Terminating Decimal/Examples/0.625
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Example of Terminating Decimal
The number $\dfrac 5 8$ can be expressed as a terminating decimal:
- $\dfrac 5 8 = 0 \cdotp 625$
Proof
| \(\ds 0 \cdotp 625\) | \(=\) | \(\ds \dfrac 6 {10} + \dfrac 2 {100} + \dfrac 5 {1000}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac {600} {100} + \dfrac {20} {100} + \dfrac 5 {1000}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac {600 + 20 + 5} {1000}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac {625} {1000}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac {5 \times 5^3} {8 \times 5^3}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac 5 8\) |
$\blacksquare$
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): decimal
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): decimal