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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: Locate the digit in that place. Consider the next digit to the right. 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.

$212.56$

## 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.