Ch. 08. Decimals
लेखक
ॐ जितेन्द्र सिंह तोमर
M.A., B.Ed., DNYS, MASSCOM.
10/4/10/2/2022
* Fraction and Decimals
* interchanging of fraction into decimal and decimal into fraction
* Fraction as Decimals
* Decimals ad Fractions
* Reading And Writing Of Decimal Numbers
* Place Value
* Representing Decimals on number line
* Comparing Decimal Numbers
Like Decimals
Unlike Decimals
* Addition And Subtraction Of Decimals
* Multiplication Of Decimals
* Division Of Decimals
* Using Decimals In
Reading, Writing, Addition, Subtraction, Multiplication And Division
* Money. 0.00
Paies are written after decimal and rupees (₹) are written before decimal.
* In Length
Less than metre
Bigger than metre
* In Weight
Less than gram
Bigger than gram
* In Volume
Less than litre
Bigger than litre
What have we discussed?
1. To understand the parts of one whole (i.e. a unit) we represent a unit by a block. One block divided into 10 equal parts means each part is
1/10 (one-tenth) of a unit. It can
be written as 0.1 in decimal notation. The dot represents the decimal point and it comes between the units place and the tenths place.
2. Every fraction with denominator 10 can be written in decimal notation and vice-versa.
3. One block divided into 100 equal parts means each part is (1/100) (one-hundredth) of a unit. It can be written as 0.01 in decimal notation.
4. Every fraction with denominator 100 can be written in decimal notation and vice-versa.
5. In the place value table, as we go from left to the right, the multiplying factor becomes 1/10 of the previous factor.
The place value table can be further extended from hundredths to 1/10 of hundredths i.e. thousandths (1/1000), which is written as 0.001 in decimal notation.
6. All decimals can also be represented on a number line.
7. Every decimal can be written as a fraction.
8. Any two decimal numbers can be compared among themselves. The comparison can start with the whole part. If the whole parts are equal then the tenth parts can be compared and so on.
9. Decimals are used in many ways in our lives. For example, in representing units of money, length and weight.
Chapter 8
Decimals
Points to remember:
Decimal fractions: Fractions with denominator 10, 100, 1000.......... are called
decimal fractions.
Place value chart:
Ten
Thousands
Thousands
Hundreds
Tens
Ones
Tenths
Hundredths
Thousandths
10,000
1000
1
100
10
1
10
100
1
1000
Representing decimals on number line:
-0.4 -0.3-0.2 -0.10 01 02 03 04 05 06 07 08 09 10
11
12
13
14
15
Expansion and contraction of decimal numbers: For example: (i) 157.305-100+50 +7+-+ 3 5
+
10
3 4 (ii) 700+8+ + -708.034
Writing decimals as fractions and vice versa:
374
For example: (1) 3.74-5
100
(ii) 0.135 135 1000
(iii) 41 1000 -0.041
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Conversions:
(1)
rupees to paise
: multiply by 100
For example: 5-5×100-500 paise
(ii)
paise to rupees
: divide by 100
For example: 5 paise =
-0.05 100
(iii)
kilogram (kg) to grams
: multiply by 1000
(iv)
grams to kilogram (kg)
: divide by 1000
(v)
kilometre (km) to metres (m) metres (m) to kilometre (km)
: multiply by 1000
(vi)
: divide by 1000
(vii)
metres (m) to centimetres (cm)
: multiply by 100
(viii)
centimetres (cm) to metres (m) centimetres (cm) to millimetres (mm): multiply by 10
: divide by 100
(ix)
(x)
millimetres (mm) to centimetres (cm)
: divide by 10
metres (m) to millimetres (mm)
: multiply by 1000
(xii)
millimetres (mm) to metres (m) kilolitres (kl) to litres (1)
: divide by 1000
(xiii)
: multiply by 1000
(xiv)
litres (1) to kilolitres (kl)
: divide by 1000
(xv) litres (1) to millilitres (ml) : multiply by 1000
(xvi)
millilitres (ml) to litres (1)
: divide by 1000
Like and Unlike decimals:
(i)
Decimals having same number of decimal places are called like decimals.
For example: In 3.714 and 105.303, both have 3 decimal places.
(ii)
Decimals having different number of decimal places are called unlike
decimals.
For example: 17.8, 17.08, and 17.108
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When decimal numbers are multiplied by 10, 100, 1000 etc. the decimal point shifts to the right depending upon the number of zeros in 10, 100,
1000, etc..
0.05 x 100-5
For example: 0.5x 10-5, 0.5 100-50, When decimal numbers are divided by 10, 100, 1000, etc. the decimal point shifts to the left depending upon the number of zeros in 10, 100,
1000, etc..
For example: -0.0075, 0.75 100
3.57 100 -0.0357
To convert the fractions into equivalent fractions with denominator as
multiples of 10.
1 1×5 5 2 2x5 10
1x2 5x2 10
1x5 20 x 5 5 100
28 100 25 25 x 4
7x4
3x8 24 = = 125 125 x 8 1000
Questions:
1. Find the decimal form of
2.
Find the decimal for the following: (1) Twelve and seven tenths.
(ii) Four tens seven ones and three hundredths.
Find the decimal number for the points A, B and C as shown in the
number line.
3.
4.
Find 3 km and 120m in km using decimal.
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