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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.

Decimal Notation

The dot represents a decimal point where place values are separated by what is to the left and right. To the right of the decimal points such as a tenth \(\frac{1}{10}\), a hundredth \(\frac{1}{100}\), and so on. 


Examples:

Name the following numbers:

1) \(203.65\) = Two hundred three and sixty-five hundredths

2) \(2.008\) = Two and eight thousandths

Write out the following numbers:

1) One thousand twenty-two and three tenths = \(1022.3\)

2) Eighty thousand and eighty thousandths = \(80,000.080\)

Converting Between Fractions and Decimals

The decimal place value determines how to convert a decimal into a fraction.

For example, \[0.045\] 

ends at the thousandths place value. Therefore you put the number over 1000

\[=\frac{45}{1000}\]

Simplify the fraction

\[=\frac{9}{20}\]

See video below for more examples, including mixed fractions and converting from fractions back to decimals.

Rounding

Rounding Decimal Notation

To round to a certain place:

  1. Locate the digit in that place.
  2. Consider the next digit to the right.
  3. If the digit to the right is 5 or greater, round up; if the digit to the right is 4 or lower, keep digit the same. 

Example:

1. Round \(0.084\) to the nearest tenth.

Solution:

Locate the digit in the tenths place

\[0.\underline{0}84\]

Consider the next digit to the right, 8

Since 8 is greater than or equal to 5, round up.

\[0.1\]

2. Round \(212.5604\) to the nearest hundredths

Solution:

Locate the digit in the hundredths place

\[212.5\underline{6}04\]

Consider the next digit to the right, 0

Since 0 is 4 or lower, keep digit the same.

\[212.56\]

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Designed by Matthew Cheung. This work is licensed under a Creative Commons Attribution 4.0 International License.

Decimal Arithmetic Operations

Example 1: Find the total resistance for the circuit diagram below. The total resistance of a series circuit is equal to the sum of the individual resistances.

Solution

The total resistance is the sum of the individual resistances in this series circuit.

\[2.34+37.5+.09=39.93\,ohms\]


Example 2: A series circuit containing two resistors has a total resistance (\(R_T\)) of 37.272 ohms. One of the resistors (\(R_1\)) has a value of 14.88 ohms. What ist eh value of the other resistor (\(R_2\))?

Solution

We have to subtract \(R_1\) from the total resistance \(R_T\).

\[R_2=R_T-R_1=37.272-14.88=22.392\,ohms\]


Example 3: Using the formula Watts = Amperes \(\times\) Voltage, what is the wattage of an electric drill that uses 9.45 amperes from a 120 volt source?

Solution

We need to multiple 120 amperes by 9.45 volts to find the wattage of the electric drill.

\[120\times 9.45=1134\,watts\]

The electric drill is 1134 watts.


Example 4: The wing area of an airplane is 262. square feet and its span is 40.4 feet. Find the mean chord of its wing using the formula: Area \(\div\) span = mean chord.

Solution

For long division, you want to work with a divisor that does not have a decimal value. We can transform it by multiplying both the dividend and divisor by 10.

\[40.4\overline{)262}=404\overline{)2620}=6.5\]

The mean chord is 6.5 feet.

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