Real Numbers - Decimal expansion of rational numbers for Grade x & class 10th maths. Lets tute is an online learning centre. We provide quality education for all learners and 24/7 academic guidance through E-tutoring. Our Mission- Our aspiration is to be a renowned unpaid school on Web-World. Contact Us - Website - www.letstute.com YouTube - www.youtube.com/letstute

1.  Decimal Expansion Of Rational numbers
 Euclid’s Division Algorithm
 Fundamental Theorem Of Arithmetic
 Proofs Based On Irrational Numbers

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3. Q) Write down the decimal expansions of the rational
numbers by expressing the denominators in the form 2m×5n,
where m & n are non-negative integers.
SOLUTION:
Multiplying the numerator and the denominator with 53 we get:
The decimal expansion of
𝟑
𝟖
is 0.375
a)
a)
b)
𝟑
𝟖
𝟏𝟗
𝟏𝟔𝟎𝟎
2 8
2 4
2 2
1
Decimal Expansion Of Rational Numbers
Chapter : Real Numbers Website: www.letstute.com
𝟑
𝟖
𝟑
𝟐 𝟑
=
=
𝟑 × 𝟓 𝟑
𝟐 𝟑 × 𝟓 𝟑
=
𝟑 × 𝟏𝟐𝟓
(𝟐 × 𝟓) 𝟑
=
𝟑𝟕𝟓
𝟏𝟎𝟎𝟎
= 𝟎. 𝟑𝟕𝟓
=
𝟑
𝟐 × 𝟐 × 𝟐

4. Multiplying the numerator and the
denominator with 54 we get,
= 0.011875
The decimal expansion of
𝟏𝟗
𝟏𝟔𝟎𝟎
is 0.011875.
b) 2 1600
2 800
2 400
2 200
2 100
2 50
5 25
55
1
Decimal Expansion Of Rational Numbers
Chapter : Real Numbers Website: www.letstute.com
𝟏𝟗 × 𝟓 𝟒
𝟐 𝟔 × 𝟓 𝟐 × 𝟓 𝟒
=
𝟏𝟗 × 𝟔𝟐𝟓
(𝟐 × 𝟓) 𝟔
=
𝟏𝟏𝟖𝟕𝟓
𝟏𝟎𝟎𝟎𝟎𝟎𝟎
𝟏𝟗
𝟏𝟔𝟎𝟎
=
𝟏𝟗
𝟐 𝟔 × 𝟓 𝟐

5. HOW TO
SOLVE

6. Real Numbers