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Found in: Page 292

### Physics Principles with Applications

Book edition 7th
Author(s) Douglas C. Giancoli
Pages 978 pages
ISBN 978-0321625922

# (a) How many seconds are there in 1.00 year? (b) How many nanoseconds are there in 1.00 year? (c) How many years are there in 1.00 second?

(a) The number of seconds in a year is $$3.15 \times {10^7}\;{\rm{s}}$$. (b) The number of nanoseconds in a year is $${\rm{3}}{\rm{.15}} \times {\rm{1}}{{\rm{0}}^{16}}\;{\rm{ns}}$$. (c) The number of years in one second is $${\rm{3}}{\rm{.17}} \times {\rm{1}}{{\rm{0}}^{ - 8}}\;{\rm{years}}$$.

See the step by step solution

## Step 1: Types of unit conversion

The types of unit conversion are as follows:

• Metric to metric (Example: kilograms to decigrams)
• Standard to standard (Example: miles to inches)
• Time (Example: days to seconds)
• Metric to standard or reverse (Example: pounds to grams or centimeters to miles)

## Step 2: Unit conversion from years to seconds

Convert the unit of time from years to seconds.

\begin{aligned}{l}T = \left( {{\rm{1}}\;{\rm{year}}} \right)\left( {\frac{{{\rm{365}}\;{\rm{days}}}}{{{\rm{1}}\;{\rm{year}}}}} \right)\left( {\frac{{{\rm{24}}\;{\rm{hours}}}}{{{\rm{1}}\;{\rm{day}}}}} \right)\left( {\frac{{{\rm{60}}\;{\rm{min}}}}{{{\rm{1}}\;{\rm{hour}}}}} \right)\left( {\frac{{{\rm{60}}\;{\rm{s}}}}{{{\rm{1}}\;{\rm{min}}}}} \right)\\T \approx 3.15 \times {10^7}\;{\rm{s}}\end{aligned}.

Thus, there are $$3.15 \times {10^7}\;{\rm{s}}$$ in one year.

## Step 3: Unit conversion from years to nanoseconds

Convert the unit of time from years to nanoseconds.

\begin{aligned}{l}T = \left( {{\rm{1}}\;{\rm{year}}} \right)\left( {\frac{{{\rm{365}}\;{\rm{days}}}}{{{\rm{1}}\;{\rm{year}}}}} \right)\left( {\frac{{{\rm{24}}\;{\rm{hours}}}}{{{\rm{1}}\;{\rm{day}}}}} \right)\left( {\frac{{{\rm{60}}\;{\rm{min}}}}{{{\rm{1}}\;{\rm{hour}}}}} \right)\left( {\frac{{{\rm{60}}\;{\rm{s}}}}{{{\rm{1}}\;{\rm{min}}}}} \right)\left( {\frac{{{\rm{1}}\;{\rm{ns}}}}{{{\rm{1}}{{\rm{0}}^{{\rm{ - 9}}}}\;{\rm{s}}}}} \right)\\T \approx 3.15 \times {10^{16}}\;{\rm{ns}}\end{aligned}.

Thus, there are $$3.15 \times {10^{16}}\;{\rm{ns}}$$ in one year.

## Step 4: Unit conversion from seconds to years

Convert the unit of time from seconds to years.

\begin{aligned}{l}T = \left( {1\;{\rm{s}}} \right)\left( {\frac{{1\;\min }}{{60\;{\rm{s}}}}} \right)\left( {\frac{{{\rm{1}}\;{\rm{hour}}}}{{{\rm{60}}\;{\rm{min}}}}} \right)\left( {\frac{{{\rm{1}}\;{\rm{day}}}}{{{\rm{24}}\;{\rm{hours}}}}} \right)\left( {\frac{{{\rm{1}}\;{\rm{year}}}}{{{\rm{365}}\;{\rm{days}}}}} \right)\\T \approx 3.17 \times {10^{ - 8}}\;{\rm{years}}\end{aligned}.

Thus, there are $$3.17 \times {10^{ - 8}}\;{\rm{years}}$$ in one second.