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Gyaan Maths
CBSE · Class 6-12
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Class 7 · Ganita Prakash
Unit 12 · Class 7Ganita Prakash
Another Peek Beyond the Point
Deeper decimals — recurring decimals, comparing, rounding.
Lessons
3 concepts
1
Terminating vs Recurring
p
/
q
p/q
p
/
q
in lowest form terminates iff denominator has only 2s and 5s as prime factors.
2
Recurring to Fraction
Let
x
=
0.
3
‾
x = 0.\overline 3
x
=
0.
3
. Then
10
x
=
3.
3
‾
10x = 3.\overline 3
10
x
=
3.
3
; subtract:
9
x
=
3
9x = 3
9
x
=
3
, so
x
=
1
/
3
x = 1/3
x
=
1/3
. For
0.
a
b
‾
0.\overline{ab}
0.
ab
: multiply by 100.
3
Rounding Rules
If digit right of rounding place is ≥5, round up; else keep.
3.147
→
3.15
3.147 \to 3.15
3.147
→
3.15
(2 dp).
Skills to practise
Skill · medium
Another Peek Beyond the Point — Practice