This is a finish lesson with a video & practice showing, an initial of all, the typical shortcut for multiplying & separating decimals by powers of ten: you move the decimal allude as many steps together there are zeros in the number 10, 100, 1000 etc.

You are watching: 12,000 divided by 10

Then, I additionally show wherein this faster way originates, using ar value charts. In reality, the decimal point moving is kind of one illusion, and instead, the digits of the number move within the ar value chart. This explanation deserve to really aid students to know the factor behind the "trick" of moving the decimal point.


The lesson listed below explains the faster way in much more detail, add to has different kinds that exercises, word problems, and even a fun riddle because that students.
Remember?When you multiply entirety numbers by 10, 100, 1000, and so top top (powers that ten), you deserve to simply “tag” as many zeros on the product as there space in the aspect 10, 100, 1000 etc.

There is a similar shortcut for multiplying decimal numbers by number such together 10, 100, and 1000:Move the decimal point to the appropriate as many places as there room zeros in the factor.

10 × 0.49= 04.9 = 4.9
Move the decimal suggest one step to the appropriate (10 has one zero).

100 × 2
.65 = 265. = 265

Move the decimal suggest two measures to the right (100 has two zeros).The number 265. Is 265 (as presented above).

1000 × 0
.370= 370. = 370

1000 method we move the allude three steps. Write a zeroat the finish of 0.37 sothat the decimal allude can “jumpover to” that place.


1. Multiply.

a. 10 × 0.04 = ________

b. 100 × 0.04 = ________

c. 1000 × 0.04 = ________

d. 10 × 0.56 = ________

e. 100 × 0.56 = ________

f. 1000 × 0.56 = ________

g. 10 × 0.048 = ________

h. 100 × 0.048 = ________

i. 1000 × 0.048 = _______


Another helpful shortcut! Since 100 × 2 = 200, clear the answer come 100 × 2.105 will certainly be a little more than 200. Hence, you can just write the digits2105 and also put the decimal allude so that the answer is 200-something:210.5.

2. Let"s practice some more.

a. 100 × 5.439 = ________

b. 100 × 4.03 = ________

c. 1000 × 3.06 = ________

d. 100 × 30.54 = ________

e. 30.73 × 10 = ________

f. 93.103 × 100 = _______

105 × 0.12000= 12000. = 12,000
105 = 100,000 has 5 zeros. Again, write extr zeros so the the decimal suggest can “jump end to” those places.3. Now let"s practice using powers of ten.

a. 102 × 0.007 = _____________

103 × 2.01 = _____________

105 × 4.1 = ______________

b. 105 × 41.59 = _____________

3.06 × 104 = ______________

0.046 × 106 = _____________


The faster way for department by 10, 100 and 1000 (powers of ten) is similar. Deserve to you guess it?

Move the decimal allude to the ( left / appropriate ) for as many places (steps) together there room _________________________ in the aspect 10, 100, or 1000.

0 0 2.8÷ 100 = 0.028
Move the decimal allude two actions to the ____________. You have to write zeros in former of the number.

0 0 0 5 6.
÷ 104 = 0.0056

Move the decimal pointfour actions to the ____________.You need to write zerosin front of the number.


4. Divide.

a. 0.4 ÷ 10 = ________

0.4 ÷ 100 = ________

4.4 ÷ 100 = ________

b. 15.4 ÷ 100 = ________

21.03 ÷ 10 = ________

0.39 ÷ 10 = ________

c.5.6 ÷ 10 = ________

34.9 ÷ 100 = ________

230 ÷ 1000 = ________

5. Now let"s exercise using strength of ten.

a.0.7 ÷ 102 = _____________

45.3 ÷ 103 = _____________

568 ÷ 105 = _____________

b.2.1 ÷ 104 = _____________

4,500 ÷ 106 = _____________

9.13 ÷ 103 = _____________

Why walk this faster way work?

When 0.01 (a hundredth) is multiplied by ten, we gain ten hundredths, i m sorry is same to one tenth. Or, 10 × 0.01 = 0.1.

The entire number relocated one “slot” come the left on the place value chart. This looks like relocating the decimal allude in the number to the right.

Othth
0.01

Othth
0.1

A hundred times two tenths is favor multiplying each tenth by 10, and by 10 again. Ten time two-tenths gives us two, andten time that offers us 20.

Again, the is like moving the number over two “slots” come the left in the location value chart, or relocating a decimal point in 0.2, two measures to the right.

TOthth
00.2

TOthth
20.
When 3.915 is multiplied by 100, we get 391.5. Each part of the number (3, 9 tenths, 1 hundredth, 5 thousandths)is multiplied by 100, for this reason each among those moves two “slots” in the ar value chart. This is similar to reasoning that the decimal suggest moves two actions to the right.
HTOthth
3.915

HTOthth
391.5
The similar shortcut for department works because department is the opposite procedure of multiplication—it “undoes” multiplication. If we relocate the decimal suggest to the right once multiplying by 10, 100, 1000 and also so on, then it is quite natural that the dominance for department would occupational the “opposite” way.

Fractions vs. Division. If we relocate the decimal allude to solve6 ÷ 100, we get:


0 0 6
.0÷ 100 = 0.060 = 0.06

Let’s compose 6 ÷ 100 using the portion line: it is 6/100 or 6 hundredths, i beg your pardon is written 0.06 as a decimal. Therefore, in this case you do not need the “shortcut,” however you canjust think of fractions and also decimals.These kinds of “connections” make math so neat!
6. Divide. Think of fractions to decimals, or use the shortcut. To compare the problems in every box!

a. 2100=
2.1100=
b.
491000=
4901000=
c.
610=
6.510=
d.
510=
5.0410=
e.
4.710=
4.7100=
f.
72100=
72.9100=

7. A 10-lb sack of nuts costs $72. just how much does one lb cost?

8. Discover the price the 100 ping-pong balls if one ping pong ball expenses $0.89.


Thinking much more about fractions and decimals

If us divide any kind of whole number through 1,000, the prize will have thousandths or three decimal digits. This makes it simple to divide totality numbers by 1,000: merely copy the dividend as your answer (without the commas), and also then make it have actually three decimal digits:

Examples:819,3021000
=819.302
41,3001000=41.300 = 41.3
8,0001000=8.000 = 8

Notice in the last 2 cases, we deserve to simplify the results: 41.300 to 41.3 and also 8.000 come 8.


9. Divide whole numbers through 1000. Simplify the final answer by dropping any ending decimal zeros.

a. 2391000=
b.
35,4031000=
c.
671000=
d.
263,0001000=
e.
3,8901000=
f.
1,692,4001000=
g.
12,560,0001000=
h.
91000=
i.
506,9401000=

Similarly:

If you divide any whole number by 10, copy the dividend and also make it have actually one decimal digit. If girlfriend divide any type of whole number by 100, copy the dividend and make it have actually two decimal digits.

Examples:

7210
=7.2
3,090100 =30.90 = 30.9
74,992100 =749.92
82,00010 =8200.0 = 8,200

10. Divide whole numbers by 10 and also 100.

a. 239100=
d.
89,803100=
g.
6910=
b.
23910=
e.
26,600100=
h.
69100=
c.
23,133100=
f.
3,402100=
i.
910=
11. Find one-tenth of...a.
$8

b. $25.50

c. $126

12. Find one-hundredth of...

a.
$78

b. $4

c. $390

13. A pair of pair of shoes that price $29 was discounted by 3/10 of its price. What is the new price?(Hint: very first find 1/10 the the price.)

*

14. Find the discounted price:

a. A bicycle that expenses $126 is discounted by 2/10 the its price.

b. A $45 cell phone is discounted by 5/100 the its price. (Hint: an initial find 1/100 of the price.)

15. One-hundredth of a certain number is 0.03. What is the number?

16. Which vacuum cleaner ends up gift cheaper? model A, v the early price $86.90, is discounted through 3/10 of its price. Version B expenses $75 now, but you will obtain a discount the 1/4 that its price.


An vital tip

In the difficulty ____ × 3.09 = 309, the number 3 becomes 300, for this reason obviouslythe absent factor is 100. You execute not even have to think about the decimal point!

The very same works through division, too. In the problem7,209 ÷ _____ = 7.209, the missing divisoris one thousand, since the worth of the digit 7was first 7000, and then it came to be 7.Of course, in some difficulties it will be easier to think in regards to “moving the decimal point.”


17.It is time because that some final practice. Uncover the lacking numbers. Complement the letter that each difficulty with the right answer in the boxes, and also solve the riddle. There space two set of boxes. The an initial boxes belong come the an initial set of exercises, and the latter boxes belong come the last set.

Why didn’t 7 recognize what 3.14 was talking about?

E ____ × 0.04 = 40D ____ × 9.381 = 938.1

H 1,000 × 4.20 =

D ____ × 7.31 = 731T ____ × 0.075 = 0.75

I 10 × 3.55 = ______

N 100 ×______ = 4.2S 1,000 × ______ = 355

E ____ × 60.15 = 60,150


4,200100010035.51000.042100.35510001000


T _____ ÷100 = 0.42P _____ ÷ 10 = 2.3

N _____ ÷ 1000 = 4.2

H
100 =2.3
I
10 =0.42

S 0.31 ÷_____ = 0.031O 4,360 ÷ _____ = 4.36

I 304.5 ÷ _____ = 3.045


230100102310004.24,20042


I additionally offer cost-free worksheets:Worksheets because that multiplying decimal by powers of tenWorksheets for separating decimals by strength of ten. Math Mammoth decimal 2
*

A self-teaching worktext for 5th-6th grade that covers the four operations v decimals increase to 3 decimal digits, concentrating top top decimal multiplication and division. The book also covers place value, comparing, rounding, addition and subtraction of decimals. There space a lot of of mental math problems.

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