In this Topic let's learn about decimals: The decimal numeral system is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as decimal notation.

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DECIMALS

2. What’s a decimal number?
A decimal number is a number which contains a decimal point.
Example: 0.13, 16.52, 0.009
A decimal may have both a whole-number part and a fractional part.
The whole-number part of a decimal are those digits to the left of the
decimal point. The fractional part of a decimal is represented by
the digits to the right of the decimal point.
DECIMALS
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3. How many decimal digits are there?
Example: In the decimal number 1.0827, the digits 0, 8, 2 and 7 are
called decimal digits.
In a decimal number, the digits to the right of the decimal point that
name the fractional part of that number, are called decimal digits.
Example: In the decimal number 1.0827, the digits 0, 8, 2 and 7 are
called decimal digits.
DECIMALS
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DECIMALS
What is the place value of 1006787.222451?

5. How can decimals be written as fractions and phrases?
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DECIMALS
Decimal Fraction Phrase
0.6 6/10 Six tenth
0.05 5/100 Five hundredth
0.32 32/100 Thirty two hundredth
0.267 267/1000
Two sixty seven
thousandth
0.001 1/1000 One thousandth
0.0054 54/10000 Fifty four ten thousandth

6. How do you expand a decimal number?
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DECIMALS
Decimal Expanded form
4.12 = 4 x 1 + 1 x 1/10 + 2 x 1/100
0.9 = 9 x 1/10
9.735 = 9 x 1 + 7 x 1/10 + 3 x 1/100 + 5 x 1/1000
1.0827 = 1 x 1 + 8 x 1/10 + 2 x 1/1000 + 7 x 1/10000
32.567 = 3 x 10 + 2 x 1 + 5 x 1/10 + 6 x 1/100 + 7 x 1/1000

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Some decimals and fractions equivalent in simplified
form
DECIMALS
Decimal Fraction Simplified form
0.5 5/10 1/2
0.25 25/100 1/4
0.75 75/100 3/4
0.2 2/10 1/5
0.4 4/10 2/5
0.6 6/10 3/5
0.8 8/10 4/5

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DECIMALS
Practice questions
1) What is the value of -58.63 + 100.12 – (87.1 + 34.62)?
a) -64.83 b) -80.23 c) -50.63 d) 40.23
1) b
Explanation:
-58.63 + 100.12 – (87.1 + 34.62) = 41.49 - 121.72 = -80.23

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DECIMALS
2) Arrange the following decimal numbers in ascending order:
6.6, 0.66, 0.066, 0.006
(a) 6.6, 0.066, 0.006, 0.66 (b) 0.66, 0.006, 0.066, 6.6
(c) 6.6, 0.66, 0.055, 0.006 (d) 0.006, 0.066, 0.66, 6.6
2) d

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DECIMALS
3) Which of the following is in standard form?
4 + (7 x 0.1) + (3 x 0.01) + (2 x 0.001)
a) 0.4732 b) 4.732 c) 47.32 d) 4732
3) b
Explanation: 4 + 0.7 + 0.03 + 0.002 = 4.732

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DECIMALS
4) What is the value of 0.1 x 0.02 x 0.003 x 0.0004?
a) 0.00000024 b) 0.0000000024
c) 0.000024 d) 0.000000000024
4) b
Explanation:
Number of decimal digits of 0.1 = 1
Number of decimal digits of 0.02 = 2
Number of decimal digits of 0.003 = 3
Number of decimal digits of 0.0004 = 4
Number of decimal digits = 1 + 2 + 3 + 4 = 10
0.1 x 0.02 x 0.003 x 0.0004 = 0.0000000024

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DECIMALS
5) If 2275 ÷ 12.5 = 182, then 22.75 ÷ 1.25 = ?
a) 0.182 b) 1.82 c) 18.2 d) 182
5) c

13. 6) The product of two numbers is 11.13. If one number is 2.1,
find the other.
a) 6.3 b) 3.5 c) 5.3 d) 3.3
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DECIMALS
6) c
Explanation: 11.13/2.1 = 5.3

14. 7) The correct expanded form of 4.08 is
a) (4 x 1) + (8 x 1/100) b) (4 x 1) + (8 x 1/10)
c) (4 x 10) + (8 x 1/10) d) (4 x 10) + (8 x 1/100)
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DECIMALS
7) a
Explanation:
4.08 = (4 x 1) + (0 x 1/10) + (8 x 1/100) = (4 x 1) + (8 x 1/100)

15. 8) If 133/0.133 = 13.3/m, then the value of m is
a) 0.0133 b) 0.133 c) 1.33 d) 133
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DECIMALS
8) a
Explanation:
133 x m = 13.3 x 0.133
 m = (13.3 x 0.133)/133 = 0.0001 x (133 x 133)/133 = 0.0133

16. 9) Which of the following fractions is less than 7/11 and greater
than 1/4?
a) 13/44 b) 9/44 c) 30/44 d) 43/44
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DECIMALS
9) a
Explanation:
7/11 = 28/44 and 1/4 = 11/44
Only 13/44 is between the above two fractions

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DECIMALS
10) 0.008/? = 0.02
a) 40 b) 4 c) 0.04 d) 0.4
10) d
Explanation:
? = 0.008/0.02 = 0.4

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DECIMALS
11) How many digits will be there to the right of the decimal
point in the product of 10.01 and 0.01234?
a) 7 b) 6 c) 5 d) None of these
11) a
Explanation:
Number of decimal digits of 1st number + number of decimal digits of
2nd number = 2 + 5 = 7

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DECIMALS
12) What approximate value should come in place of y in the
following question?
132 + y + 0.132 + 0.0132 = 133.4652
a) 13.32 b) 130.32 c) 1.32 d) 1.1234
12) c
Explanation:
y = 133.4652 - 132 - 0.132 - 0.0132 = 1.32

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DECIMALS
13) Which one is the odd one out?
a) i) b) iv)
c) iii) and iv) d) ii)

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DECIMALS
Answer to Q13)
13) d
Explanation:
1st shaded portion represents 1/2
2nd shaded portion represents 3/4
3rd shaded portion represents 3/6 = 1/2
4th shaded portion represents 4/8 = 1/2

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