Topic 1
1. Express the following numbers in scientific notation with the appropriate prefix multipliers:
a. 8,960,000,000
d. 0.0000000321
a) 8.960,000,000 x 109
b) 3.21 x 108
Conversion:
a. 9.4 megahertz to microhertz
b. 2.8 centigrams to kilograms
a) 9.4 M HZ = 9.4 μ HZ
b) 2.8 c g = 0.28 k g
2. Perform the following arithmetic operation and express the answers in scientific notation with the appropriate prefix multipliers
(1.8 x 10(-4)) / (6.4 x 107)
2.8 x 10 -12 = 2.8 pico
Divide 15.67 g by 2.34 mL, and round your answer to the correct number of significant figures.
6.70 g/mL
What prefix multipliers/numbers do these symbols indicate?
1.M 2.m 3.n
4.k 5.c 6.μ
1. Mega= 106
2. milli = 10-3
3. nano= 10-9
4. kilo = 103Express the following numbers in standard form.
a) 8.91 x e4
b) 3.45 x 10^-6
a) 89100
b) 0.00000345
Convert 4.2 hours to seconds
4.2 h = 15120 s = 1.5 x 10 4 s
Perform the following calculation while paying attention to significant figures. Adjust the final answer to the correct number of significant figures.
a) (14.3 g / 2.1 cm³) * 0.0342 cm³
0.23 g = 2.3 x 10 -1 g
Subtract 7.895 mL from 0.000453 mL, and round your answer to the correct number of decimal places
7.895 ml
What is the difference between accuracy and precision?
1. Accuracy = how close a measurement is to actual value
2. Precision = how close repeated measurements are to each other (reproducibility)
How many significant numbers does each number have/ how many decimal places?
a) 60.09
b) 786000.000000
c) 0.000000005820
a) 4 sig-figs and 2 D.P
b) 12 sig-figs and 6 D.P
c) 4 sig-figs and 12 D.P
351.1 K to °C (average temperature of the universe as measured from background blackbody radiation)
77.95 = 78.0 °C
Multiply and divide the following numbers, taking into account significant figures, and then express the result in standard notation with the correct number of decimal places.
(12.345 * 6.789) / (1.23 + 0.04567)
68.1 = 6.81 x 10 1
Calculate the following expression and round the answer to the correct number of significant figures:
a) (5.6721 - 0.123) x 4.56
25.3 = 2.53 x 10 1
Two parts of every measurement?
Two parts of every measurement:
1.) The unit= measurement standard
2.) The number
- multiple of the standard
- uncertainty in measurement
Round the following numbers:
a) 94.49 (to one decimal place)
b) 56.634 (to two decimal places)
c) 34.05 ( to 2 decimal places)
a) 94.5
b) 56.63
c) 34.10
Convert a concentration of 0.025 moles per liter (mol/L) to millimoles per milliliter (mmol/mL).
0.025 mmol/mL = 2.5 x 10 -2
Perform the following operations and express the result in standard notation with the correct number of decimal places:
(3.725 x 10-6 ) / (2.54 x 10-2 )
1.47 x 10-4
Perform the following calculations, considering significant figures and rounding.
d) (3.45 x 103) + (2.1 x 104) - (6.78 x 10-2)
2.4
What is an exact number?
Exact Numbers: a number whose value is known with complete certainty is exact.
- Come from:
1) counting individual objects
2) definitions
3) integer values in equations
*Exact numbers have an unlimited number of significant figures.*
3. Determine the prefix multipliers for the following metric units:
a. Gigaseconds
c. Nanovolts
a. Giga = G = 109
b. Nano = n = 10-9 or 1/ 109
Convert a speed of 60.0 Kilometers per hour to meters per second.
16.7 m/s
Do the following operation
a. 106.125
1.33 x 106
Perform the following calculations and express the results in scientific notation with the appropriate number of significant figures:
(2.35 x 106) x (8.9 x 10(-4)) / (7.15 x 102)
2.9
Order of Operations?
subtraction- multiplication- addition- division- parenthesis
1. parenthesis
2. multiplication and division
3. Subtraction and addition