Question

The age of the universe is thought to be about 14 billion years. Assuming two significant figures, write this in powers of ten in (a) years, (b) seconds.

Answer 1

A ) 14 billion years =  14,000,000,000
$1.4 * 10^{10}$
b ) 1 year = 365 · 24 · 3,600 = 31,536 · 10³ 
$1.4 * 10 ^{10}*3.1536 * 10^{7} =4.4 * 10 ^{17}$

Answer 2

Answers:

a) 1.4 × 10¹⁰ years

b) 4.4 × 10¹⁷ seconds

Explanation:

1) Significant figures are the digits of a measure which are reported as known plus one uncertain digit.

This is, given 14 billion, the number of signficant figures is two, meaning the the second digit (4) is not exact. The right measure (number) might perfectly be 13 or 15 because, the last digit is not exact.

2) Now write 14 billions as a power of ten:

14 billions = 14,000,000,000.

Those are 9 zeros after 14.

Then, in power of ten that is: 14 × 10⁹

3) It is usual also to write in scientific notation; that is with a base greater than 0 and less than 10:

⇒1.4 × 10¹⁰ years (1 and 4 are the two signiticant digits)

4) Now convert to seconds

1.4 × 10¹⁰ years × 365 days/year × 24 hours/day × 3600 s/hour = 44,150,400 × 10¹⁰ s

5) Pass to scientific notation: 4.4150400 × 10¹⁷ s

6) Round to two significant figures: 4.4 × 10¹⁷ s (4 and 4 are the two significant figures)