Chapter 2: Measurement and Problem Solving

c) 21.2 mL

A graduated cylinder has markings every milliliter. Which measurement is accurately reported for this graduated cylinder? a) 21 mL b) 21.23 mL c) 21.2 mL d) 21.232 mL

b) negative

A ___ exponent (-n) means 1 divided by 10 n times. a) positive b) negative

a) positive

A ____ exponent means 1 multiplied by 10 n times. a) positive b) negative

a) 4.3 g/cm³

A cube measures 2.5 cm on each edge and has a mass of 66.9 g. Calculate the density of the material that composes the cube. (The volume of a cube is equal to the edge length cubed.) a) 4.3 g/cm³ b) 0.234 g/cm³ c) 26.7 g/cm³ d) 10.7 g/cm³

a) 8.09 mi/hr

A runner runs 4875 ft in 6.85 minutes. What is the runner's average speed in miles per hour? a) 8.09 mi/hr b) 8.087 mi/hr c) 0.135 mi/hr d) 712 mi/hr

d) 29.0 mi/gal

An automobile travels 97.2 km on 7.88 L of gasoline. What is the gas mileage for the automobile in miles per gallon? a) 0.034 mi/gal b) 46.7 mi/gal c) 7.67 mi/gal d) 29.0 mi/gal

b) 97 km/hr

Convert 27 m/s to km/hr. a) 7.5 km/hr b) 97 km/hr c) 0.027 km/hr d) 1.6 km/hr

a) 2.855 × 10⁻³kg

Convert 2855 mg to kg. a) 2.855 × 10⁻³kg b) 0.02855 kg c) 2.855 kg d) 3.503 × 10⁻⁴kg

c) 0.768 m

Convert 76.8 cm to m. a) 7.68 × 10⁻² m b) 7.68 m c) 0.768 m d) 0.0768 m

a) 0.01437 m³

Convert 876.9 in³ to m³ a) 0.01437 m³ b) 22.27 m³ c) 0.014 m³ d) 5.351 × 10⁷ m³

d) 4.2 × 10⁻⁵

Express the number 0.000042 in scientific notation. a) 0.42 × 10⁻⁴ b) 4 × 10^⁻⁵ c) 4.2 × 10⁻⁴ d) 4.2 × 10⁻⁵

In calculations involving both multiplication/division and addition/subtraction, do the steps in parentheses first; next determine the correct number of significant figures in the intermediate answer; then do the remaining steps.

How do we determine significant figures in calculations involving both addition/subtraction and multiplication/division?

Exact numbers have an unlimited number of significant figures. Exact numbers originate from three sources: 1. Exact counting of discrete objects. For example, 10 pencils means 10.0000. pencils and 3 atoms means 3.00000 ... atoms. 2. Defined quantities, such as the number of centimeters in 1 m. Because 100 cm is defined as 1 m, 100 cm = 1m means 100.00000 ... cm = 1.0000000 ... m 3. Integral numbers that are part of an equation. For example, in the equation, radius = diameter/2, the number 2 is exact and therefore has an unlimited number of significant figures.

How many significant digits are there in exact numbers? What kinds of numbers are exact?

d) 3

How many significant figures are in the number 0.00620? a) 4 b) 5 c) 2 d) 3

If I measured quantity is written correctly, all but last digit of the quantity or certain. The last digit is uncertain as it could have been due to instruments in accuracy. When we report the length of a line segment to be 2.45 units, we are actually approximating it's last bit.

If a measured quantity is written correctly, which digits are certain? Which are uncertain?

a) left

If the decimal point is moved to the ___, the exponent is positive. a) left b) right

b) right

If the decimal point is moved to the ____, the exponent is negative. a) left b) right

Volume is defined to be the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic meter. Any unit of length gives a corresponding unit of volume, namely the volume of a cube whose side has the given length. -For example, a cubic centimeter cm³ would be the volume of a cube whose sides are one centimeter in length. -The common units of volume are liter (L), cubic meters (cm), milliliter (ml), etcetera. Other traditional units include gallon, pint, gill, peck, and etcetera.

List the common units of volume.

d) 20.49

Perform this addition to the correct number of significant figures: 8.32 + 12.148 + 0.02 a) 20.488 b) 20.5 c) 21 d) 20.49

b) 39

Perform this calculation to the correct number of significant figures: 78.222 × (12.02 − 11.52) a) 39.111 b) 39 c) 39.11 d) 39.1

d) 1.2

Perform this multiplication to the correct number of significant figures: 65.2 × 0.0015 × 12.02 a) 1.18 b) 1.17 c) 1.176 d) 1.2

b) 89.0

Round the number 89.04997 to three significant figures. a) 89.03 b) 89.0 c) 89.04 d) 89.1

c) non-zero

Rules to determine significant numbers: 1. All _____ digits are significant. 2. Interior zeros (zeros between two numbers) are significant. 3. Trailing zeros (zeros to the right of a nonzero number) that fall after a decimal point are significant. 4. Trailing zeros that fall before a decimal point are significant. 5. Leading zeros (zeros to the left of the first nonzero number) are not significant. They only serve to locate the decimal point. 6. Trailing zeros at the end of a number, but before an implied decimal point, are ambiguous and should be avoided by using scientific notation. (350 should be written as 3.5 x 10² a) zero b) whole c) non-zero d) negative

a) ambiguous

Rules to determine significant numbers: 1. All nonzero digits are significant. 2. Interior zeros (zeros between two numbers) are significant. 3. Trailing zeros (zeros to the right of a nonzero number) that fall after a decimal point are significant. 4. Trailing zeros that fall before a decimal point are significant. 5. Leading zeros (zeros to the left of the first nonzero number) are not significant. They only serve to locate the decimal point. 6. Trailing zeros at the end of a number, but before an implied decimal point, are ______ and should be avoided by using scientific notation. (350 should be written as 3.5 x 10² a) ambiguous b) total c) superior d) nonzero

d) trailing zeros

Rules to determine significant numbers: 1. All nonzero digits are significant. 2. Interior zeros (zeros between two numbers) are significant. 3. ______ (zeros to the right of a nonzero number) that fall after a decimal point are significant. 4. ______ that fall before a decimal point are significant. 5. Leading zeros (zeros to the left of the first nonzero number) are not significant. They only serve to locate the decimal point. 6. ______ at the end of a number, but before an implied decimal point, are ambiguous and should be avoided by using scientific notation. (350 should be written as 3.5 x 10² a) ambiguous b) exterior zeros c) superior zeros d) trailing zeros

b) interior zeros

Rules to determine significant numbers: 1. All nonzero digits are significant. 2. ______ (zeros between two numbers) are significant. 3. Trailing zeros (zeros to the right of a nonzero number) that fall after a decimal point are significant. 4. Trailing zeros that fall before a decimal point are significant. 5. Leading zeros (zeros to the left of the first nonzero number) are not significant. They only serve to locate the decimal point. 6. Trailing zeros at the end of a number, but before an implied decimal point, are ambiguous and should be avoided by using scientific notation. (350 should be written as 3.5 x 10² a) ambiguous b) interior zeros c) exterior zeros d) positive numbers

b) between -65.18℃ and -65.20℃

The Curiosity Rover on the surface of Mars recently measured a daily low temperature of -65.19℃. What is the implied range of the actual temperature? a) between -65.190℃ and -65.199℃ b) between -65.18℃ and -65.20℃ c) between -65.1℃ and -65.2℃ d) exactly -65.19℃

c) 0.0045 mm

The radius of a dust speck is 4.5 x 10⁻³mm. What is the correct value of this number in decimal notation (i.e., express the number without using scientific notation)? a) 4500mm b) 0.045 mm c) 0.0045 mm d) 0.00045 mm

The basic SI unit of length is the meter. The kilogram is the SI unit of mass. Lastly, the second is the SI unit of time.

What are the basic SI units of length, mass, and time?

1. We round down if the last (or leftmost) digit dropped is 4 or less; we round up if the last (or leftmost) digit dropped is 5 or more. -For example, when we round each of these numbers to two significant figures: 2.33 rounds to 2.3 & 2.37 rounds to 2.4 2. We consider only the last (or leftmost) digit being dropped when we decide in which direction to round—we ignore all digits to the right of it. -For example, to round 2.349 to two significant figures, only the 4 in the hundredths place (2.349) determines which direction to round—the 9 is irrelevant. 2.349 rounds to 2.3 3. For calculations involving multiple steps, we round only the final answer—we do not round the intermediate results. This prevents small rounding errors from affecting the final answer.

What are the rules for rounding numbers?

b) 2.70 cm

What is the edge length of a 155-g iron cube? (The density of iron is 7.86 g/cm³, and the volume of a cube is equal to the edge length cubed.) a) 19.7 cm b) 2.70 cm c) 0.0197 cm d) 1218 cm

b) 198 g

What is the mass of 225 mL of a liquid that has a density of 0.880 g/mL? a) 256 g b) 198 g c) 0.00391 g d) 0.198 g

The number of significant digits in addition and subtraction problems is determined by which ever number contains the fewest significant digits. It's because in this procedure, the error in the answer is due to the error of the least accurate number. Therefore, the final result should be given to you as many significant figures as are contained in the least significant number and no more.

What limits the number of significant digits in a calculation involving only addition and subtraction?

For calculations involving only multiplication and division, the result carries the same number of significant figures as the factor with the fewest significant figures.

What limits the number of significant digits in a calculation involving only multiplication and division?

Zeros count as significant digits when they are interior zeros parentheses zeros between two number) and when they are trailing zeros parentheses zero after a decimal point). Zeros are not significant numbers when they are leading zeros, which are zeros to the left of the first nonzero number.

When do you zeros count as significant digits, and when don't they count?

b) (3+15)/12

Which calculation would have its results reported to the greater number of significant figures? a) 3+(15/12) b) (3+15)/12

a) 12 in/1 ft

Which conversion factor should you use to convert 4 ft to inches (12 in. = 1 ft.)? a) 12 in/1 ft b) 1 ft/ 12 in c) 1 in/ 12 ft d) 12 ft/1 ft

c) 1 km/10³ m

Which conversion factor should you use to convert a distance in meters to kilometers? a) 1 m/ 10³km b) 10³ m/ 1 km c) 1 km/10³ m d) 10³ km/ 1 m

d) nm

Which is the most convenient unit to use to express the dimensions of a poliovirus, which is about 2.8x10⁻⁸ m in diameter? a) Mm b) mm c) µm d) nm

-As the number of digits reported increases, the precision of the measurement also increases. -It also affects the degree of certainty which is usually represented by the last reported digit.

Why are the number of digits reported in scientific measurements important?

Without units, the results are unclear and it is hard to keep track of what each separate measurement entails.

Why is it necessary to include units when reporting scientific measurements?

Often scientist work with very large or very small numbers that contain a lot of zeros. Scientific notation allows these numbers to be written more compactly, and the information is more organized.

Why is scientific notation useful?

d) 27

You know that there are 3 feet in a yard. How many cubic feet are there in a cubic yard? a) 3 b) 6 c) 9 d) 27