# 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

Examples

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 order 3 appetizers: one for $7.99, one for$12.49 and another for $15.89. How much did the appetizers cost? Solution The total is the sum of the individual appetizers. $7.99+12.49+15.89 = 36.37$ The total for the appetizers was$36.37.

Example 2

A meal plus tip costs $75.83. If the meal alone costs$64.26, how much was the tip?

Solution

We have to subtract the meal price from the total price.

Total - Meal = $75.83 - 64.26 = 11.57$

The tip is $11.57. Example 3 If one beverage costs$12.89 per bottle, how much will 15 bottles cost?

Solution

We need to multiply $12.89 by 15 to find the total cost. $12.89\times 15=193.35$ 15 bottles cost$193.35.

Example 4

500 g of potatoes costs $3.50. How much do potatoes cost per gram? Solution $500\overline{)3.50}=0.0068$ Potatoes cost$0.0068/g