How to Pass Level 7 Dividing in Is Ten Again

Multiply and Divide Decimals past x, 100, and thou
(powers of x)

This is a complete lesson with a video & exercises showing, kickoff of all, the common shortcut for multiplying & dividing decimals by powers of ten: you lot move the decimal bespeak as many steps as there are zeros in the number 10, 100, chiliad etc.

And so, I likewise show where this shortcut originates, using identify value charts. In reality, the decimal point moving is sort of an illusion, and instead, the digits of the number move within the identify value chart. This explanation can really assistance students to sympathize the reason behind the "trick" of moving the decimal betoken.

The lesson beneath explains the shortcut in more than detail, plus has unlike kinds of exercises, word problems, and even a fun riddle for students.

---

Think? When you multiply whole numbers by 10, 100, thou, and and so on (powers of 10), you tin just "tag" as many zeros on the product as there are in the gene 10, 100, 1000 etc. There is a similar shortcut for multiplying decimal numbers by numbers such as 10, 100, and 1000: Motion the decimal betoken to the right as many places as there are zeros in the cistron.

10 × 0 . 4 nine  = 04.9 = 4.9 Motion the decimal point one pace to the right (ten has i zero).

100 × 2 . 6 5 = 265. = 265 Movement the decimal point two steps to the right (100 has two zeros). The number 265. is 265 (equally shown above).

1000 × 0 . iii vii 0 = three 7 0 . = 370 1000 means nosotros move the signal three steps. Write a zero at the finish of 0.37 so that the decimal point can "jump over to" that identify.

1. Multiply.

a.   10 × 0.04 = ________ b.   100 × 0.04 = ________ c.   1000 × 0.04 = ________

d.   x × 0.56 = ________ e.   100 × 0.56 = ________ f. 1000 × 0.56 = ________

g. ten × 0.048 = ________ h. 100 × 0.048 = ________ i. 1000 × 0.048 = _______

Another helpful shortcut! Since 100 × 2 = 200, evidently the answer to
100 × 2.105 will be a picayune more than 200. Hence, you can just write the digits
2105 and put the decimal point so that the reply is 200-something: 210.5.

two. Allow'south practice some more.

a.   100 × 5.439 = ________ b.   100 × four.03 = ________

c.   yard × iii.06 = ________ d.   100 × 30.54 = ________

e.   30.73 × 10 = ________ f. 93.103 × 100 = _______

3. Now let'south practice using powers of ten.

a.   ten2 × 0.007 = _____________      103 × two.01 = _____________    ten5 × four.1 = ______________

b.   10five × 41.59 = _____________   iii.06 × 104 = ______________   0.046 × 10half dozen = _____________

The shortcut for division by 10, 100 and 1000 (powers of ten) is similar. Can you guess it? Motion the decimal bespeak to the ( left / correct ) for as many places (steps) as there are _________________________ in the factor 10, 100, or grand.

Move the decimal betoken 2 steps to the ____________. You need to write zeros in front of the number.

Move the decimal point four steps to the ____________. You need to write zeros in front of the number.

four. Carve up.

a.   0.4 ÷ 10 = ________ 0.4 ÷ 100 = ________   4.4 ÷ 100 = ________

b. 15.4 ÷ 100 = ________ 21.03 ÷ 10 = ________ 0.39 ÷ ten = ________

c.   5.6 ÷ 10 = ________    34.ix ÷ 100 = ________    230 ÷ thou = ________

5. Now let'south practice using powers of ten.

a.   0.7 ÷ 102 = _____________   45.3 ÷ xthree = _____________   568 ÷ 10five = _____________

b.    2.1 ÷ 10four  = _____________     4,500 ÷ 106 = _____________   9.13 ÷  ten3 = _____________

Why does this SHORTCUT work? When 0.01 (a hundredth) is multiplied by ten, we get ten hundredths, which is equal to one tenth. Or, 10 × 0.01 = 0.ane. The entire number moved ane "slot" to the left on the place value chart. This looks similar moving the decimal indicate in the number to the right. O t h th 0 . 0 1 O t h th 0 . 1

A hundred times ii tenths is like multiplying each tenth by x, and by ten over again. Ten times 2-tenths gives us 2, and ten times that gives us xx. Again, it is like moving the number over two "slots" to the left in the place value chart, or moving a decimal point in 0.2, 2 steps to the correct. T O t h th 0 0 . ii T O t h th 2 0 .

When 3.915 is multiplied past 100, we get 391.5. Each role of the number (3, 9 tenths, i hundredth, 5 thousandths) is multiplied past 100, and so each one of those moves two "slots" in the place value chart. This is identical to thinking that the decimal betoken moves 2 steps to the right. H T O t h th three . 9 1 5 H T O t h th 3 9 1 . five

The similar shortcut for division works because division is the opposite performance of multiplication—it "undoes" multiplication. If we motion the decimal point to the correct when multiplying by 10, 100, 1000 and so on, then information technology is quite natural that the rule for sectionalization would work the "contrary" way.

Fractions vs. division. If we movement the decimal bespeak to solve 6 ÷ 100, we become:

Let's write 6 ÷ 100 using the fraction line: it is   vi/100 or 6 hundredths, which is written 0.06 equally a decimal. Therefore, in this case you do not demand the "shortcut," simply you tin merely think of fractions and decimals. These kinds of "connections" make mathematics so bang-up!

half dozen. Dissever. Think of fractions to decimals, or utilize the shortcut. Compare the issues in each box!

seven. A 10-lb sack of nuts costs $72.
How much does one pound price?

viii. Find the price of 100 ping-pong balls if one ping pong ball costs $0.89.

Thinking more than nearly fractions and decimals

If we split whatsoever whole number past i,000, the answer volition have thousandths or iii decimal digits. This makes information technology piece of cake to carve up whole numbers by 1,000:  simply copy the dividend every bit your respond (without the commas), and then make it have three decimal digits:

Examples:

819,302 1000

= 819.302

41,300 1000

= 41.300 = 41.3

8,000 1000

= 8.000 = 8

Notice in the last 2 cases, we can simplify the results:  41.300 to 41.iii and eight.000 to 8.

nine. Divide whole numbers past 1000. Simplify the final respond by dropping any ending decimal zeros.

Similarly:

• If you divide any whole number by ten, copy the dividend and make information technology have one decimal digit.
• If y'all divide any whole number by 100, copy the dividend and make it take 2 decimal digits.

Examples:

72 10

= 7.two

three,090 100

= 30.ninety = xxx.nine

74,992 100

= 749.92

82,000 10

= 8200.0 = 8,200

ten. Dissever whole numbers by 10 and 100.

11. Discover one-tenth of...

a. $8

b. $25.50

c. $126

12. Detect 1-hundredth of...

a. $78

b. $4

c. $390

13. A pair of shoes that cost $29 was discounted by three/x of its cost. What is the new price?(Hint: First observe 1/ten of the price.)

14. Observe the discounted price:

      a. A bike that costs $126 is discounted by two/10 of its price.

      b. A $45 cell phone is discounted by 5/100 of its toll.
(Hint: Outset find i/100 of the price.)

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

sixteen. Which vacuum cleaner ends upward being cheaper?
Model A, with the initial price $86.xc, is discounted by three/10 of its price.

Model B costs $75 now, only y'all will become a discount of 1/4 of its toll.

An important tip

In the trouble  ____ ×  3.09  = 309, the number iii becomes 300, and so obviously
the missing gene is 100. You practice not even accept to consider the decimal point!

The same works with division, too. In the problem 7,209 ÷ _____ = 7.209, the missing divisor
is yard, because the value of the digit seven was commencement 7000, and and so information technology became 7.

Of course, in some problems it volition be easier to think in terms of  "moving the decimal signal."

17. Information technology is time for some final practice. Notice the missing numbers. Match the letter of each problem with the correct respond in the boxes, and solve the riddle. There are two sets of boxes. The first boxes belong to the first set up of exercises, and the latter boxes belong to the latter set.

Why didn't vii empathize what 3.14 was talking about?

Due east ____ ×  0.04  = 40 D  ____ × nine.381 = 938.1 H 1,000 × four.20 = D  ____ ×  7.31  = 731 T  ____ × 0.075 = 0.75

I 10 × iii.55 = ______ Northward   100 × ______ = 4.2 S 1,000 × ______ = 355 E ____ × 60.xv = 60,150

iv,200	1000		100	35.five	100	0.042		x		0.355	1000	1000
							'

T  _____ ÷ 100 = 0.42 P  _____ ÷ 10 = two.3 N  _____ ÷ one thousand = iv.2 H 100   = 2.iii

I 10   = 0.42 S 0.31 ÷ _____ = 0.031 O 4,360 ÷ _____ = 4.36 I 304.5 ÷ _____ = 3.045

230	100	10		23	k	four.2	4,200	42

---

I as well offer gratis worksheets:
Worksheets for multiplying decimals by powers of ten
Worksheets for dividing decimals past powers of x .

---

This lesson is taken from Maria Miller'southward book Math Mammoth Decimals 2, and posted at world wide web.HomeschoolMath.cyberspace with permission from the writer. Copyright © Maria Miller.

---

Math Mammoth Decimals 2

A cocky-teaching worktext for 5th-sixth grade that covers the four operations with decimals up to three decimal digits, concentrating on decimal multiplication and partition. The book also covers place value, comparison, rounding, addition and subtraction of decimals. In that location are a lot of mental math problems.

Download ($6.25). Also available as a printed copy.

=> Acquire more and run into the free samples!

moralespusting.blogspot.com

Source: https://www.homeschoolmath.net/teaching/d/multiply_divide_by_10_100_1000.php

Share this post