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Mathematics, Decimal numbers and its operations(add,subtract,Multiply and Divide)
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DecimalsAdd, Subtract, Multiply &
Divide
28.9 + 32.5
61.4
T- 91-901-568-0202Email- [email protected]
By NM Spirit
Adding or Subtracting Decimals
Write the numbers in a vertical column, aligning digits according to their places.
Attach extra zeros to the right end of each number so each number has the same quantity of digits.
Add or subtract as though the numbers are whole numbers.
Place the decimal point in the sum or difference to align with the decimal point in the respective operation.
NM Spirit
Adding Decimals
Add the ones. There are 18 ones.
Add the tenths. There are 20 tenths.• Since 20 hundredths is 2 ones 0 tenths, write 0 in the tenths place. Write 2 as an addend in the ones place.
8.7842.560
+ 6.721
Ones
Tenth
s
Thousa
ndth
s
Add the hundredths. There are 16 hundredths.
• Since 16 hundredths is 1 tenth 6 hundredths, write 6 in the hundredths place. Write 1 as an addend in the tenths place.
12
0
Add up the thousandths. There are 5 thousandth.
So 8.784 + 2.56 + 6.721 = 18.065.NM Spirit
Subtracting Decimals
Try to subtract the hundredths. You will need more hundredths.• There are no tenths to use, so use a one. Change the
number of ones from 4 to 3. Raise the number of tenths from 0 to 9 and the number of hundredths from 3 to 13.
Now subtract. There are 9 thousandths.4.040 -2.6811.359
• Use one of the hundredths.• Since 1 hundredth = 10 thousandths, change the number of the hundredths from 4 to 3 and the number of thousandths from 0 to 10.
To subtract the thousandths, you will need more thousandths.
So, 4.040 – 2.681 = 1.359
Subtract the hundredths. There are 5 hundredths.
Subtract the tenths. There are 3 tenths.
Subtract the ones. There is 1 one.
9 13 10
NM Spirit
Multiply Decimals Multiply the decimal numbers as though they are
whole numbers.
Count the digits in the decimal parts of both decimal numbers.
Place the decimal point in the product so that there are as many digits in its decimal part as there are digits you counted in the previous step.
If necessary, attach zeros to the left end of the product to place the decimal point accurately.
21.4x 0.36
3 total decimal places
7 704.NM Spirit
Look at this example.3.45 x 4.082 =
How many places are there to the right of the decimal point?
Five; so, the answer will have five places to the right of the decimal.
The answer is 14.08290
The last zero can be dropped and the answer would be 14.0829.
Examples 920 x 3.7
= 3404.00.00079 x 0.025
= 0.00001975
Class Examples870 x 4.6
= 4002.00.000086 x 0.057
= 0.000004902NM Spirit
Dividing decimals is similar to dividing whole numbers. Same question…what about the decimal place?
Where does that go?
Steps
1. Make the divisor a whole number by shifting the decimal to the right as many times as necessary.
2. Move the decimal in the dividend the same number of times that we moved it in the divisor
7 0 6 4 2 0 9. . 0 ??????
Division of Decimals
NM Spirit
• Dividing decimals…… Steps1. Add zeros to the end of the dividend so that
we can round to the desired place value– Example: Round quotient to nearest tenth write 2
zeros after the decimal
– Round quotient to nearest thousandth need 4 zeros after the decimal
706 42090.00
706 42090.0000
NM Spirit
Dividing decimals……. Steps1. Do the division as if it were whole numbers2. Put the decimal place in the quotient
directly over the decimal point in the dividend
706 42090.00
00059.61 ≈ 59.6
NM Spirit
Each of the digits are the same. Each of the steps are the same. But the place values are different because of the decimal points.
3751814
7.38.5114
-570 76 -76 0
-57 0 7 6 -7 6 0
Examples #
0.378.514.1
-57 0 7 6 -7 6 0
NM Spirit
Comparing & Converting Fractions & Decimals
To convert a fraction decimalSteps
1. Divide the numerator of the fraction by the denominator
2. Round the quotient to a desired place value
Example Convert 3/7 to a decimal and round to nearest
Hundredth and Thousandth = 0.42857
Nearest Hundredth: 0.43 Nearest Thousandth: 0.429
NM Spirit
To convert a decimal fractionSteps
1. Count the number of decimal places
2. Remove the decimal point (and any leading zeros)
3. Put the decimal part over a denominator, – The denominator is a factor of 10 that has the same number of
zeros as decimal places (from step 1)
4. Put the fraction in simplest form
Example Convert 0.47 to a fraction
= 47/100
Convert 0.275 to a fraction 275/1000 = 11/40
Comparing & Converting Fractions & Decimals
NM Spirit
