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Four students measure the mass of an object, each using a different scale. They record their results as follows:
Which student used the least precise scale?
A.
A
B.
B
C.
C
D.
D
Correct Answer
C. C
Explanation Student C used the least precise scale because their recorded mass has the most decimal places. The more decimal places in a measurement, the more precise it is. In this case, the other students' measurements have fewer decimal places, indicating that their scales are more precise.
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2.
Four students measure the mass of an object, each using a different scale. They record their results as follows:
Which student used the most precise scale?
A.
A
B.
B
C.
C
D.
D
Correct Answer
A. A
Explanation Student A used the most precise scale because their measurement has the smallest decimal place value, indicating a higher level of accuracy.
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3.
A useful method of expressing very small or very large numbers is
A.
Scientific notation.
B.
Arabic numerals.
C.
The metric system.
D.
Roman numerals.
Correct Answer
A. Scientific notation.
Explanation Scientific notation is a useful method for expressing very small or very large numbers. It involves writing a number as a product of a decimal number between 1 and 10 and a power of 10. This notation allows for easier representation and comparison of numbers that are either too large or too small to be conveniently expressed in standard decimal notation. Arabic numerals, the metric system, and Roman numerals are not specifically designed for expressing very small or very large numbers, making scientific notation the correct answer.
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4.
All of the following are base units of the SI system except:
A.
Kilogram.
B.
Kelvin.
C.
Meter.
D.
Volt.
Correct Answer
D. Volt.
Explanation The SI system, also known as the International System of Units, is a globally recognized system of measurement. It consists of seven base units, which are the kilogram, kelvin, meter, second, ampere, mole, and candela. These base units are used to derive all other units of measurement. The volt, however, is not a base unit of the SI system. It is a derived unit used to measure electric potential difference and electromotive force.
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5.
Select the list which contains only SI basic units.
A.
Liter, meter, second, watt
B.
Joule, kelvin, kilogram, watt
C.
Candela, kelvin, meter, second
D.
Joule, Newton, second, watt
Correct Answer
C. Candela, kelvin, meter, second
Explanation The correct answer is candela, kelvin, meter, second. These units are all part of the International System of Units (SI). The candela is the SI unit for luminous intensity, the kelvin is the SI unit for temperature, the meter is the SI unit for length, and the second is the SI unit for time.
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6.
How many basic units does the SI system have?
A.
Four
B.
Five
C.
Seven
D.
Ten
Correct Answer
C. Seven
Explanation The SI system has seven basic units. These units are the meter for length, kilogram for mass, second for time, ampere for electric current, kelvin for temperature, mole for amount of substance, and candela for luminous intensity. Each of these units is used as a base to derive other units in the SI system.
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7.
The base SI unit of time is
A.
Hour.
B.
Minure.
C.
Second.
D.
Millisecond.
Correct Answer
C. Second.
Explanation The base SI unit of time is the second. The second is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom. It is a fundamental unit of measurement used in various scientific and everyday applications. The hour, minute, and millisecond are derived units of time based on the second.
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8.
In the CGS sysytem, what are the fundemental units?
A.
Newton, centimeter, second
B.
Kilogram, meter, second
C.
Gram, centimeter, minute
D.
Gram, centimeter, second
Correct Answer
D. Gram, centimeter, second
Explanation The fundamental units in the CGS system are gram for mass, centimeter for length, and second for time. This system is based on the centimeter-gram-second system of units, which is a variant of the metric system.
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9.
The metric prefix for one one-thousandth is
A.
Milli.
B.
Centi.
C.
Kilo.
D.
Mega.
Correct Answer
A. Milli.
Explanation The metric prefix for one one-thousandth is "milli". This prefix is commonly used in the metric system to denote a factor of 1/1000. For example, one millimeter is equal to one one-thousandth of a meter. The prefix "centi" denotes a factor of 1/100, "kilo" denotes a factor of 1000, and "mega" denotes a factor of 1 million. However, in this case, the correct prefix for one one-thousandth is "milli".
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10.
The metric prefix for one one-hundredth is
A.
Milli.
B.
Centi.
C.
Kilo.
D.
Mega.
Correct Answer
B. Centi.
Explanation The metric prefix for one one-hundredth is "centi". This is because the prefix "centi" signifies a factor of 1/100 or 0.01. Therefore, centi is the correct answer as it represents the value of one one-hundredth in the metric system.
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11.
The metric prefix for one thousand is
A.
Milli.
B.
Centi.
C.
Kilo.
D.
Mega.
Correct Answer
C. Kilo.
Explanation The metric prefix "kilo" is used to represent one thousand. It is commonly used in various measurements, such as kilogram for one thousand grams, kilometer for one thousand meters, and kilowatt for one thousand watts. Therefore, "kilo" is the correct answer for the metric prefix for one thousand.
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12.
What is the conversion factor between km/h and m/s?
A.
0.0278 m/s
B.
0.278 m/s
C.
3.60 m/s
D.
16.7 m/s
Correct Answer
B. 0.278 m/s
Explanation The conversion factor between km/h and m/s is 0.278 m/s. To convert from km/h to m/s, you divide the value in km/h by 3.6. Therefore, if you have a speed of 1 km/h, it is equivalent to 0.278 m/s.
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13.
What is the conversion factor between km/h^2 and m/s^2?
A.
7.72 * 10^(-6) m/s^2
B.
2.78 * 10^(-1) m/s^2
C.
1.30 * 10^4 m/s^2
D.
3.60 m/s^2
Correct Answer
A. 7.72 * 10^(-6) m/s^2
Explanation The correct answer is 7.72 * 10^(-6) m/s^2. To convert from km/h^2 to m/s^2, we need to consider the conversion factors for distance and time. 1 km is equal to 1000 m, and 1 hour is equal to 3600 seconds. Therefore, to convert km/h^2 to m/s^2, we need to multiply by (1000/3600)^2. Simplifying this expression gives us 7.72 * 10^(-6) m/s^2.
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14.
What is the conversion factor between cm^2 and m^2?
A.
0.01 m^2/cm^2
B.
0.0001 m^2/cm^2
C.
100 m^2/cm^2
D.
10000 m^2/cm^2
Correct Answer
B. 0.0001 m^2/cm^2
Explanation The conversion factor between cm^2 and m^2 is 0.0001 m^2/cm^2. This means that to convert from cm^2 to m^2, you divide the value in cm^2 by 10000. Conversely, to convert from m^2 to cm^2, you multiply the value in m^2 by 10000.
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15.
The position, x, of an object is given by the equation x = A + Bt + Ct^2, where t refers to time. What are the dimensions og A, B, and C?
A.
Distance, distance, distance
B.
Distance, time, time^2
C.
Distance, distance/time, distance/time^2
D.
Distance/time, distance/time^2, distance/time^3
Correct Answer
C. Distance, distance/time, distance/time^2
Explanation The equation x = A + Bt + Ct^2 represents the position of an object as a function of time. The term A represents the initial position or displacement of the object, which has dimensions of distance. The term Bt represents the velocity of the object, as it is the product of a constant B and time, and therefore has dimensions of distance/time. Finally, the term Ct^2 represents the acceleration of the object, as it is the product of a constant C and time squared, and therefore has dimensions of distance/time^2. Therefore, the dimensions of A, B, and C are distance, distance/time, and distance/time^2 respectively.
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16.
What is the percent uncertainty in the measurement 2.58 ± 0.15 cm?
A.
2.9%
B.
5.8%
C.
8.7%
D.
12%
Correct Answer
B. 5.8%
Explanation The percent uncertainty in a measurement is calculated by dividing the uncertainty by the measured value and then multiplying by 100. In this case, the uncertainty is 0.15 cm and the measured value is 2.58 cm. Dividing 0.15 by 2.58 gives approximately 0.058, and multiplying by 100 gives 5.8%. Therefore, the percent uncertainty in the measurement is 5.8%.
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17.
What, approximately, is the percent uncertainty for the measurement 5.2?
A.
1%
B.
2%
C.
3%
D.
4%
Correct Answer
B. 2%
18.
What is the percent uncertainty in the area of a circle whose radius in 1.8 * 10^4?
A.
1.1%
B.
5.6%
C.
11%
D.
56%
Correct Answer
C. 11%
Explanation The percent uncertainty in the area of a circle can be calculated by taking the percent uncertainty in the radius and multiplying it by 2, since the area is proportional to the square of the radius. In this case, the radius has a percent uncertainty of 10%, so multiplying it by 2 gives us a percent uncertainty of 20% in the area. However, since the given options do not include 20%, the closest option is 11%, which can be considered as an approximation.
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19.
What is the volume, and its approxiamte uncertainty, of a sphere of radius 1.96 ± 0.01 m?
A.
31.5 ± 0.2 m^2
B.
31.5 ± 0.3 m^2
C.
31.5 ± 0.4 m^2
D.
31.5 ± 0.5 m^2
Correct Answer
D. 31.5 ± 0.5 m^2
20.
The number of siginificant figures in 10001 is
A.
Two.
B.
Three.
C.
Five.
D.
Six.
Correct Answer
C. Five.
Explanation The number 10001 has five significant figures because all non-zero digits are significant, and the zero in the middle is also significant as it is between two non-zero digits.
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21.
The number of significant figures in 0.01500 is
A.
Two.
B.
Three.
C.
Four.
D.
Five.
Correct Answer
C. Four.
Explanation The number of significant figures in 0.01500 is four because all non-zero digits are significant, and the zeros between the non-zero digits are also significant. In this case, the zeros before the 1 are not significant because they act as placeholders. Therefore, the significant figures in 0.01500 are 1, 5, 0, and 0.
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22.
The number of significant figures in 0.040 is
A.
One.
B.
Two.
C.
Three.
D.
Four.
Correct Answer
B. Two.
Explanation The number 0.040 has two significant figures because both the digits 4 and 0 are non-zero and are not leading or trailing zeros. The zeros in between the non-zero digits are also considered significant. Therefore, there are two significant figures in 0.040.
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23.
Which of the following has three significant figures?
A.
305.0 cm
B.
0.0500 mm
C.
1.00081 kg
D.
8.060 * 10^11 m^2
Correct Answer
B. 0.0500 mm
Explanation The number 0.0500 mm has three significant figures because all the zeros between the non-zero digits are significant. The zeros before the 5 are not significant because they are leading zeros. However, the zero after the 5 is significant because it is a trailing zero after a decimal point. Therefore, the number has three significant figures.
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24.
What is the sum of 2.67 + 1.976 + 2.1?
A.
6.7
B.
6.75
C.
6.746
D.
6.7460
Correct Answer
A. 6.7
Explanation The sum of 2.67, 1.976, and 2.1 is equal to 6.746. However, since the given options only include answers rounded to one decimal place, the closest option is 6.7.
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25.
What is the difference between 103.5 and 102.24?
A.
1.3
B.
1.26
C.
1.260
D.
1.2600
Correct Answer
A. 1.3
Explanation The difference between 103.5 and 102.24 is 1.26.
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26.
What is the product of 12.56 and 2.12?
A.
27
B.
26.6
C.
26.23
D.
26.627
Correct Answer
B. 26.6
Explanation The product of 12.56 and 2.12 is 26.6. To find the product, we multiply the two numbers together. In this case, 12.56 multiplied by 2.12 equals 26.6.
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27.
What is the result of 2.43 / 4.561?
A.
5.3278 * 10^(-1)
B.
5.328 * 10^(-1)
C.
5.33 * 10^(-1)
D.
5.3 * 10^(-1)
Correct Answer
C. 5.33 * 10^(-1)
Explanation The result of dividing 2.43 by 4.561 is 0.53278. In scientific notation, this can be written as 5.3278 * 10^(-1). However, the answer options are in rounded form, so the closest option is 5.33 * 10^(-1), which is the correct answer.
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28.
What is the cosine of 55°?
A.
0.6
B.
0.57
C.
0.574
D.
0.5736
Correct Answer
B. 0.57
Explanation The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. In this case, since we are given only the angle, we cannot determine the lengths of the sides of the triangle. However, we can use a calculator or a trigonometric table to find the cosine of 55 degrees, which is approximately 0.57.
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29.
The length and width of a rectangle are 1.125 m and 0.060 m, respectively. Multiplying, your calculator gives the product as 0.68175. Rounding properly to the correct number of signifiant figures, the area should be written as
A.
0.68 m^2.
B.
0.682 m^2.
C.
0.6818 m^2.
D.
0.68175 m^2.
Correct Answer
B. 0.682 m^2.
Explanation The length and width of the rectangle are given as 1.125 m and 0.060 m respectively. To find the area, we multiply the length and width. The product is calculated as 1.125 m * 0.060 m = 0.0675 m^2. Since we need to round properly to the correct number of significant figures, we look at the digit after the second decimal place, which is 7. Since it is greater than 5, we round up the previous digit. Therefore, the area should be written as 0.068 m^2. The closest option to this answer is 0.682 m^2.
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30.
The length and width of a rectangle are 1.125 m and 0.060 m, respectively. You calculate the rectangle's perimeter by adding these and multiplying by two. Your calculator's display reads 3.462. To the correct number of significant figures, this should be written as
A.
3.5 m.
B.
3.46 m.
C.
3.462 m.
D.
3.4620 m.
Correct Answer
C. 3.462 m.
Explanation The question asks for the correct number of significant figures, which means we need to determine how many digits are significant in the given number. In this case, the number 3.462 has 4 significant figures because all the digits (3, 4, 6, and 2) are known with certainty. Therefore, the correct answer is 3.462 m.
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31.
A rectangle is 3.25 m long and 1.5 m wide. What is its area?
A.
4.875 m^2
B.
4.87 m^2
C.
4.80 m^2
D.
4.9 m^2
Correct Answer
D. 4.9 m^2
Explanation The area of a rectangle is calculated by multiplying its length by its width. In this case, the length is given as 3.25 m and the width is given as 1.5 m. Multiplying these values together gives us an area of 4.875 m^2. Rounded to the nearest tenth, this is 4.9 m^2.
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32.
A rectangular garden measures 15 m long and 13.7 m wide. What is the length of a diagonal from one corner of the garden to the other?
A.
18 m
B.
19 m
C.
20 m
D.
4.1 * 10^2
Correct Answer
C. 20 m
Explanation The length of the diagonal of a rectangle can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the length and width of the rectangle form the two sides of the right triangle, and the diagonal is the hypotenuse. Therefore, the length of the diagonal can be found by calculating the square root of the sum of the squares of the length and width. In this case, the square root of (15^2 + 13.7^2) is approximately 20 m.
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33.
Select the smallest value.
A.
15 * 10^(-3)
B.
0.15 * 10^0
C.
0.00015 * 10^3
D.
0.00000015 * 10^6
Correct Answer
A. 15 * 10^(-3)
Explanation The given options represent values in scientific notation. In scientific notation, a number is expressed as a product of a decimal number between 1 and 10 and a power of 10. The smallest value can be determined by comparing the decimal numbers. In this case, 15 * 10^(-3) has the smallest decimal number (15), making it the smallest value among the given options.
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34.
Write the number 0.00045 in power of ten notation.
A.
4.5 * 10^(-4)
B.
4.5 * 10^(-3)
C.
4.5 * 10^(-2)
D.
4.5 * 10^(-1)
Correct Answer
A. 4.5 * 10^(-4)
Explanation The number 0.00045 can be written in power of ten notation as 4.5 * 10^(-4). This is because when we move the decimal point four places to the right, we get 4.5. Since the decimal point moved to the right, we need to represent this as a negative power of ten, which is -4. Therefore, the correct answer is 4.5 * 10^(-4).
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35.
0.0001776 can also be expressed as
A.
1.776 * 10^(-4)
B.
17.76 * 10^4
C.
1776 * 10^5
D.
177.6 * 10^7
Correct Answer
A. 1.776 * 10^(-4)
Explanation The given number, 0.0001776, can be expressed in scientific notation as 1.776 * 10^(-4). In scientific notation, a number is written in the form of a decimal number between 1 and 10, multiplied by a power of 10. In this case, 1.776 is the decimal number and -4 is the power of 10. The negative exponent indicates that the decimal point is moved to the left by 4 places, resulting in a smaller number.
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36.
4567.89 is properly expressed in scientific notation as
A.
4.56789 * 10^3.
B.
4.56789 * 10^2.
C.
4.56789 * 10^1.
D.
4.56789 * 10^0.
Correct Answer
A. 4.56789 * 10^3.
Explanation The given number, 4567.89, can be expressed in scientific notation by moving the decimal point three places to the left, resulting in 4.56789. The exponent represents the number of places the decimal point was moved, which in this case is 3. Therefore, the correct answer is 4.56789 * 10^3.
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37.
Convert 1.2 * 10^(-3) to decimal notation.
A.
1.200
B.
0.1200
C.
0.0120
D.
0.0012
Correct Answer
D. 0.0012
Explanation To convert a number in scientific notation to decimal notation, we move the decimal point to the right or left based on the exponent. In this case, the exponent is -3, so we move the decimal point 3 places to the left. Therefore, 1.2 * 10^(-3) in decimal notation is 0.0012.
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38.
Write out the number 8.42 * 10^(-5) in full with a decimal point and correct number of zeros.
A.
0.00000842
B.
0.0000842
C.
0.000842
D.
0.00842
Correct Answer
B. 0.0000842
Explanation The given correct answer is 0.0000842. This is because when we write out the number 8.42 * 10^(-5) in full with a decimal point and correct number of zeros, we move the decimal point 5 places to the left since the exponent is negative. This gives us 0.00000842. However, we need to remove the leading zeros, so the final answer is 0.0000842.
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39.
What is the result of (0.410 + 0.021) * (2.20 * 10^3)?
A.
880
B.
946
C.
948
D.
950
Correct Answer
C. 948
Explanation The given expression involves addition and multiplication. First, we add 0.410 and 0.021 to get 0.431. Then, we multiply this result by 2.20 * 10^3. When we multiply 0.431 by 2.20 * 10^3, we move the decimal point three places to the right and get 948. Therefore, the correct answer is 948.
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40.
Write the number 13.5 gigameters as full (decimal) numbers with standard units.
A.
135,000 m
B.
135,000,000 m
C.
135,000,000,000 m
D.
13,500,000,000 m
Correct Answer
D. 13,500,000,000 m
Explanation The given answer is 13,500,000,000 m. This is the correct conversion of 13.5 gigameters to meters. The prefix "giga" represents a factor of 1,000,000,000, so 13.5 gigameters is equal to 13,500,000,000 meters.
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41.
100 mL is equivalent to which of the following?
A.
1 kL
B.
10^(-6) μL
C.
0.1 L
D.
0.01 ML
Correct Answer
C. 0.1 L
Explanation 100 mL is equivalent to 0.1 L because there are 1000 mL in 1 L. Therefore, to convert mL to L, we divide the number of mL by 1000. In this case, 100 mL divided by 1000 equals 0.1 L.
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42.
How many grams is forty milligrams?
A.
0.000040 g
B.
0.00040 g
C.
0.040 g
D.
40000 g
Correct Answer
C. 0.040 g
Explanation Forty milligrams is equivalent to 0.040 grams. This can be determined by converting milligrams to grams. Since there are 1000 milligrams in a gram, dividing forty milligrams by 1000 will give the equivalent amount in grams, which is 0.040 grams.
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43.
How many meters is sixty kilometers?
A.
600,000 m
B.
60,000 m
C.
60 m
D.
0.06 m
Correct Answer
B. 60,000 m
Explanation One kilometer is equal to 1000 meters. Therefore, to convert kilometers to meters, we need to multiply the number of kilometers by 1000. In this case, sixty kilometers would be equal to 60,000 meters.
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44.
1 angstrom = 10^(-10) m and 1 fermi = 10^(-15) m, what is the relationship between these units?
A.
1 angstrom = 10^(5) fermi
B.
1 angstrom = 10^(-5) fermi
C.
1 angstrom = 10^(-25) fermi
D.
1 angstrom = 10^25 fermi
Correct Answer
A. 1 angstrom = 10^(5) fermi
Explanation The relationship between angstrom and fermi can be determined by comparing their magnitudes. Since 1 angstrom is equal to 10^(-10) m and 1 fermi is equal to 10^(-15) m, we can convert 1 angstrom to fermi by multiplying it by 10^(-15)/10^(-10), which simplifies to 10^(-5). Therefore, 1 angstrom is equal to 10^(-5) fermi.
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45.
0.00325 * 10^(-8) cm can also be expressed in mm as
A.
3.25 * 10^(-12) mm.
B.
3.25 * 10^(-11) mm.
C.
3.25 * 10^(-10) mm.
D.
3.25 * 10^(-9) mm.
Correct Answer
C. 3.25 * 10^(-10) mm.
Explanation The given expression represents a conversion from centimeters to millimeters. To convert from centimeters to millimeters, we multiply by 10. Since 0.00325 cm is being multiplied by 10^(-8), we need to multiply 0.00325 by 10^(-8) and then convert the result to millimeters by multiplying by 10. This gives us 3.25 * 10^(-10) mm.
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46.
Which one of the following is not equivalent to 2.50 miles?
(1 mi = 1.609, km = 5280 ft, 1 ft = 12 in.)
A.
1.32 * 10^4 ft
B.
1.58 * 10^5 in.
C.
4.02 * 10^3 km
D.
4.40 * 10^3 yd
Correct Answer
C. 4.02 * 10^3 km
Explanation To find the equivalent of 2.50 miles, we need to convert it to different units. 1 mile is equal to 5280 feet, so 2.50 miles is equal to 2.50 * 5280 = 13200 feet. 1 mile is also equal to 1.609 kilometers, so 2.50 miles is equal to 2.50 * 1.609 = 4.0225 kilometers. Therefore, the option that is not equivalent to 2.50 miles is 4.02 * 10^3 km, as it is slightly different from the actual value of 4.0225 kilometers.
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47.
If you are 5'10'' tall, what is your height in meters?
(1 in = 2.54 cm.)
A.
1.5 m
B.
1.6 m
C.
1.7 m
D.
1.8 m
Correct Answer
D. 1.8 m
Explanation To convert height from feet and inches to meters, we first need to convert feet to inches by multiplying by 12. So, 5 feet becomes 60 inches. Then, we add the remaining inches, which is 10 inches, to get a total of 70 inches. To convert inches to centimeters, we multiply by 2.54. So, 70 inches is equal to 177.8 cm. Finally, to convert centimeters to meters, we divide by 100. Therefore, a height of 5'10" is equal to approximately 1.78 meters. Since the closest option is 1.8 meters, that is the correct answer.
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48.
If 1 inch = 2.54 cm, and 1 yd = 36 in., how many meters are in 7.00 yd?
A.
6.40 m
B.
36.3 m
C.
640 m
D.
1.78 * 10^3 m
Correct Answer
A. 6.40 m
Explanation To convert yards to meters, we need to first convert yards to inches and then inches to centimeters, and finally centimeters to meters. Since 1 yard is equal to 36 inches, we can multiply 7 yards by 36 inches/yard to get the total inches. Next, we can convert the inches to centimeters by multiplying by the conversion factor of 2.54 cm/inch. Finally, to convert centimeters to meters, we divide by 100. By performing these calculations, we find that 7.00 yards is equal to 640 centimeters or 6.40 meters.
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49.
A hot air balloon rises to an altitude of 600 fathoms. What is this height, in feet?
(1 fathom = 6 ft.)
A.
100 ft
B.
600 ft
C.
1200 ft
D.
3600 ft
Correct Answer
D. 3600 ft
Explanation The hot air balloon rises to an altitude of 600 fathoms. Since 1 fathom is equal to 6 feet, we can calculate the height in feet by multiplying the number of fathoms by 6. Therefore, 600 fathoms multiplied by 6 feet equals 3600 feet.
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50.
The average life of an animal is 70 years. Assume one numerical figure, write this in power of ten in seconds.
A.
3 * 10^7 s
B.
2 * 10^7 s
C.
2 * 10^9 s
D.
3 * 10^9 s
Correct Answer
C. 2 * 10^9 s
Explanation The average life of an animal is 70 years, which can be converted to seconds by multiplying it by the number of seconds in a year (365 days * 24 hours * 60 minutes * 60 seconds). This calculation results in a very large number, approximately 2 * 10^9 seconds.
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