Transcript Dividing by decimal powers of 10

3-6 Dividing by Decimals
Dividing by Decimals
3-6 Dividing by Decimals
Dividing by Decimals
Essential Question:
How do operations with decimals compare
to operations with whole numbers?
3-6 Dividing by Decimals
Sunshine State Standards
MA.6.A.1.3 Solve real-world problems
involving…division of…decimals.
Also MA.6.A.1.1, MA.6.A.1.2. MA.6.A.5.3
3-6 Dividing by Decimals
Warm Up
Divide.
1. 4.8 ÷ 2
2. 16.1 ÷ 7
2.4
2.3
3. 0.36 ÷ 3
0.12
4. 25.28 ÷ 4
6.32
3-6 Dividing by Decimals
Remember!
Quotient
0.15
5 0.75
Divisor
Dividend
3-6 Dividing by Decimals
What is a terminating
decimal?
What is a repeating
decimal?
3-6 Dividing by Decimals
What is a terminating
decimal?
A terminating decimal is one
that terminates or ends.
What is a repeating
decimal?
3-6 Dividing by Decimals
What is a terminating
decimal?
What is a repeating
decimal?
A terminating decimal is one
A repeating decimal is one
that terminates or ends.
that keeps going and
repeats a pattern.
3-6 Dividing by Decimals
What is a terminating
decimal?
What is a repeating
decimal?
A terminating decimal is one
A repeating decimal is one
that terminates or ends.
that keeps going and
repeats a pattern.
1 ÷ 8 = .125
3-6 Dividing by Decimals
What is a terminating
decimal?
What is a repeating
decimal?
A terminating decimal is one
A repeating decimal is one
that terminates or ends.
that keeps going and
repeats a pattern.
1 ÷ 8 = .125
_
1 ÷ 3 = .3
3-6 Dividing by Decimals
3-6 Dividing by Decimals
3-6 Dividing by Decimals
Complete the table below:
Whole Number
Powers of 10
Decimal
Powers of 10
10 x 8.3 =
0.1 x 8.3 =
100 x 8.3 =
0.01 x 8.3 =
1,000 x 8.3 =
0.001 x 8.3 =
10,000 x 8.3 =
0.0001 x 8.3 =
3-6 Dividing by Decimals
Complete the table below:
Whole Number
Powers of 10
Decimal
Powers of 10
10 x 8.3 =
83
0.1 x 8.3 =
100 x 8.3 =
830
0.01 x 8.3 =
1,000 x 8.3 =
8,300
0.001 x 8.3 =
10,000 x 8.3 = 83,000
0.0001 x 8.3 =
3-6 Dividing by Decimals
Complete the table below:
Whole Number
Powers of 10
Decimal
Powers of 10
10 x 8.3 =
83
0.1 x 8.3 =
0.83
100 x 8.3 =
830
0.01 x 8.3 =
0.083
1,000 x 8.3 =
8,300
0.001 x 8.3 =
0.0083
10,000 x 8.3 = 83,000
0.0001 x 8.3 = 0.00083
3-6 Dividing by Decimals
What do you notice about the
decimal point when you
multiply by whole number
powers of 10?
Of decimal powers of 10?
3-6 Dividing by Decimals
Multiplying by Powers of 10
Multiplying by whole number powers of 10:
• Move the decimal point one place to the right for each zero in
the whole number power of 10.
• 3.995 x 100 = 3 9 9. 5
Multiplying by decimal powers of 10:
• Move the decimal point one place to the left for each decimal
place in the decimal power of 10.
• 399.5 x 0.001 = 0.3 9 9 5
3-6 Dividing by Decimals
What do you think will happen
to the decimal point when you
divide by whole number
powers of 10?
Of decimal powers of 10?
3-6 Dividing by Decimals
Dividing by Powers of 10
Dividing by whole number powers of 10:
• Move the decimal point one place to the left for each zero in the
whole number power of 10.
• 35 ÷ 100 = 0 . 3 5
Dividing by decimal powers of 10:
• Move the decimal one place to the right for each decimal place in
the decimal power of 10.
•
35 ÷ 0.001 = 3 5 0 0 0 .
3-6 Dividing by Decimals
Helpful Hint
Multiplying the divisor and the dividend by the
same number does not change the quotient.
42 ÷ 6 = 7
10
 10
420 ÷ 60 = 7
 10
 10
4,200 ÷ 600 = 7
3-6 Dividing by Decimals
Dividing a Decimal by a Decimal
Find the quotient.
5.2 ÷ 1.3
1.3 5.2
4
13 52
–52
0
5.2 ÷ 1.3 = 4
Multiply the divisor by 101, or 10 to
make it a whole number. Multiply the
dividend by the same power of 10.
Think: 1.3 x 10 = 13
5.2 x 10 = 52
Divide as with whole numbers.
3-6 Dividing by Decimals
Check It Out:
51.2 ÷ 0.24
0.24 51.2 0
24 5120.00
Multiply the divisor by 102, or
100, to make it a whole number.
Multiply the dividend by the same
power of 10.
Think: 0.24 x 100 = 24
51.2 x 100 = 5,120
3-6 Dividing by Decimals
Check It Out:
2 13.3 3
24 5,120.00
-48
32
-24
80
-72
80
-72
80
-72
8
Place the decimal point in
the quotient. Divide as with
whole numbers.
When a repeating pattern
occurs, show three dots or
draw a bar over the repeating
part of the quotient.
__
51.2 ÷ 0.24 = 213.3
3-6 Dividing by Decimals
Make a Problem Solving Plan:
1
2
3
4
Understand the Problem
Make a Plan
Solve
Look Back
3-6 Dividing by Decimals
Problem Solving Application
After driving 216.3 miles, the Yorks filled
up with 10.5 gallons of gas. On average,
how many miles did they drive per gallon
of gas?
1
Understand the Problem
The answer will be the average number of
miles per gallon.
List the important information:
They drove 216.3 miles. They used 10.5
gallons of gas.
3-6 Dividing by Decimals
2
Make a Plan
Solve a simpler problem by replacing the
decimals in the problem with whole numbers.
If they drove 10 miles using 2 gallons of gas,
they averaged 5 miles per gallon. You need to
divide miles by gallons to solve the problem.
3
Solve
First estimate the answer. You can use
compatible numbers.
216.3 ÷ 10.5
200 ÷ 10 = 20
3-6 Dividing by Decimals
3
Solve Continued
10.5 216.3
2 0.6
105 2163.0
-210
63
-0
630
-630
0
Multiply the divisor and dividend
by 10. Think: 10.5 x 10 = 105
216.3 x 10 = 2,163
Place the decimal point in the
quotient. Divide as with whole
numbers.
The York family averaged 20.6 miles per gallon.
3-6 Dividing by Decimals
4
Look Back
The answer is reasonable since 20.6 is close
to the estimate of 20.
3-6 Dividing by Decimals
John spent $13.44
renting 4 videos for the
weekend. What was the
cost per video?
3-6 Dividing by Decimals
John spent $13.44
renting 4 videos for the
weekend. What was the
cost per video?
$3.36