Answer:
19439 seconds (nearest second)
5 hours 23 minutes 59 seconds (nearest second)
Step-by-step explanation:
Definitions
Nonillion and Septillion and extremely large numbers:
- Nonillion = 10³⁰ (1 with 30 zeros)
- Septillion = 10²⁴ (1 with 24 zeros)
Therefore:
- 5 nonillion = 5 × 10³⁰
- 257.21 septillion = 257.21 × 10²⁴
To find how long it will take to get 5 nonillion if you get 257.21 septillion per second, divide the number of nonillion by the number of septillion:
[tex]\implies \sf \dfrac{5 \times 10^{30}}{257.21 \times 10^{24}}[/tex]
[tex]\implies \sf \dfrac{5}{257.21} \times \dfrac{10^{30}}{10^{24}}[/tex]
[tex]\implies \sf \dfrac{500}{25721} \times \dfrac{10^{30}}{10^{24}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies \sf \dfrac{500}{25721} \times 10^{(30-24)}[/tex]
[tex]\implies \sf \dfrac{500}{25721} \times 10^6[/tex]
[tex]\implies \sf 0.01943936861... \times 10^6[/tex]
[tex]\implies \sf 19439.36861... seconds[/tex]
There are 3600 seconds in an hour, so to convert seconds to hours, divide by 3600:
[tex]\implies \sf \dfrac{19439.36861...}{3600}=5.399824614...hours[/tex]
[tex]\implies \sf 5\:hours\:23\:minutes\:59 \:seconds[/tex]
