her windows at night, Maria saved $120 \%$ on her monthly energy bill.

What are three-dimensional graphics? Explain the difference between graphics that only appear three-dimensional and those that show truly three-dimensional data.

In the following statement, express the first number as a percentage of the second number. The $2015$ population of California was approximately $39.1$ million. The $2010$ population was approximately $33.9$ million.

In the following statement, express the first number as a percentage of the second number. Donald Trump won $302$ electoral votes in $2016$, out of a total of $538$.

In the following statement, express the first number as a percentage of the second number. Apple's $2015$ revenue was $\$ 233$ million, compared to Walmart's $\$ 482$ million.

By using Figure $5.18$ to answer the following questions. a. Within a group of $500$ typical first-year college students, approximately how many have loans to help pay for their education? b. Can you conclude that some students who are satisfied with their coursework also text in class? Explain.