# 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.

Example

Name the following numbers:

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

2) $$2.008$$ = Two and eight thousandths

Example

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.

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.

$0.1$

Example 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

You bought 3 items: one for $4.50, one for$0.35 and one for $15.04. What was your total? Solution The total price is the sum of the prices of each individual item. $4.50+0.35+15.04=18.98$ Example 2 The price of a jacket originally costing$80.89 was discounted by $15.49. What is the new price of the jacket? Solution We have to subtract the discount from the original price. $Original \; price - discount = 80.89-15.49 = 65.40$ Example 3 Using the formula $$Interest = Principal \times rate \times time$$, what is the interest earned on a principal of$1000 with an interest rate of $$4%$$ over 5 years?

Solution

We need to multiply $1000 by 0.04 and 5 to get the total interest. $1000 \times 0.04 \times 5 = 200$ The interest earned is$200.

Example 4

You paid $128.94 for 6 lamps. How much does each lamp cost? Round to the nearest cent. Solution $6\overline{)128.94}=21.49$ Each lamp costs$21.49.