Transcript Math Skills - kriegerhonors9th

+
Math Skills
+
Fence Posting

Used to convert units



Ex. Km/s to mi/hr
Rules:

Use horizontal lines, not slashes for division to avoid confusion

Find a conversion factor

Multiply so units cancel out

Cross out units as you go
Example: Convert 20 mi/hr to m/s
+
Step 1: Write given with horizontal
lines
20mi
hr
+
Step 2: Find a conversion factor

We can’t directly convert from miles to meters, but we can
convert from miles to feet, feet to inches, inches to
centimeters, and finally centimeters to meters.

1 mi = 5280 feet

1 in = 2.54 cm
+
Continued
Let’s convert miles to feet:

20mi
hr
The conversion factor is 1 mi = 5280 ft

We want to multiply so that the miles cancels out, like this:

20mi 5280 ft
x
hr
1mi

Notice that with miles on both the numerator and
denominator, it cancels out.

Now we have ft/hr. We will convert feet to meters in several
steps, and then hours to seconds.
+
Step 3: Multiply so units cancel out
20mi 5280 ft 12in 2.54cm
1m
3600s 8.9m
x
x
x
x
x
=
hr
1mi
1 ft
1in
100cm 1hr
s
+
Scientific Notation


To convert from scientific notation to decimals:

If the exponent is positive, move the decimal that many places to
the right.

If the exponent is negative, move the decimal that many places to
the left.

Ex: 5.4*103 = 5400

Ex: 5.2*10-3 = 0.0052
To convert from decimals to scientific notation

Move the decimal such that number ranges between 0-10

The number of places you moved the decimal becomes the
exponent

Ex: 2730 = 2.73*103

Ex: 0.00351 = 3.51*10-3
+
Math with Scientific Notation



Multiplication:

Add the exponents

Perform the mathematical operation to the base numbers
Division:

Subtract the exponents

Perform the mathematical operation to the base numbers
Examples:

(6*104) * (3*102) = 18 * 106 = 1.8 * 107

(6*108) / (3*102) = 2 * 106  106 NOT 104

(6*108) / (3*10-2) = 2 * 108 -- -2 = 2 * 1010
+
Metric Prefixes

YOU MUST MEMORIZE KILO, CENTI, and MILLI :
Multiple
Prefix
Abbreviation
109
Giga
G
106
Mega
M
103
Kilo
k
10-2
Centi
c
10-3
Milli
m
10-6
Micro
µ
10-9
Nano
n
+
Metric Conversions

2.8 km = 2.8 * 103 m = 2800 m

17.1 mL = 17.1 * 10-3 L = 0.0171 L

Convert 50 m to km
50m 1km
x
= 0.050km
1 1000m

Convert 15 mg to kg
15mg 1*10-3 g 1kg
x
x
=15*10-6 kg =1.5*10-5 kg
1
1mg
1000g