Transcript Study Guide for Dilutions and Concentrations problems
DILUTION PROBLEM ONE: Prepare a serial 2 fold dilution to 1:64
• • • • • Draw a test tube. Under it, write “1” and a colon. Why do we write a “1”? That is the number to the left of the colon in our problem 1:64. We will continue to use a “1” for the entire series. The “1” represents how many ml we are putting into each tube.
How many fold does the problem say? Write that fold number (2) to the right of the colon under the test tube.
Write “1ml” above an arrow going into the test tube.
Take the number to the right of the colon (2) and subtract by the number of ml going into the test tube (1) to get the total volume of the inside of the test tube (2-1 = 1 ml total volume). Write the total volume on the inside of the test tube.
There is a picture illustrating this on the next slide.
DILUTION PROBLEM ONE: Prepare a serial 2 fold dilution to 1:64
• • • • Draw a test tube. Under it, write “1” and a colon. Write the fold number (2) to the right of the colon under the test tube.
Write “1ml” above an arrow going into the test tube.
Write the total volume on the inside of the test tube.
1 ml 1 ml 1:2
• • • • •
DILUTION PROBLEM ONE:
Prepare a serial 2 fold dilution to 1:64
Draw a second test tube. Under it, write “1” and a colon. To find the number to the right of that colon, multiply the fold number (2) with the number that is to the right of the colon under the first test tube (2 x 2 = 4).
Write “1ml” above an arrow going into the second test tube, and repeat this for each additional test tube we will do.
Inside the second test tube, write the same number for total volume as you did for the first test tube (1ml). The total volume will also be the same for each additional test tubes we will do. Are we done yet? No, the number to the right of the colon has to get to 64.
The next slide shows what your drawing should now look like.
DILUTION PROBLEM ONE: Prepare a serial 2 fold dilution to 1:64
• • • • Draw a second test tube. Under it, write “1” and a colon. Multiply the fold number (2) with the number that is to the right of the colon under the first test tube (2 x 2 = 4).
Write “1ml” above an arrow going into the test tube.
Write the total volume on the inside of the test tube.
1 ml 1 ml Are we done yet? No, the number to the right of the colon has to get to 64.
1 ml 1:2 1 ml 1:4
DILUTION PROBLEM ONE: Prepare a serial 2 fold dilution to 1:64
• • • • Draw another test tube. Under it, write “1” and a colon. Multiply the fold number (2) with the number that is to the right of the colon under the previous test tube (2 x 4 = 8).
Write “1ml” above an arrow going into the test tube.
Write the total volume on the inside of the test tube.
1 ml 1 ml 1 ml 1 ml 1:2 1 ml 1:4 1 ml 1:8
DILUTION PROBLEM ONE: Prepare a serial 2 fold dilution to 1:64
• • • • Draw another test tube. Under it, write “1” and a colon. Multiply the fold number (2) with the number that is to the right of the colon under the previous test tube (2 x 8 = 16).
Write “1ml” above an arrow going into the test tube.
Write the total volume on the inside of the test tube.
1 ml 1 ml 1 ml 1 ml 1 ml 1:2 1 ml 1:4 1 ml 1:8 1 ml 1:16
DILUTION PROBLEM ONE: Prepare a serial 2 fold dilution to 1:64
• • • • Draw another test tube. Under it, write “1” and a colon. Multiply the fold number (2) with the number that is to the right of the colon under the previous test tube (2 x 16 = 32).
Write “1ml” above an arrow going into the test tube.
Write the total volume on the inside of the test tube.
1 ml 1 ml 1 ml 1 ml 1 ml 1 ml 1:2 1 ml 1:4 1 ml 1:8 1 ml 1:16 1 ml 1:32
DILUTION PROBLEM ONE: Prepare a serial 2 fold dilution to 1:64
• • • • Draw another test tube. Under it, write “1” and a colon. Multiply the fold number (2) with the number that is to the right of the colon under the previous test tube (2 x 32 = 64).
Write “1ml” above an arrow going into the test tube.
Write the total volume on the inside of the test tube.
1 ml 1 ml 1 ml 1 ml 1 ml 1 ml Are we done yet? YES!
1 ml 1:2 1 ml 1:4 1 ml 1:8 1 ml 1:16 1 ml 1:32 1 ml 1:64
DILUTION PROBLEM TWO:
Prepare a serial 10 fold dilution to 1:10,000 • • • • • Draw a test tube. Under it, write “1” and a colon.
How many fold? Write that fold number (10) to the right of the colon under the test tube.
Write “1ml” above an arrow going into the test tube.
Take the number to the right of the colon (10) and subtract by the number of ml going into the test tube (1) to get the total volume of the inside of the test tube (10-1 = 9 ml total volume). Write the total volume on the inside of the test tube.
A picture illustrating this is on the next slide.
DILUTION PROBLEM TWO: Prepare a serial 10 fold dilution to 1:10,000
• • • • Draw a test tube. Under it, write “1” and a colon. Write the fold number (10) to the right of the colon under the test tube.
Write “1ml” above an arrow going into the test tube.
Write the total volume on the inside of the test tube.
1 ml 9 ml 1:10
DILUTION PROBLEM TWO:
Prepare a serial 10 fold dilution to 1:10,000 • • • • • Draw a second test tube. Under it, write “1” and a colon. To find the number to the right of that colon, multiply the fold number (10) with the number that is to the right of the colon under the first test tube (10 x 10 = 100).
Write “1ml” above an arrow going into the second test tube, and repeat this for each additional test tube we will do.
Inside the second test tube, write the same number for total volume as you did for the first test tube (9ml). The total volume will also be the same for each additional test tubes we will do. Are we done yet? No, the number to the right of the colon has to get to 10,000. A picture illustrating this is on the next slide.
• • • •
DILUTION PROBLEM TWO: Prepare a serial 10 fold dilution to 1:10,000
Draw a second test tube. Under it, write “1” and a colon. Multiply the fold number (10) with the number that is to the right of the colon under the first test tube (10 x 10 = 100).
Write “1ml” above an arrow going into the test tube.
Write the total volume on the inside of the test tube.
1 ml 1 ml 9 ml 9 ml 1:10 1:100
• • • •
DILUTION PROBLEM TWO: Prepare a serial 10 fold dilution to 1:10,000
Draw another test tube. Under it, write “1” and a colon. Multiply the fold number (10) with the number that is to the right of the colon under the previous test tube (10 x 100 = 1000).
Write “1ml” above an arrow going into the test tube.
Write the total volume on the inside of the test tube.
1 ml 1 ml 1 ml 9 ml 1:10 9 ml 9 ml 1:100 1:1000
• • • •
DILUTION PROBLEM TWO: Prepare a serial 10 fold dilution to 1:10,000
Draw another test tube. Under it, write “1” and a colon. Multiply the fold number (10) with the number that is to the right of the colon under the previous test tube (10 x 1000 = 10,000).
Write “1ml” above an arrow going into the test tube.
Write the total volume on the inside of the test tube.
1 ml 1 ml 1 ml 1 ml 9 ml 1:10 9 ml 9 ml 9 ml 1:100 1:1000 1:10,000
DILUTION PROBLEM THREE:
Prepare a serial 5 fold dilution to 1:3125 • • • • • Draw a test tube. Under it, write “1” and a colon.
How many fold? Write that fold number (5) to the right of the colon under the test tube.
Write “1ml” above an arrow going into the test tube.
Take the number to the right of the colon (5) and subtract by the number of ml going into the test tube (1) to get the total volume of the inside of the test tube (5-1 = 4 ml total volume). Write the total volume on the inside of the test tube.
A picture illustrating this is on the next slide.
DILUTION PROBLEM THREE: Prepare a serial 5 fold dilution to 1:3125
• • • • Draw a test tube. Under it, write “1” and a colon. Write the fold number (5) to the right of the colon under the test tube.
Write “1ml” above an arrow going into the test tube.
Write the total volume on the inside of the test tube.
1 ml 4 ml 1:5
DILUTION PROBLEM THREE:
Prepare a serial 5 fold dilution to 1:3125 • • • • • Draw a second test tube. Under it, write “1” and a colon. To find the number to the right of that colon, multiply the fold number (5) with the number that is to the right of the colon under the first test tube (5 x 5 = 25).
Write “1ml” above an arrow going into the second test tube, and repeat this for each additional test tube we will do.
Inside the second test tube, write the same number for total volume as you did for the first test tube (4ml). The total volume will also be the same for each additional test tubes we will do. Are we done yet? No, the number to the right of the colon has to get to 3125.
A picture illustrating this is on the next slide.
• • • •
DILUTION PROBLEM THREE:
Prepare a serial 5 fold dilution to 1:3125
Draw a second test tube. Under it, write “1” and a colon. Multiply the fold number (5) with the number that is to the right of the colon under the first test tube (5 x 5 = 25).
Write “1ml” above an arrow going into the test tube.
Write the total volume on the inside of the test tube.
1 ml 1 ml 4 ml 4 ml 1:5 1:25
• • • •
DILUTION PROBLEM THREE:
Prepare a serial 5 fold dilution to 1:3125
Draw another test tube. Under it, write “1” and a colon. Multiply the fold number (5) with the number that is to the right of the colon under the previous test tube (5 x 25 = 125).
Write “1ml” above an arrow going into the test tube.
Write the total volume on the inside of the test tube.
1 ml 1 ml 1 ml 4 ml 1:5 4 ml 1:25 4 ml 1:125
• • • •
DILUTION PROBLEM THREE:
Prepare a serial 5 fold dilution to 1:3125
Draw another test tube. Under it, write “1” and a colon. Multiply the fold number (5) with the number that is to the right of the colon under the previous test tube (5 x 125 = 625).
Write “1ml” above an arrow going into the test tube.
Write the total volume on the inside of the test tube.
1 ml 1 ml 1 ml 1 ml 4 ml 1:5 4 ml 1:25 4 ml 1:125 4 ml 1:625
• • • •
DILUTION PROBLEM THREE:
Prepare a serial 5 fold dilution to 1:3125
Draw another test tube. Under it, write “1” and a colon. Multiply the fold number (5) with the number that is to the right of the colon under the previous test tube (5 x 625 = 3125).
Write “1ml” above an arrow going into the test tube.
Write the total volume on the inside of the test tube.
1 ml 1 ml 1 ml 1 ml 1 ml 4 ml 1:5 4 ml 1:25 4 ml 4 ml 4 ml 1:125 1:625 1:3125
CONCENTRATION PROBLEM ONE: What is the concentration of a suspension that results in
35 colonies on a plate with a dilution factor of 1:164?
• • • • • Multiply Colonies x Dilution Factor (35 x 164 = 5740). Are we done yet? No.
Move the decimal point on your answer over so there is only one digit to the left of the decimal point (5.740). Are we done yet? No.
Count the number of spaces you moved the decimal point over (3). This becomes the superscript number above your power of 10 (write 5.740 x 10 3 ). Are we done yet? No.
We will just record our final answer with two significant digits to the right of the decimal point, so look at the third number to the right of the decimal point. If it is 5 or higher, change the second to the last number to the right of the decimal point to one digit higher. If it was less than 5, don’t do anything to the second digit to the right of the decimal point. Then drop all the other digits except the first two to the right of the decimal point. Are we done yet? No.
Write the units (organisms/ml). Are we done yet? YES!
CONCENTRATION PROBLEM TWO: What is the concentration of a suspension that results in
16 colonies on a plate with a dilution factor of 1:320?
• • • • • Multiply Colonies x Dilution Factor (16 x 320 = 5120). Are we done yet? No.
Move the decimal point on your answer over so there is only one digit to the left of the decimal point (5.120). Are we done yet? No.
Count the number of spaces you moved the decimal point over (3). This becomes the superscript number above your power of 10 (write 5.120 x 10 3 ). Are we done yet? No.
Round off the second digit to the right of the decimal point if the third digit is 5 or higher, then drop the third number to the right of the decimal point, leaving just two numbers to the right of the decimal point. Are we done yet? No.
Write the units (organisms/ml). Are we done yet? YES!
CONCENTRATION PROBLEM THREE: What is the concentration of a suspension that results in
237 colonies on a plate with a dilution factor of 1:486?
• • • • • Multiply Colonies x Dilution Factor (237 x 486 = 115,182). Are we done yet? No.
Move the decimal point on your answer over so there is only one digit to the left of the decimal point (1.15182). Are we done yet? No.
Count the number of spaces you moved the decimal point over (5). This becomes the superscript number above your power of 10 (write 1.15182 x 10 5 ). Are we done yet? No.
Round off the second digit to the right of the decimal point as needed, then drop the rest of the numbers to the right of the decimal point, leaving just two numbers to the right of the decimal point. Are we done yet? No.
Write the units (organisms/ml). Are we done yet? YES!
EXTRA CONCENTRATION PROBLEM (not on study guide):
What is the concentration of a suspension that results in
70 colonies on a plate made with 0.1 dilution from a culture with a dilution of 1:10,000?
• • • • • First convert to ml (10,000 ÷ 0.1 = 100,000) Multiply Colonies x Dilution Factor (70 x 100,000 = 7,000, 000). Are we done yet? No.
Move the decimal point on your answer over so there is only one digit to the left of the decimal point 7.0 (you need to move the decimal over 6 places). By the way, we have only one significant figure (one number to the right of the decimal point) this time because the smallest number we were given in the problem was 0.1, and that is only one figure to the right of the decimal point. Make sure you round off that last digit as needed. Are we done yet? No.
Count the number of spaces you moved the decimal point over (6). This becomes the superscript number above your power of 10 (write 7.0 x 10 6 ). Are we done yet? No.
Write the units (organisms/ml). Are we done yet? YES!
• • • • •
EXTRA CONCENTRATION PROBLEM (not on study guide):
What is the concentration of a suspension that results in
90 colonies on a plate made with 0.01 dilution from a culture with a dilution of 1:10,000?
First convert to ml (10,000 ÷ 0.01 = 100,000) Multiply Colonies x Dilution Factor (90 x 1,000,000 = 90,000,000). Are we done yet? No.
Move the decimal point on your answer over so there is only one digit to the left of the decimal point 9.0 (you need to move the decimal over 7 places). Round off that last digit as needed. Are we done yet? No.
Count the number of spaces you moved the decimal point over (7). This becomes the superscript number above your power of 10 (write 9.0 x 10 7 ). Are we done yet? No.
Write the units (organisms/ml). Are we done yet? YES!
• • • • •
EXTRA CONCENTRATION PROBLEM (not on study guide):
What is the concentration of a suspension that results in
60 colonies on a plate made with 0.01 dilution from a culture with a dilution of 1:100,000?
First convert to ml (100,000 ÷ 0.01 = 10,000,000) Multiply Colonies x Dilution Factor (60 x 1,000,000 = 600,000,000). Are we done yet? No.
Move the decimal point on your answer over so there is only one digit to the left of the decimal point 6.0 (you need to move the decimal over 8 places). Round off that last digit as needed. Are we done yet? No.
Count the number of spaces you moved the decimal point over (8). This becomes the superscript number above your power of 10 (write 6.0 x 10 8 ). Are we done yet? No.
Write the units (organisms/ml). Are we done yet? YES!
CONCENTRATION PROBLEM FOUR: Given a Staph aureus suspension with a concentration of 4.6 x 10 6 organisms/ml, What is the concentration of a mixture of 1 ml of Staph aureus in 3 ml of TSB? •
Write the formula: A = BD/C
A = x B = Original number of ml (1) C = Total ml (1 + 3 = 4) D = Concentration (4.6)
X = (1)(4.6) 4 X = 4.6
4 X = 1.15
Are we done yet? No.
Add the power to the 10, and add the units (organisms/ml)
X = 1.15 x 10
6
organisms/ml
CONCENTRATION PROBLEM FIVE: Given a Staph aureus suspension with a concentration of 4.6 x 10 6 organisms/ml, What is the concentration of a mixture of 3 ml of Staph aureus in 9 ml of TSB? •
Write the formula: A = BD/C
A = x B = Original number of ml (3) C = Total ml (3 + 9 = 12) D = Concentration (4.6)
X = (3)(4.6) 12 X = 13.8
12 X = 1.15
Are we done yet? No.
Add the power to the 10, and add the units (organisms/ml)
X = 1.15 x 10
6
organisms/ml
CONCENTRATION PROBLEM SIX: Given a Staph aureus suspension with a concentration of 4.6 x 10 6 organisms/ml, What is the concentration of a mixture of 5 ml of Staph aureus in 10 ml of TSB? •
Write the formula: A = BD/C
A = x B = Original number of ml (5) C = Total ml (5 + 10 = 15) D = Concentration (4.6)
X = (5)(4.6) 15 X = 23 15 X = 1.53
Are we done yet? No.
Add the power to the 10, and add the units (organisms/ml)
X = 1.53 x 10
6
organisms/ml
CONCENTRATION PROBLEM SEVEN: Given a Staph aureus suspension with a concentration of 4.6 x 10 6 organisms/ml, What is the concentration of a mixture of 4 ml of Staph aureus in 16 ml of TSB? •
Write the formula: A = BD/C
A = x B = Original number of ml (4) C = Total ml (4 + 16 = 20) D = Concentration (4.6)
X = (4)(4.6) 20
Add the power to the 10, and add the units (organisms/ml)
X = 18.4
20 X = 0.920
X = 0.920 x 10 6 organisms/ml Are we done yet? No.
Are we done yet? No.
Move the decimal point over and change the power
X = 9.20 x 10
5