0
(a)
1. Let x = the repeating decimal. (a) x = 0.151 515 151 5…
2. Multiply
x by the power of 10 that
contains the same number of zeros as
there are digits in the repeating pattern.
The pattern contains 2 digits so
multiply by 100.
100
x = 15.151 515 15…
3. Subtract
x from the new value. 100x - x = 15.151 515 15 - 0.151 515 15
99
x = 15
4. Solve the linear equation found, putting
your answer in simplest (improper if
necessary) fraction form.
x
=
=
5. Check your answer by doing the division
on your calculator.
5
÷ 33 = 0.15151515…
(b)
1. Let x = the repeating decimal. (b) x = 1.244 444 44…
2. Multiply
x by the power of 10 that
contains the same number of zeros as
there are digits in the repeating pattern.
The pattern contains 1 digit so
multiply by 10.
10
x = 12.444 444…
3. Subtract
x from the new value. 10x - x = 12.444 444 - 1.244 444
9
x = 11.2
4. Solve the linear equation found, putting
your answer in simplest (improper if
necessary) fraction form.
x
= = =
5. Check your answer on your calculator. 56
÷ 45 = 1.244 44…
(c)
1. Let x = the repeating decimal. (c) x = 0.114 211 421 142…
2. Multiply
x by the power of 10 that
contains the same number of zeros as
there are digits in the repeating pattern.
The pattern contains 4 digits so
multiply by 10 000.
10 000
x = 1142.114 211 421 142…
3. Subtract
x from the new value. 10 000x - x = 1142.114 211 421 142
- 0.114 211 421 142
9999
x = 1142
4. Solve the linear equation found, putting
your answer in simplest (improper if
necessary) fraction form.
x
=
5. Check your answer on your calculator. 1142
÷ 9999 = 0.114 211 421 142…
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Presuming you are using limits, the exponentiation of two limits which diverge to infinity, also diverge to infinity. Or, using shorthand notation: ∞∞= ∞
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What is the shorthand notation for the electron configuration and germanium?
[Ar]4s23d104p2
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A shorthand method of writing very large or very small numbers?
Scientific notation.
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[Ar]4s^2 3d^6
What is the shorthand notation for Lead?
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1s^2 2s^2 2p^6 3s^2
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This is pharmacologic shorthand notation that means "administer this drug every 4 hours".
