Module 3: Chapter 1: Understanding Number Systems and Operations
Estimate the sum of $7.87 + $2.32 by rounding to the nearest whole number. $9.00 $10.00 $11.00 $12.00
$10.00 Round each of the numbers to the nearest whole number before adding them together.
A patient's prescriptions are $3.74, $7.28, $12.01, and $15.27. Rounding to the nearest whole dollar, how much do you estimate the patient will pay for their prescriptions? $38.30 $38.00 $37.30 $37.00
$38.00 Rounded, $4.00 + $7.00 + $12.00 + $15.00 = $38.00
Rewrite 1.02 x 10'3 using standard notation. 1,020 10,200 10.2 0.00102
1,020 Since the exponent three is a positive number, the decimal will be moved to the right three places.
A patient is receiving the following fluids: 1,248 mL of normal saline, 100 mL of coffee, and 175 mL of juice. Estimate the patient's fluid intake to the nearest 10 mL. (Note: the abbreviation mL stands for milliliter.) 1,523 mL 1,530 mL 1,500 mL 1,520 mL
1,150 mL Estimating to the nearest 10 mL means you should round each number to the nearest tens place before adding them together. Therefore, 1,250 mL + 100 mL + 180 mL = 1,150 mL.
A patient consumed 1,248 mL of IV fluids, 204 mL of juice, 120 mL of milk, and 167 mL of coffee in the last 24 hours. Calculate the patient's total fluid intake to the nearest hundreds place. (Note: The abbreviation mL means "milliliter.") 2,000 1,700 1,500 1,200
1,700 Round each of the numbers to the nearest 100 before adding them together.
How many significant figures are in the number 109.8? 1 2 3 4
4 In this case, the zero will be counted as a significant figure because it is necessary to convey the accuracy of this number.
Reduce 42/10 to the lowest terms. Rewrite the fraction as a mixed number, if necessary. 22/5 4 1/5 4 2/10 2 1/15
4 1/5 The numerator (42) and the denominator (10) can both be divided evenly by 2, resulting in 21/5. The denominator (5) can be divided into the numerator (21) four times evenly with 1 remaining. The 1 is kept over the same denominator (5) and 4 becomes the whole number. The answer is 4 1/5.
Determine how many significant figures the number 1.3074 has after being rounded to the nearest thousandth. 1 significant figure 2 significant figures 3 significant figures 4 significant figures
4 significant figures Significant figures are the digits of a number that contribute to the degree of accuracy of the value. Since the 0 (zero) is located between two other numbers., it is included as a significant figure.
What is the difference between 82.71 - 42.1? 4.061 7.85 78.5 40.61
40.61 Be sure to line up the decimals in each number and fill in the empty spaces with zeros before subtracting. Carry the decimal point straight down.
A patient consumed 212 mL of water, 130 mL of juice and 95 mL of milk in the last day. Estimate the patient's intake to the nearest 100 mL. (Note: the abbreviation mL stands for milliliter. 437 mL 400 mL 500 mL 450 mL
400 mL By rounding to th nearest 100 mL you will estimate: 200 mL + 100 mL + 100 mL = 400 mL
What is the sum of 28.79 + 12.5? 41.29 30.04 3.004 4.129
41.29 Be sure to line up the decimals in each number and fill in the empty spaces with zeros before adding. Carry the decimal straight down.
Your patient calls into the pharmacy and asks for an estimate on how much their prescriptions will cost to pick up. Estimate the patient's cost to the nearest whole dollar. Levothyroxine: $2.38; Lisinopril: $7.98; Sotalol: $21.47; Simvastatin: $12.77; Torsemide: $25.21 $69.61 $70.00 $69.00 $72.00
$69.00 By rounding to the nearest whole dollar you will estimate: $2 + $8 + $21 + $13 + $25 = $69.
The pharmacy needs to place an order for the following supplies. Estimate the total cost by rounding to the nearest whole dollar. Cherry Flavoring: $4.28 4 gallons of Distilled Water: $0.93 per gallon Paper Towels: $7.28 Ointment Jars: $21.78 Empty Capsules: $34.65 $73.00 $70.00 $72.22 $69.46
$70.00 First round each value to the nearest whole dollar. It is important to note that $0.93 is the price for one gallon of distilled water and your pharmacy needs to order 4 (four). Therefore, $4 + ($1 + $1 + $1 + $1) + $8 + $22 + $35 = $73.
A patient calls into the pharmacy and asks for an estimated cost of the following prescriptions that are ready to be picked up. What is the estimated cost that you will tell them? Round to the nearest whole dollar glipizide $10.32 metformin $4.28 tamsulosin $44.78 lisinopril $21.62 $83.00 $79.00 $81.00 $80.00
$81.00 Round each of the numbers to the nearest whole number before adding them together.
Write 9.37 × 10'-3 using standard notation. 0.0937 0.00937 937 9370
0.00937 A negative exponent of 3 indicates that you should move the decimal to the left three places.
Round 0.01923 to three significant figures. 0.0192 0.019 0.02 0.01923
0.0192 The zeros before and after the decimal do not count as significant figures.
What is 0.0988 rounded to the nearest tenth? 0 0.9 0.1 0.09
0.1 The tenths place is the first number after the decimal. Therefore, the 8 in the hundredths place rounds the 9 up and the 0 in the tenths place becomes a 1 and the answer is 0.1.
Express 3/8 in decimal form. Round to the nearest thousandth. 0.375 0.37 0.3 0.4
0.375 To convert 3/8 to a decimal, set up the following calculation: 3 ÷ 8. The answer is 0.375.
Convert 12/13 to decimal form and round your answer to the nearest thousandth. 1 0.900 0.922 0.923
0.923 To convert 12/13 to a decimal, set up the following calculation: 12 ÷ 13. The answer is 0.92307, which rounds to 0.923.
A unit dose of levothyroxine contains 200 mcg. If this number is accurate to the nearest 100, how many significant figures does this number have? (Note: the abbreviation mcg stands for microgram.) 1 2 3 4
1 In this case, the two 0's (zeros) are not included as significant figures because the amount is accurate to the nearest 100.
What is the simplified sum of 3/4 + 2/3 + 3/12? 20/12 1 2/3 1 8/12 2/3
1 2/3 First, you must find the common denominator for each of the fractions. 4, 2, and 12 can be divided evenly into 12. Next, what is done to the denominator must also be done to the numerator. For the fraction 3/4: 4 x 3 = 12. Therefore, you must multiply the numerator by 3 as well (3 x 3 = 9). Now, 3/4 is 9/12. Next, do the same to the numerator of the second fraction (2/3) as you did to the denominator. 3 x 4 = 12 so you must multiply the numerator by the same (2 x 4 = 8). Now, 2/3 is 8/12. 3/12 is already in lowest terms. Finally, add the fractions together: 9/12 + 8/12 + 3/12 = 20/12. To find the simplified sum, we must reduce this fraction to the lowest terms which is 1 2/3.
You have three orders calling for distilled water. The first order calls for 1/2 fluid ounce, the second calls for 2/3 fluid ounce, and the third calls for 1/4 fluid ounce. How much total distilled water will you need to fill these orders? 1 5/12 19/12 4/9 19/36
1 5/12 Find the least common denominator. In this case it is 12. Add the numerators and keep the common denominator. The answer is 17/12, reduced to its lowest terms is 1 5/12.
What is the simplified sum of 5/8 + 2/3? 15/24 1 12/24 1 7/24 7/11
1 7/24 First, find the least common denominator. In this case it would be 24. Then multiply the numerators by the same factor as the denominators to get two fractions with common denominators, 15/24 + 16/24. Add the numerators and keep the denominator the same, resulting in 31/24. The simplified sum would be written as a mixed number: 1 7/24.
A patient takes one half (1/2) of a 1 mg tablet three times daily. How many milligrams total does the patient take in one day? (Note the abbreviation mg stands for milligram.) 0.5 mg 1 mg 1.5 mg 3 mg
1.5 mg 1 mg / 2 = 0.5 mg per dose. 0.5 mg x 3 doses = 1.5 mg daily.
What is the product of 1.3 x 1.2 rounded to the nearest tenth? 2 1.56 1.6 1.7
1.6 1.3 x 1.2 = 1.56. The 6 in the hundredths place rounds the 5 up., and the answer is 1.6.
Reduce 3/36 to it's lowest terms. 3/13 3/12 9/108 1/12
1/12 The fraction can be reduced by dividing the numerator by 3, giving you a numerator of 1. What we do to the numerator must be the same for the denominator. The denominator must be divided by 3. So, 36 / 3 = 12. Therefore, you are left with 1/12.
Which fraction has the largest value? 1/2 1/16 1/4 1/8
1/2 Find the least common denominator for each fraction. In this case it is 16. 8/16 is the largest value of out of 8/16, 1/16. 4/16, 2/16.
Which of these fractions has the largest value? 1/3 1/6 1/9 1/18
1/3 When comparing fractions with the same numerator, the fraction with the smaller denominator has the larger value.
What is the simplified product of 5/8 x 2/5? 10/40 2/5 1/4 4/5
1/4 When multiplying fractions, you must multiply the two numerators and then multiply the two denominators. Be sure to keep these numbers in the respective numerator or denominator positions. Therefore, 5 x 2 = 10 and 8 x 5 = 40. Your answer is 10/40 and it should be simplified by dividing the numerator and denominator by 10. Therefore, the answer is 1/4.
What is 12.469 rounded to the nearest hundredth? 12 12.5 12.47 12.469
12.47 The hundredths place is the second number after the decimal. Therefore, the 9 in the thousandths place rounds the 6 in the hundredths place up to 7. The answer is 12.47.
If a patient split a scored 250 mg tablet in half, how many milligrams would each half contain? (Note: mg means "milligrams.") 500 mg 250 mg 125 mg 25 mg
125 mg 250 ÷ 2 = 125. Therefore, half of a 250 mg tablet would mean each half contains 125 mg.
You must prepare the following five orders that require reconstitution. Estimate the total amount of sterile water for injection (SWFI) that you will need to complete these orders by rounding to the nearest whole number. Which SWFI vial size will you use to ensure you have enough to complete all the orders? (Note: the abbreviation mL stands for milliliter.) Order 1 for 4.2 mL; Order 2 for 1.8 mL; Order 3 for 2.2 mL; Order 4 for 3.9 mL; Order 5 for 2.5 mL 10 mL 15 mL 20 mL 30 mL
15 mL By rounding to the nearest whole number you will estimate 4 + 2 + 2+ 4 + 3 = 15.
What is the simplified product of 3/12 × 5/6? 8/18 18/60 15/72 3/10
15/72 Multiply the numerators (3 × 5 = 15) and the denominators (12 × 6 = 72); the result is 15/72. This fraction is in simplest form.
What is the least common denominator between: 1/8, 3/4, 1/2, and 5/16? 2 4 8 16
16 Each of these fractions' denominators can be evenly divided into 16
What is the least common denominator shared by 1/2, 3/4, 5/16? 2 4 8 16
2 A common denominator is the lowest number into which each of the denominators can be divided evenly. In this case, 2, 4, and 16 can evenly be divided into 16.
In the decimal 483.219, which digit is in the tenths place? 8 2 1 9
2 The tenths place is the first place after the decimal.
What is the simplified quotient of 6/7 ÷ 1/3? 126/21 2/7 2 4/7 2 1/7
2 4/7 Invert the second fraction so you will be multiplying by the reciprocal (inverse) of 1/3. Then you multiply 6/7 × 3/1. Multiply the numerators together and the denominators together to get 18/7. Now, 7 can be divided into 18 twice with 4 remaining. 2 becomes the whole number and 4 is carried over the original denominator of 7. The answer is 2 4/7.
A patient takes two lorazepam 0.5 mg tablets in the morning and in the evening. What is the patient's total daily dose in milligrams? (Note: the abbreviation mg stands for milligram.) 1 mg daily 2 mg daily 0.5 mg daily 1.5 mg daily
2 mg daily 2 tablets x 0.5 mg each = 1 mg. 1 mg x 2 times a day = 2 mg total in one day.
Write 0.0000219 using scientific notation. 2.19 × 10'-4 2.19 × 10'-5 2.19 × 10'4 2.19 × 10'5
2.19 × 10'-5 Move the decimal point to the right until it is one place to the right of the two. Since the decimal point was moved to the right the exponent will be negative.
Rewrite 0.00000231 using scientific notation. 2.31 x 10'2 2.31 x 10'-3 2.31 x 10'-4 2.31 x 10'-6
2.31 x 10'-6 Since the decimal is being moved from the left to the right to make the number 2.31 (the lowest known place value) the exponent will be negative. The decimal is moved 6 places.
What is the quotient of 15 ÷ 5.2 rounded to the nearest thousandth? 3 2.88 2.885 2.9
2.885 15 / 5.2 is 2.8846. The 6 rounds the 4 in the thousandths place up to 5.
What is the simplified difference of 12/15 - 2/5? 2/5 18/15 1 3/15 1/2
2/5 Find the least common denominator, 15. Multiply the numerator and denominator by the same factor to get two fractions with the same denominator. In this case the result is 12/15 - 6/15. Subtract the numerators and keep the denominator the same. The result is 6/15, which can be reduced to 2/5.
Estimate the quotient of 188.7 ÷ 9.1 by rounding to the nearest whole number. 21 20.7 20.9 20
21 Round each of the numbers to the nearest whole number before dividing.
Write the number two hundred sixty-one and fifteen hundredths in decimal form. 261.015 261.15 261.00015 261.0015
261.15 The whole number part of the decimal (two hundred sixty-one) should appear to the left of the decimal point. The fractional part of the decimal (fifteen hundredths) should appear to the right of the decimal point. The hundredths place occupies two place values to the right of the decimal point.
What is the product of 21.02 × 1.3? Round your answer to the nearest thousandth. 27.3 27.326 27.334 27.129
27.326 Multiply the decimal numbers the same way you would multiply whole numbers and omit the decimal places until the last step of the calculation. Add the total number of decimal places that are in the two numbers being multiplied, count that number of places from right to left in the answer, and insert a decimal point.
Estimate the product of 423.1 × 7.8 by rounding to the nearest whole number. 3,300 3,384 3,200 2,961
3,384 Round each of the numbers to the nearest whole number before multiplying. 423X8=3,384
Write 32,100,000,000 using scientific notation. 3.21 × 10'-8 3.21 × 10'-10 3.21 × 10'8 3.21 × 10'10
3.21 × 10'10 Move the decimal point to the left until you have a number with one digit in front of the decimal (in this case that is 10 places). Since the decimal has moved to the left, your exponent will be positive.
What is the simplified product of 1/8 × 3/4? 1/8 4/24 3/32 1/12
3/32 Multiply the numerators together and then then multiply the denominators together.
A patient's prescription calls for XXX tablets to be dispensed, how many tablets will you dispense? 30 10 50 40
30 The Roman numeral X represents the number 10 (ten), therefore, 10 + 10 + 10 = 30.
What is the Arabic number for XXXII? 33 32 28 22
32 The Roman numeral X represents the number 10 (ten) and the Roman numeral I represents the number 1 (one). Therefore, 10 + 10 + 10 + 1 + 1 = 32.
What is the product of 2.61 × 14? Retain the correct number of significant figures in your answer. 36.54 36.5 36.4 36
36.5 Multiply the decimal numbers the same way you would multiply whole numbers and omit the decimal places until the last step of the calculation. Count the number of significant figures in each number and identify which number has the highest amount of significant figures (in this case it is 2.61). Keep this amount of significant figures (in this case it is 3) in your answer.
How many significant figures are in the number 1.021? 1 2 3 4
4 In this case, the zero will be counted as a significant figure because it is necessary to convey the accuracy of this number.
What is the Arabic number for CDXIV? 416 414 164 144
414 The Roman numeral C represents the number 100 (one hundred), and it is to the left of Roman numeral D, which represents the number 500 (five hundred). This configuration means you should subtract 100 from 500 leaving you with 400. Next, the Roman numeral X represents the number 10 (ten). The Roman numeral I represents the number 1 (one), and it is to the left of Roman numeral V, which represents the number 5 (five). Again, this configuration of a lesser number to the left of a larger number means you should subtract so, IV represents the number 4 (four). Therefore, (500 - 100) + 10 + (5 - 1) = 414
What is the Arabic number for CDXVI? 416 116 414 66
416 Roman numeral D represents 500 (five hundred). Since there is a C, which represents 100 (one hundred), to the left of the D you must subtract 100 from 500 which equals 400. X represents 10 (ten), V represents 5 (five), and I represents 1 (one). Therefore, (500 - 100) + 10 + 5 + 1 = 416.
Which number is the standard notation for 4.21 x 10 to the 5th power? 4,210 42,100 421,000 4,210,000
421,000 A positive exponent of 5 means you will move the decimal five places to the right.
What is the quotient of 12.42 ÷ 2.2? Round your answer to the nearest thousandth. 5.655 5.645 5.600 5.000
5.645 Change both the divisor (the number you are dividing by) and the dividend (the number being divided) to whole numbers by moving their decimal points the same number of places to the right. Since 12.42 has more digits, move its decimal point a sufficient number of places to make it a whole number. Then move the decimal point of 2.2 the same number of places, adding a zero at the end.
A physician writes a prescription with the amount to be dispensed as LVI. How many tablets will you dispense? 506 104 56 54
56 The Roman numeral L represents the number 50 (fifty). The Roman numeral V represents the number 5. The Roman Numeral I represents the number 1 (one). Therefore, 50 + 5 + 1 = 56
How many significant figures are in the number 1204.3900? 4 5 6 7
6 The two trailing zeros do not add to the accuracy of the value, so they are not included as significant figures. The 0 (zero) found in the number (between the 2 and 4) does add to the accuracy of the values so it is included as a significant figure.
Calculate the product of 0.55 x 12.3 and retain the appropriate number of significant figures. 6.765 7 6.8 6.77
6.77 The product of 6.765 is accurate to significant figure of the hundredths place.
Round 621.49 to the nearest tenths place. 621.49 621.4 621.5 621
621.5 The tenths place is the first place after the decimal. The 9 in the hundredths place rounds the 4 in the tenths place up to 5.
What is the Arabic number for DCXXIV? 174 424 624 626
624 Roman numeral D represents 500 (five hundred), C represents 100 (one hundred), and X represents 10 (ten). I represents 1 (one) and it is found to the left of the larger value V, which represents 5 (five), so it must be subtracted. Therefore, 500 + 100 + 10 + 10 + (5 - 1) = 624
What is the product of 7.41 × 9? Retain the appropriate number of significant figures. 66.7 66.69 6.67 6.669
66.7 Multiply the decimal numbers the same way you would multiply whole numbers and omit the decimal places until the last step of the calculation. Count the number of significant figures in each number and identify which number has the highest amount of significant figures (in this case it is 7.41). Keep this amount of significant figures in your answer (in this case it is three).
A physician writes a prescription for LXXIII tablets of prednisone to be dispensed. How many tablets are needed to fill the prescription? 43 53 63 73
73 Roman numeral L represents 50 (fifty), X represents 10 (ten), and I represents 1 (one). Therefore, 50 + 10 + 10 + 1 + 1 + 1 = 73
A physician orders a prescription for metformin with XC tablets to be dispensed. How many tablets are needed to fill the prescription? 110 90 80 60
90 Roman numeral X, which represents 10 (ten), is located to the left of the Roman numeral C, which represents 100 (one hundred), meaning that 10 (ten) should be subtracted from 100 (one hundred). Therefore, 100 - 10 = 90.
Convert 192 to Roman numerals. XCCII LLLXXXXII CXCII CLXXXXII
CXCII Roman numeral C represents 100 (one hundred). Since 90 is closer to 100 than to 50 we should use the Roman numeral for 100 and subtract 10 by placing the Roman numeral X to the left of Roman numeral C. I represents 1 (one). Therefore, 100 + (100 - 10) + 1 + 1 = 192.
What is the Roman numeral for 120? XX LXX CXX DXX
CXX The number 100 is represented by the letter C. The number 20 is represented by the letters XX. Because X = 10, and 10 + 10 = 20. Therefore CXX (or 100 + 10 + 10) represents the number 120.
What is the Roman numeral for 802? DCII DDCII DCCI DCCCII
DCCCII Roman numeral D represents 500 (five hundred), C represents 100 (one hundred), and I represents 1 (one). Therefore, 500 + 100 + 100 + 100 + 1 + 1 = 802.
What is the Roman numeral for 723? DXXIII DCCXXIII DCXI CCXII
DCCXXIII Using multiples of 100 and 500, the number 700 is broken down into 500 + 100 + 100. Using multiples of 10 the number 20 can be broken down to 10 + 10. The number 500 is represented by the letter D. The number 100 is represented by the letter C. The number 10 is represented by the letter X. The number 1 is represented by the letter I. Therefore, DCCXXIII (or 500 + 100 + 100 + 10 + 10 + 1 + 1 + 1) represents the number 723.
What is the Roman numeral for 84? LXXXIV XXCIV LXIV LXXXIIII
LXXXIV Roman numeral L represents 50 (fifty), X represents 10 (ten), I represents 1 (one), and V represents 5 (five). Since the I is to the left of the V it should be subtracted. Therefore, 50 + 10 + 10 + 10 + (5 - 1) = 84
For a decimal number with a value less than one, a leading zero should be a. used to prevent errors. b. avoided to prevent errors. c. used because the value of the number would change without it. d. avoided because the value of the number would change.
a. used to prevent errors. When a decimal number has a value less than one, a leading zero should be used to prevent errors. For example: .5 can easily be mistaken for the number 5. Whereas, 0.5 more clearly identifies five-tenths, or one-half.
