Transcript Dividing by a Decimal Example Step 1

Dividing Decimals and Order of Operations
Section Objectives

Dividing Decimals

Estimating When Dividing Decimals

Dividing Decimals by Powers of 10

Solving Problems by Dividing Decimals

Simplifying Expressions with Decimals
Dividing Decimals
Dividing by a Whole Number
Example
Step 1: Place the decimal point in
the quotient directly above the
decimal point in the dividend.
.
2 11.8
Step 2: Divide as with whole
numbers.
5 .9
2 11.8
 10
18
1 8
0
Dividing Decimals
Dividing by a Decimal
Example
Step 1: Move the decimal point in
the divisor to the right until the
divisor is a whole number.
0.92 3.312
Step 2: Move the decimal point in
the dividend to the right the same
number of places as the decimal
point was moved in step 1.
92 331.2
Step 3: Divide. Place the decimal
point in the quotient directly over
the moved decimal point in the
dividend
3. 6
92 331.2
 276
55 2
 55 2
0
Estimating When Dividing Decimals
EXAMPLE
Divide:
0.54  12
SOLUTION
Exact
0.04 5
12 0.54
 48
60
- 60
0
0.0 5
Estimate
10 0.50
- 50
0
Since 0.045 is close to our estimate of 0.05, the answer is reasonable.
Dividing Decimals by Powers of 10
Type
Example
Dividing Decimals by Powers of 10
such as 10, 100, 1000 . . .: Move the
decimal point to the left the same
number of places as there are zeros in
the power of 10.
324.54
= 3.4254
100
Solving Problems by Dividing Decimals
EXAMPLE
Dorren Schmidt pays $73.86 per month to pay back a loan of $1772.64. In how many
months will the loan be paid off?
SOLUTION
73.86 1772.64
24
7386 177264
- 14772
29544
- 29544
0
Dorrin Schmidt will have his loan paid off in 24 months.
Simplifying Expressions with Decimals
Order of Operations
1. Perform all operations within parentheses ( ), brackets [ ], or other grouping
symbols such as fraction bars or square roots.
2. Evaluate any expressions with exponents.
3. Multiply or divide in order from left to right.
4. Add or subtract in order from left to right.
EXAMPLE
Simplify 1.4(2-1.8).
SOLUTION
1.4(2 - 1.8) = 1.4(.2)
1 .4
= ´ .2
.28
Fractions and Decimals
Section Objectives

Writing Fractions as Decimals

Comparing Decimals and Fractions

Solving Area Problems Containing Fractions and Decimals
Writing Fractions as Decimals
EXAMPLE
Write 1 as a decimal.
20
SOLUTION
1
20
0.05
20 1.00
-0
10
-0
100
-100
0
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC COLLEGE MATHEMATICS, 3e – Slide #38
Comparing Decimals and Fractions
Original numbers
Decimals
9
100
.0932
.09
.0932
.09 < .0932
Compare
Thus,
9
< .0932.
100
Solving Area Problems
Containing Fractions and Decimals
EXAMPLE
The area of a triangle is Area =
1
× base × height.
2
Find the area of the following triangle.
4.4 feet
SOLUTION
17 feet
1
Area  17 14.4
2
 .5 17 14.4
 37.4 sq ft
Write
1
as .5.
2