Download Measurement, Sci. Notation and SF

Objective of the day:
To understand how to measure using a
graduated cylinder, triple beam balance and a
ruler
Daily Question # 1
What is the volume measurement in the
following diagram?
Back to the Basics
Science Lab Equipment
Graduated Cylinder
• Measure about
26.1 mL
Scale
• Weigh the object
Ruler
• Measure the length of the object
SI Units
• International System of Units (SI)
Metric Prefixes
BIGGER
SMALLER
1000
BIG
k
kilo
100
h
hecto
10
dk
deca
1
BASE
(m, g, L)
.1
d
deci
.01
c
centi
.001
m
milli
SMALL
How do you convert between metric units?
1. Determine whether you are going up the
ladder or down the ladder.
•If you go up, move the decimal to the left.
•If you go down, move the decimal to the
right.
2. Use the ladder to determine how many
places to move the decimal.
•The number of steps on the ladder is equal
to the number of decimal places.
3. Write the correct units with your answer.
• Practice Problems
1. 0.7834 mg = ____________ g
2. 100 cm = ______________ m
3. 345,000 kg = ____________ g
4. 2.5 mm = _______________ hm
5. 3.46 cg = ________________ mg
6. 1.00 km = _______________ cm
Scientific Notation
• Method of writing very small or very large numbers
– A positive exponent means the decimal moved to the
left. A negative exponent means the decimal moved to
the right
Scientific Notation
• 602,200,000,000,000,000,000,000 = ?
– Step 1: Make the Coefficient less than 10 and more
than 1.
– Step 2: Find out how many places over the decimal has
to move to give you the number in step 1.
Scientific Notation
① 5,300,000 = ?
② 4,302,000,000 = ?
③ -24,500 = ?
④ .000034 = ?
⑤ -.0000007 = ?
Scientific Notation
① 5.3 x 104 = ?
② 7.02 x 108 = ?
③ -3.21 x 103 = ?
④ 7.093 x 10-4 = ?
⑤ -5 x 10-3
Scientific Notation
• Addition and Subtraction:
1) Make the exponents the same number
2) Add/Subtract the coefficient
5.3x102 + 2.6x103 =
5.3x102 + 26.x102 =
31.3x102=
3.13x103
Scientific Notation
• Multiplication and Division
1) Add or Subtract exponents
2) Multiply or Divide coefficients
Multiply
5.2x102 x 4.8x104 =
(5.2 x 4.8) x10(2 + 4)
3)=
24.96x106
2.496x107
Divide
5.0x104 ÷ 2.5x103=
(5.0 ÷ 2.5) x10(42.0x101
Scientific Notation
① 5.6x104 + 4.3x102 = ?
② 4.0x106 – 8.3x105 = ?
③ 2.3x105 x 4.3x106 = ?
④ 8.2x1012 ÷ 4.1x107 = ?
Derive a relationship between the
following
17 = 2
300 = 1
345 = 3
1000 = 1
1001 = 4
100.0 = 4
Accuracy vs. Precision
• Accuracy: How close to the real value
• Precision: How close a series of measurements are
to each other
Significant Figures
– Rounding Numbers:
-Round up if the digit to the right is between 5-9
59.48  59.5
-Drop the number to the right if it’s between 0-4
3.84  3.8
Significant Figures Tell You What Number To Round To!
Significant Figures
• All Non-zero numbers (1,2,3,4,5,6,7,8,9) are significant
• Zeros –
1) Front of number are NEVER significant
0.0071, 0.42, .000099 all have 2 sig. figs
2) Middle of number are ALWAYS significant
7003, 40.79, 1.503 all have 4 sig. figs
3) End are SOMETIMES significant
At end AFTER decimal, ALWAYS significant
36.00, 1.010, 9.000 all have 4 sig figs
At end BEFORE decimal, NEVER significant
300, 7000, 20000 all have 1 sig fig
Significant Figures
① 5.30 = ?
② 76009.0 = ?
③ 1900 = ?
④ .0000000891 = ?
Significant Figures
• Addition and Subtraction
– Match the number with the least number of decimals
• Ex:
13.21 + 4.1 = 17.3
13.21 + 4.100 = 17.31
13.21 + 4 = 17
• Multiplication and Division
– Match value with fewest number of sig figs
• Ex:
2.00 x 11 =22
2.00 x 11.0 = 22.0
2 x 11 = 20