Download X and div by powers of 10

1.
How do we multiply a whole number by a power of 10?
36 × 10
Add on as many 0's as appear in the power.
Examples.
2.
36 × 10 =
36 × 100 =
36 × 1000 =
360
3600
36,000
Add on one 0.
Add on two 0's.
Add on three 0's.
How do we multiply a decimal by a power of 10?
7.32 × 10
Move the decimal point right as many digits
as there are zeros in the power.
Examples.
7.32 × 10= 73.2
7.32 × 100= 732
7.32 × 1000= 7,320
Move the decimal point one place right.
Move the point two digits right: 732. However, since all the digits fall to the left of the decimal point, the
whole number, 732, which we write without a decimal point.
Move the point three digits right. To do this, we must add on a 0.
Again, the answer is a whole number.
Problem. If 5 pounds of sugar cost $2.79, how much will 50 pounds cost?
Answer. Since 50 pounds are ten times 5 pounds, they will cost ten times more. Move the decimal
point one place right: $27.90. Since money has two decimal digits, we added on a 0. (Lesson 3,
Question 8)
3.
How do we divide a decimal by a power of 10?
63.4 ÷ 10
Move the decimal point left as many digits as there are 0's in the power. If there are not enough digits, ad
Examples.
63.4 ÷ 10=
6.34
Move the point one place left.
63.4 ÷ 100=
.634
Move the point two digits left.
63.4 ÷ 1000=
.0634
Move the point three digits left.
do this, add on a 0.
These example illustrate that, whenever we multiply or divide by a power of 10, the digits do not change
We simply move the decimal point or add on 0's.
Finally, we must see how to divide a whole number by a power of 10. Now in Lesson 1 we saw that
when a whole number ends in 0's, we simply take off 0's. (Lesson 1, Question 11)
265,000 ÷ 100 = 2,650
But when a whole number does not end in 0's -- as 265 -- then there are no 0's to chop off We will see
that we must place a decimal point to separate digits on the right.
4.
How do we divide a whole number by a power of 10?
265 ÷ 10
Starting from the right of the whole number, separate as many decimal digits as there are 0's in the powe
not enough digits, add on 0's.
Examples.
265 ÷ 10 = 26.5
Starting from the right of 265,
separate one decimal digit.
265 ÷ 100 = 2.65
Separate two decimal digits.
265 ÷ 1000 = .265
Separate three decimal digits.
Again, as in Lesson 1, consider this array:
As we move down the list -- as we push the digits one place left -- the number has been multiplied by 10,
because each next place is worth 10 times more. (As we move from 2.658 to 26.58, we go from 2 ones
to 2 tens.) It appears, though, as if the decimal point has shifted one place right, or, with whole
numbers, that a 0 has been added on.
As we move up the list -- as we push the digits to the right -- each number has been divided by 10.
And so we can easily multiply or divide by a power of 10 because of the written system itself. Each
place belongs to the next power of 10