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Math help from the Learning Centre

This guide provides useful resources for a wide variety of math topics. It is targeted at students enrolled in a math course or any other Centennial course that requires math knowledge and skills.

Measurement Systems

You may have experienced two types of measurement systems such as the metric and imperial systems. The imperial system consist of units such as inchesmiles, or pounds. The metric system consists of units such as metresgrams, or litres.

The metric system is based on powers of 10 and each power has a prefix.

Prefixes
Prefix Name Prefix Symbol Exponent of 10 Value
zetta Z \(10^{21}\) Sextillion
exa E \(10^{18}\) Quintillion
peta P \(10^{15}\) Quadrillion
tera T \(10^{12}\) Trillion
giga G \(10^{9}\) Billion
mega M \(10^{6}\) Million
kilo k \(10^{3}\) Thousand
hecto h \(10^{2}\) Hundred
deka da \(10^{1}\) Ten
\(10^{0}\) One
deci d \(10^{-1}\) Tenth
centi c \(10^{-2}\) Hundredth
milli m \(10^{-3}\) Thousandth
micro \(\mu\) \(10^{-6}\) Millionth
nano n \(10^{-9}\) Billionth
pico p \(10^{-12}\) Trillionth
femto f \(10^{-15}\) Quadrillionth
atto a \(10^{-18}\) Quintillionth
zepto z \(10^{-21}\) Sextillionth

Practical Method

A method of moving left or right depending on the operation of divide or multiply can be used to move the decimal point operation with powers of 10.

Steps of the Practical Method:

  1. Ask if the unit in the answer is larger or smaller than the unit given?
    1. If the unit you want to get to is larger than the given: the decimal will move to the left, creating a smaller number.
    2. If the unit you want to get to is smaller than the given: the decimal will move to the right, creating a larger number.
  2. How much larger or smaller is the unit in the answer? This determines how many times the decimal moves.

Examples:

1. Convert \(25\, L\) to \(kL\). 

  • The unit we want to get to is larger then the given, so the decimal will move to the left.
  • kilo compared to the ones unit differ by 3 places, so we move to the left 3 places.

\[25\, L = 0.025\, kL\]

2. Convert \(1.8\, cg\) to \(\mu g\). 

  • The unit we want to get to is smaller then the given, so the decimal will move to the right.
  • micro compared to the centi unit differ by 4 places, so we move to the right 4 places.

\[1.8\, cg = 18,000\, \mu g\]

Cancel the Units Method

We can make a conversion by multiplying the given ratio that cancels the unwanted units and moves the decimal the correct number of places.

Examples:

1. Convert \(3.8\, hm\) to cm.

\[3.8\,hm \times \frac{10,000\,cm}{1\,hm} = 38,000\,cm\]

2. Convert \(9.01\, kL\) to daL.

\[9.01\,kL \times \frac{100\,daL}{1\,kL} = 901\,daL\]

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