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Chapter 7

- Decimals, Ratio, Proportion and Percent

7.1 Decimals

- Decimals are used to represent fractions in our

base ten place-value notation.

1000

100

10

1

1/10

1/100

1/1000

3

4

5

7

9

6

8

thousands

hundreds

tens

ones

tenths

hundredths

thousandths

- Write 3457.968 in expanded form

Write 978.314 in expanded form

- Theorem Let be a fraction in simplest form.
- Then has a terminating decimal

representation - if and only if b contains only 2s and/or 5s in

its - prime factorization.

Ordering Decimals

- Terminating decimals can be compared using a

hundreds square, using a number line, by

comparing them in their fraction form, or by

comparing place values one at a time from left to

right just as we compare whole numbers.

Multiplying or Dividing by Powers of 10

- Theorem Let n be any decimal number and m

represent any nonzero whole number. - Multiplying a number n by 10m is equivalent to

forming a new number by moving the decimal point

of n to the right m places. - Dividing a number n by 10m is equivalent to

forming a new number by moving the decimal point

of n to the left m places.

7.2 Operations with Decimals

- Addition and Subtraction requires the numbers to

be aligned at the decimal point, add or subtract

the numbers as if they were whole numbers, and

insert a decimal point directly below the numbers

being added or subtracted.

Multiplication of Decimals

- Perform multiplication as if the decimal point

were not there. Insert a decimal point in the

answer as follows The number of digits to the

right of the decimal point in the answer is the

sum of the number of digits to the right of the

decimal points in the numbers being multiplied.

Division of Decimals

- Multiply both the divisor and dividend by the

power of ten necessary to result in the divisor

being a whole number.

Repeating Decimals

Theorem Let be a fraction in simplest

form. Then has a repeating decimal

representation that does not terminate if and

only if b has a prime factor other than 2 or 5.

7.3 Ratios and Proportion

- Definition A ratio is an ordered pair of

numbers, written ab, with b not equal to 0. - Definition Equality of Ratios
- if and only if

Proportions

- Definition A proportion is a statement that two

given ratios are equal.

Rates

- Ratios involving different units are called

rates. - Examples miles per hour, miles per gallon,

cents per ounce, dollars per pound, etc.

Example 7.21 Adams School orders 3 cartons of

chocolate milk for every 7 students. If there

are 581 students in the school, how many cartons

of chocolate milk should be ordered?

n cartons to be ordered

Step 1 Define your variable.

- Step 2 Set up a proportion.

Step 3 Cross multiply and solve.

The school needs to order 249 cartons of

chocolate milk.

- Example 7.24 In a scale drawing, 0.5 centimeter

represents 35 miles. How many miles will 4

centimeters represent?

n of miles

Step 1 Define your variable.

Step 2 Set up a proportion.

Step 3 Cross multiply and solve.

Four centimeters represents 280 miles.

7.4 Percent

Percent means per hundred

Fractions

- Percents

Repeating Decimals

Conversions

Fraction Decimal Percent

Solving Percent Problems

- Grid Approach

Example 7.29a A car was purchased for 13000

with a 20 down payment. How much was the down

payment?

- Shade 20 out of the 100 squares (20)

100 squares 13000, so 1 square 130.

20 squares represent the down payment of

2600. 20 X 130 2600

Solving Percent Problems

- Proportion Approach
- Since percents can be written as ratios, percent

problems can be solved using proportions.

Ex 7.30a

The down payment was 2600.

Solving Percent Problems

- Equation Approach

Translation of Problem Equation

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