Algebra Textbook Volume 1 Student Edition wc

SKILL Development

2.9A Place Value and Rounding Name_________________________________

The value of a digit depends on its ___________________________ in a number.

Place Values

, ,_______ _______ _______ _______ _______ _______ _______ . _______ _______ _______ _______ ______

A digit in the tens place means that the number has that many ______________________. A
digit in the thousands place means that the number has that many ___________________.

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2.9A (cont.) Name__________________________________

Give the place value for each digit in the following number:

7,618,350.294

2____________________________________________ 5_________________________________________

7____________________________________________ 9_________________________________________

3____________________________________________ 6 ________________________________________

1____________________________________________ 8 ________________________________________

4____________________________________________ 0 ________________________________________

When a number is calculated, it often has more _________________________ than need to be
carried. This number will then be ______________________________.

• When rounding a number to a certain decimal place, all of the digits to the
_______________________ of that decimal place are _____________________________ or
made equal to zero if holding a decimal place. [Example: 3.546 = 3.500 or
3.5]

• If the digit to the right of the indicated decimal place is _____________ ____________
_______________, the digit in the indicated decimal place is __________________________
______________ __________________. [Example: 3.245 = 4.250]

• If the digit to the right of the indicated decimal place is ________________
_______________ _________________, the digit in the indicated decimal place
____________________ ________________ ____________________. [Example: 3.244 = 3.240]

• Sometimes when rounding a number, zeros have to be put in place of digits
that are dropped to _________________ ___________ ____________________________
______________________.

Example: Round 20.0534 to the nearest hundredth. 5 is in the hundredths place.
Looking to the right, the number 3 is less than 5, so the number of interest (the 5)
remains the same. It is not rounded up. So, 20.05345, rounded to the hundredths
place is 20.05.

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2.9A (cont.) Name__________________________________

Round each of these numbers to the indicated decimal place:
Teacher-guided practice

1) 15.3165; tenths __________________ 2) 8.48923; hundredths ________________

Student practice 8) 7,166.8; thousand
______________________
3) 2.76; tenth
_____________________

4) .00648; thousandth 9) 249,800; hundred thousand
_____________________ _______________________

5) 1.711; ones 10) 106; ten
_____________________ ________________________

6) .029675; hundredth 11) 4,900,000; million
_____________________ ________________________

7) 465.3; ten 12) 405,000; ten thousand
_____________________ _________________________

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Practice 2.9B Name__________________________________

Place Values
Label the place values below:

_______, _______ _______ _______, _______ _______ _______ . _______ _______ _______ _______ _______

Rounding
Round each of these numbers to the indicated decimal place:

1) 4.7266; tenth 7) 6,086, 500; hundred thousand
________________________ ___________________________
2) 47.266; ten
________________________ 8) .7106; thousandth
3) .00613; ten thousandth ___________________________
________________________
4) 6.475; one 9) 6,016,500; thousand
________________________ ___________________________
5) 851.4; hundred
________________________ 10) 1,950, 000; million
6) .6549; hundredth ___________________________
________________________
11) 718, 569; ten thousand
____________________________

12) .04488; ten thousandth
_____________________________

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Practice 2.9C Name__________________________________

Place Values
Label the place values below:

_______, _______ _______ _______, _______ _______ _______ . _______ _______ _______ _______ _______

Rounding
Round each of these numbers to the indicated decimal place:

1) .7248 ; hundredth 7) 5,099,000 ; million
_______________________ _________________________

2) 351.7; hundred 8) 646,500; ten thousand
_______________________ __________________________

3) 9,795; thousand 9) .03279; ten thousandth
______________________ __________________________

4) .10526; ten thousandth 10) 7.408; one
_______________________ ___________________________

5) 68.168 ; ten 11) .2609; thousandth
_______________________ ___________________________

6) 9.217; tenth 12) 5,425, 164; hundred thousand
_______________________ ___________________________

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Practice 2.9D Name__________________________________

Place Values
Label the place values below:

_______, _______ _______ _______, _______ _______ _______ . _______ _______ _______ _______ _______

Rounding
Round each of these numbers to the indicated decimal place:

1) .0678; thousandth 7) 4,968,000; hundred thousand
__________________________ ___________________________

2) 209,500; ten thousand 8) .82544; ten thousandth
__________________________ ___________________________

3) 25; ten 9) 7,250,00; million
__________________________ ___________________________

4) 19.4498; tenth 10) .2607; thousandth
__________________________ ___________________________

5) 302,500; thousand 11) 49,500; thousand
__________________________ ___________________________

6) .7236; hundredth 12) 648.7; one
__________________________ ___________________________

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Name__________________________________

2.10 A Adding and Subtracting Decimals

When decimals are added or subtracted, the _____________________ ___________________
must be lined up. When there is no decimal point given in a number, the decimal
point is located to the __________________________ of the last _________________________.

Note: When adding or subtracting decimals, filling in gaps with zeroes can be useful.

Example: 14 + .63 + 1.2 14  14  00
 63 0  63
1  20
1 2

15  83

Problems: (5) .347−.025 (9) .613−.487
(1) .09+7+.8

(2) 8.2+.04 (6) 10−3.682 (10) .613 +.487

(3) .27+.73 (7) 7−3.118 (11) .9−.026

(4) 300+.45 (8) 4000−25.75 (12) 3000−258.4

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Practice 2.10B Name__________________________________
(1) 7+.05+.6
(6) .249+.751 (11) .66+200

(2) .47+.53 (7) 3−.025 (12) .489−.035

(3) .04+8 (8) 100−92.68 (13) .211−.085

(4) .645−.397 (9) 2000−425.6 (14) 5.4+75+19.6

(5) 10−6.475 (10) 1−.036 (15) .8−.064

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Practice 2.10 C Name__________________________________
(1) .004+3
(6) .346+.654 (11) .628−.052

(2) .322−.187 (7) 1−.029 (12) .22+.78

(3) 8−1.726 (8) .704−.588 (13) .3+9+.06

(4) 300−21.18 (9) .57+400 (14) .413−.096

(5) .7−.049 (10) 2−.007 (15) 3000−178.3

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Practice 2.10D Name__________________________________
(1) 2000−206.5
(6) 3−.002 (11) 200−10.05

(2) .521−.085 (7) .48+500 (12) 6−2.584

(3) .04+.2+5 (8) 1−.082 (13) .431−.178

(4) .34+.66 (9) .409+.591 (14) .002+4

(5) .712−.049 (10) .6−.017 (15) .805−.368

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Name__________________________________

2.11 A Multiplying and Dividing Decimals

To multiply decimals, first simply _________________________________the numbers as if the

_____________________ ____________________ were not there. Then go back and put the

decimal point in the correct place in the answer. The _____________________

_____________________ in the original numbers are counted and the _____________________

_________________ in the answer is put in that many places to the left of the last

______________________________ in the answer.

Example: .08  .7 = .056 .08 [2 decimal places]
.7 [1 decimal place]
2 places 1 place = 3 places .056 [3 decimal places, beginning

from the far right]

Problems: (5) .6 x .7
(1) .05 x .007

(2) .6 x 8 (6) .8 x .004

(3) .0004 x .9 (7) 3 x .09

(4) 20 x .003 (8) .0007 x .09

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2.11A cont’d Name__________________________________

To divide decimals the ________________ ____________________ must be in the correct place.

First put the decimal point right next to the division box in the number outside the

box. If it is necessary to move it to that position, then the _________________

_______________ of the number inside the division box must be moved in exactly the

same way. Finally the _______________ _______________ is raised straight up to exactly the

same spot in the answer. Placing the decimal point in the answer is best understood

with examples.

.6

Example: .3 = .5 .30 = 5. 3.0 .6 (or .60)= answer
.5

240 4000. 4000 =answer
.06
Example: = .06 240.00 = 6. 24000.

Note: zeros were added to hold decimal places.

Problems
Teacher-guided practice:

(1) .024 ÷ 8 = (5) 24 ÷ .8 =

(2) .024 ÷ .8 = (6) 24 ÷.008 =

(3) .024 ÷ .08 = (7) 24 ÷ 80 =

(4) .024 ÷ 80 = (8) 24 ÷ 800 =

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Practice 2.11B Name__________________________________
(1) .7 x .9 =
(7) 25 ÷ .05 = (13) 6.3 ÷ .009 =

(2) .003 x .06 = (8) 1.1 x .4 = (14) 36 ÷ .04 =

(3) .54 ÷ 6 = (10) .042 ÷ 7 = (15) 40 ÷ .008 =

(4) .8 x 4 = (10) .0042 ÷ 7 = (10) .00048 ÷ .08 =

(5) .72 ÷ .8 = (11) 240 ÷ .6 = (17) .05 x 9 =

(6) .004 x .009 = (12) 50 x .04 = (18) .4 ÷ 80 =

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Practice 2.11 C (7) 40 x .06 = Name__________________________________
(1) .00042 ÷ .007 = (13) .003 x .009 =

(2) .04 x 6 = (8) 360 ÷ .6 = (14) .64 ÷ .08 =

(3) .3 ÷ 60 = (9) .0021 ÷ .003 = (15) .9 x 9 =

(4) 50 x .007 = (10) .048 ÷ 8 = (16) .72 ÷ 9 =

(5) 32 ÷ .08 = (11) 1.2 x .3 = (17) .005 x .009 =

(6) 5.4 ÷ .009 = (12) 35 ÷ .007 = (18) .6 x .8 =

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Practice 2.11 D Name__________________________________
(1) .6 x .8 =
(7) 45 ÷ .05 = (13) 36 ÷ .006 =

(2) .07 x .0008 = (6) 1.2 x .3 = (14) 48 ÷ .06 =

(3) .32 ÷ 4 = (9) .00049 ÷ 7 = (15) 20 x .009 =

(4) .7 x 3 = (10) .0035 ÷ .007 = (16) .00063 ÷ .07 =

(5) .81 ÷ .9 = (11) 270 ÷ .9 = (17) .07 x 4 =

(6) .003 x .008 = (12) 40 x .03 = (18) .3 ÷ 50 =

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Name__________________________________

Practice 2.12A Adding, Subtracting, Multiplying, and Dividing Decimals

Everything learned about decimals so far is applied here. The following problems
involve adding, subtracting, multiplying and dividing decimals.

1) .165 + .33 = 9) .0054 ÷ 6 = 17) .2 x 1.2 =

2) .04 − .0078 = 10) 7 x .008 = 18) .0045 ÷ .09 =

3) .006 x .9 = 11) .01 − .00025 = 19) .8 x 9 =

4) .63 ÷ .07 = 12) .009 x .05 = 20) 3.2 ÷ .008 =

5) .06 x .04 = 13) .042 ÷ .007 = 21) 2 − .039 =

6) 48 ÷ .06 14) .5 + 12 +.03 22) .3 x .009

7) .615 + .385 = 15) .02 x 7 = 23) .049 ÷ 70 =
8) .00005 x .7 = 16) .56 ÷ .8 = 24) .5 − .21 =

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