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| Decimal
Numbers |
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Adding and subtracting decimals |
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Multiplying and dividing decimals
by power of ten
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Place
values and place holders
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Multiplying and dividing decimals
by decimal units
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Decimal numbers scientific notation
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Multiplication of decimal numbers
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Division of decimal numbers |
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| Adding and subtracting decimals |
| To add or subtract decimals, insert zeros in empty decimal place
values so that all of the numbers have the same number of decimal
places. |
| Write the corresponding decimal places one under another,
i.e., the decimal points should be vertically aligned, and then follow
the rules for adding or subtracting whole numbers. |
| Line up the
decimal point in the answer. |
|
| Examples: |
|
a)
7.9 + 12 + 0.147 =
20.047,
b)
215.04 + 3.756 + 17.3 = 236.096 |
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|
7.900
215.040 |
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12.000
3.756 |
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+
0.147
+ 17.300 |
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20.047
236.096 |
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c)
41.56
− 9.178 =
32.382,
d)
5.08
− 0.9937 = 4.0863 |
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41.560
5.0800 |
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−
9.178
−
0.9937 |
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32.382
4.0863 |
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| Multiplying and dividing decimals
by powers of ten
|
| Place
values and place holders
|
| To the left of the decimal point, the digits represent 1's, 10's, 100's,
1000's, and so on. |
| Digits to the right of the decimal point represent
1/10's, 1/100's, 1/1000's, and so forth. |
| To find the value of a decimal
place, we divide the value of the decimal place to the left of it by 10. |
| The place value of each column is one tenth of the place value of
the column to its left. Or, we can say that each decimal unit contains
10 units of the lower place value thus, |
| 0.1 = 10 · 0.01,
0.01 = 10 · 0.001, and so on. |
| |
| Multiplying and dividing decimals
by
powers
of ten |
| To multiply decimals by powers of
10, such as 10, 100, 1000 etc. move the decimal point right as many places as there are
zeros in the power. |
| To divide decimals by powers of
10, move the decimal point left as many places as there are zeros in the
power. |
|
| Examples: |
|
a)
0.58 ·10 =
5.8,
b)
79.4 ·100 =
7940,
c)
0.001 ·10000 = 10, |
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d)
30.07 ¸
10 = 3.007,
e)
0.08 ¸
100 = 0.0008,
f)
12.0 ¸
1000 = 0.012. |
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| Multiplying and dividing decimals
by decimal units
|
| To multiply decimal by the decimal
units; 0.1, 0.01, 0.001, ... Move the decimal point of the decimal left as many places as there are
zeros in the decimal unit. |
| Divide decimal by the decimal units by
moving the decimal point of the decimal right as many places as there are zeros in the decimal unit. |
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| Examples: |
|
a)
83.05 · 0.1 = 8.305, b)
547.2 · 0.001 = 0.5472, c)
0.9 · 0.0001 = 0.00009, |
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d)
0.75 ¸
0.001 = 750,
e)
4.035 ¸
0.01 = 403.5,
f)
29.0 ¸
0.1 = 290. |
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| Decimal numbers scientific notation
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| Scientific
notation is used to express very large or very small numbers. |
| A
number in scientific notation is written as the product of a
number (the coefficient) and a power of 10 (the exponent), i.e., |
| coefficient ´
10exponent |
| The
coefficient should have exactly one non-zero digit to the left of the decimal point. The
exponent indicates, how many places the decimal point was moved to
the left or to the right. If the decimal point was moved to the left,
the exponent is positive, if moved to the right the
exponent is negative. |
|
| Converting
from a number to scientific notation: |
| Examples: |
|
a)
302,567,908 = 3.02567908 · 108 b)
0.000040635 = 4.0635 · 10−5. |
|
| Converting
from scientific notation to a decimal number: |
| Examples: |
|
a)
2.09085 · 107 = 20908500
b)
7.81 · 10−5
= 0.0000781 |
|
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| Multiplication of decimal numbers
|
| To multiply decimal numbers, ignore the decimal points and multiply
the digits. Count the total number of decimal places in both decimal
numbers being multiplied. |
| Place a decimal point in the answer so
that it has as many digits to the right of the decimal point as the total number of decimal places in the two decimals being multiplied. |
|
| Examples: |
|
a)
0.589 · 47.8,
b)
79.6 · 0.00503,
c)
629.7 · 1.03 |
|
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2356 3980
6297 |
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4123
000
0000 |
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4712
2388
18891 |
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28.1542
0.400388
648.591 |
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| Division of decimal numbers |
| To divide decimal numbers, first make the divisor into a whole
number by multiplying both the dividend and the
divisor by the same
power of 10 (such as 10, 100, 1000, . . .) or move a decimal point in
the divisor to the right end, and in the dividend the same number of
places. |
| To divide a decimal by a whole number, divide as you would
for whole numbers. Place decimal point in the answer so that it
lines up with the decimal point in the dividend. |
| If after dividing
there is a remainder, add a zero to the dividend and continue to divide
until there is no remainder or the decimals repeat. |
|
| Examples: |
|
a)
467.5 ¸ 17 = 27.5,
b)
2.773 ¸ 0.47 = (2.773 ·
100) ¸
(0.47 · 100), |
|
|
−
34
= 277.3 ¸
47 = 5.9 |
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127
− 235 |
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− 119
423 |
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85
− 423 |
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− 85
0 |
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0 |
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c)
0.15059 ¸ 3.7 = 1.5059 ¸
37 = 0.0407, d)
10.8 ¸ 0.004 =
10800 ¸
4
=
2700 |
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150
− 8 |
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− 148
28 |
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259
− 28 |
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− 259
0 |
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0 |
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| Beginning
Algebra Contents A |
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| Copyright
© 2004 - 2020, Nabla Ltd. All rights reserved. |
