Question

model it: place - value charts
use place - value charts to show multiplying and dividing by powers of 10.
3 complete each row with the product shown to the right of that row.
ones. tenths hundredths thousandths

1. 0 0 5
2. 0 5
3. 5

5.
0.005×10¹
0.005×10²
0.005×10³
4 complete each row with the quotient shown to the right of that row.
ones. tenths hundredths thousandths

1. 0 0 0
2. 5
3. 0 5
4. 0 0 5

5÷10¹
5÷10²
5÷10³
discuss it

• how do the values of t

digits and the placem
of the decimal point
change when you m
or divide any decim
power of 10?

• i think place - value

show the pattern
multiplying and
powers of 10 be
connect it
complete the problems below.
5 look at the first decimal point pattern diagram and the place - value
charts. how do the position and the value of the digit 5 change when
multiplying and dividing by 10?
6 show how to find the product 0.19×10³.
146 lesson 7 understand powers of 10
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Explanation:

Step1: Complete #3 place-value rows

For $0.005 \times 10^1$:

Ones	.	Tenths	Hundredths	Thousandths

For $0.005 \times 10^2$:

Ones	.	Tenths	Hundredths	Thousandths

For $0.005 \times 10^3$:

Ones	.	Tenths	Hundredths	Thousandths

Step2: Complete #4 place-value rows

For $5 \div 10^1$:

Ones	.	Tenths	Hundredths	Thousandths

For $5 \div 10^2$:

Ones	.	Tenths	Hundredths	Thousandths

For $5 \div 10^3$:

Ones	.	Tenths	Hundredths	Thousandths

Step3: Answer question #5

When multiplying 0.005 by 10, the digit 5 moves one place left from the thousandths place to the hundredths place, and its value becomes 10 times greater (from 0.005 to 0.05). When dividing 5 by 10, the digit 5 moves one place right from the ones place to the tenths place, and its value becomes $\frac{1}{10}$ of its original value (from 5 to 0.5).

Step4: Calculate #6 product

$10^3 = 1000$, so shift the decimal in 0.19 3 places right.
$0.19 \times 10^3 = 0.19 \times 1000 = 190$

Answer:

Completed #3 Table:

Ones	.	Tenths	Hundredths	Thousandths	Expression
0	.	0	5	0	$0.005 \times 10^1$
0	.	5	0	0	$0.005 \times 10^2$
5	.	0	0	0	$0.005 \times 10^3$

Completed #4 Table:

Ones	.	Tenths	Hundredths	Thousandths	Expression
0	.	5	0	0	$5 \div 10^1$
0	.	0	5	0	$5 \div 10^2$
0	.	0	0	5	$5 \div 10^3$