Question

The age of the universe is thought to be about 14 billion years. Assuming two significant figures, (a) write this in exponential notation in units of years, and (b) use the method shown in class to convert this to seconds. Give your answer in exponential notation.

Answer 1

a) 14×10⁹ years

b) 4.4×10¹⁷ seconds

Step-by-step explanation:

1 billion years = 1000000000 years

1000000000 years = 10⁹ years

14 billion years

= 14×1000000000 years

= 14000000000 years

= 14×10⁹ years

∴ 14 billion years = 14×10⁹ years

b) 1 year = 365.25×24×60×60 seconds

14×10⁹ years = 14×10⁹×365.25×24×60×60

= 441806400×10⁹ seconds

Rounding off, we get

= 4.4×10⁸×10⁹

= 4.4×10¹⁷ seconds

∴ 14 billion years = 4.4×10¹⁷ seconds