SI Prefixes Used with Units

Solution to Example 1

\[ \begin{aligned} \text{Using the table above, the factor corresponding to the prefix} \\ \color{red}{\textbf{pico}} &= 0.000000000001 = 1 \div 1,000,000,000,000 \\ &= \displaystyle \frac{1}{1,000,000,000,000} = 10^{-12} \end{aligned} \]

Use the symbol p for pico and the symbol m for meters to write:

\[ 7 \; \color{red}{\textbf{p}}\textbf{m} \]

Substitute p (pico) by its factor and evaluate:

\[ 7 \times \color{red}{0.000000000001} \textbf{ m} \]

Solution to Example 2

\[ \begin{aligned} \text{Using the table above, the factor corresponding to the prefix} \\ \color{red}{\textbf{nano}} &= 0.000000001 = 1 \div 1,000,000,000 \\ &= \displaystyle \frac{1}{1,000,000,000} = 10^{-9} \end{aligned} \]

Use the symbol n for nano and the symbol m for meters to write:

\[ 3.2 \; \color{red}{\textbf{n}}\textbf{m} \]

Substitute n (nano) by its factor and evaluate:

\[ 3.2 \times \color{red}{0.000000001} \textbf{ m} \]

Solution to Example 3

\[ \begin{aligned} \text{Using the table above, the factor corresponding to the prefix} \\ \color{red}{\textbf{micro}} &= 0.000001 = 1 \div 1,000,000 \\ &= \displaystyle \frac{1}{1,000,000} = 10^{-6} \end{aligned} \]

Use the symbol μ for micro and the symbol g for grams to write:

\[ 8 \; \color{red}{\boldsymbol{\mu}}\textbf{g} \]

Substitute μ (micro) by its factor and evaluate:

\[ 8 \times \color{red}{0.000001} \textbf{ g} \]

Solution to Example 4

\[ \begin{aligned} \text{Using the table above, the factor corresponding to the prefix} \\ \color{red}{\textbf{milli}} &= 0.001 = 1 \div 1000 \\ &= \displaystyle \frac{1}{1000} = 10^{-3} \end{aligned} \]

Use the symbol m for milli and the symbol L for liters to write:

\[ 0.4 \; \color{red}{\textbf{m}}\textbf{L} \]

Substitute m (milli) by its factor and evaluate:

\[ 0.4 \times \color{red}{0.001} \textbf{ L} \]

Solution to Example 5

\[ \begin{aligned} \text{Using the table above, the factor corresponding to the prefix} \\ \color{red}{\textbf{centi}} &= 0.01 = 1 \div 100 \\ &= \displaystyle \frac{1}{100} = 10^{-2} \end{aligned} \]

Use the symbol c for centi and the symbol g for grams to write:

\[ 7 \; \color{red}{\textbf{c}}\textbf{g} \]

Substitute c (centi) by its factor and evaluate:

\[ 7 \times \color{red}{0.01} \textbf{ g} \]

Solution to Example 6

\[ \begin{aligned} \text{Using the table above, the factor corresponding to the prefix} \\ \color{red}{\textbf{deci}} &= 0.1 = 1 \div 10 \\ &= \displaystyle \frac{1}{10} = 10^{-1} \end{aligned} \]

Use the symbol d for deci and the symbol m for meters to write:

\[ 2.01 \; \color{red}{\textbf{d}}\textbf{m} \]

Substitute d (deci) by its factor and evaluate:

\[ 2.01 \times \color{red}{0.1} \textbf{ m} \]

Solution to Example 7

\[ \text{Using the table above, the factor corresponding to the prefix} \quad \color{red}{\textbf{deka}} = 10 \]

Use the symbol da for deka and the symbol m for meters to write:

\[ 5 \; \color{red}{\textbf{da}}\textbf{m} \]

Substitute da (deka) by its factor and evaluate:

\[ 5 \times \color{red}{10} \textbf{ m} \]

Solution to Example 8

\[ \text{Using the table above, the factor corresponding to the prefix} \quad \color{red}{\textbf{hecto}} = 100 = 10^2 \]

Use the symbol h for hecto and the symbol L for liters to write:

\[ 9.23 \; \color{red}{\textbf{h}}\textbf{L} \]

Substitute h (hecto) by its factor and evaluate:

\[ 9.23 \times \color{red}{100} \textbf{ L} \]

Solution to Example 9

\[ \text{Using the table above, the factor corresponding to the prefix} \quad \color{red}{\textbf{kilo}} = 1000 = 10^3 \]

Use the symbol k for kilo and the symbol g for grams to write:

\[ 3.4 \; \color{red}{\textbf{k}}\textbf{g} \]

Substitute k (kilo) by its factor and evaluate:

\[ 3.4 \times \color{red}{1000} \textbf{ g} \]

Solution to Example 10

\[ \text{Using the table above, the factor corresponding to the prefix} \quad \color{red}{\textbf{Mega}} = 1,000,000 = 10^6 \]

Use the symbol M for Mega and the symbol W for Watts to write:

\[ 7.6 \; \color{red}{\textbf{M}}\textbf{W} \]

Substitute M (Mega) by its factor and evaluate:

\[ 7.6 \times \color{red}{1,000,000} \textbf{ W} \]

Solution to Example 11

\[ \text{Using the table above, the factor corresponding to the prefix} \quad \color{red}{\textbf{Giga}} = 1,000,000,000 = 10^9 \]

Use the symbol G for Giga and the symbol W for Watts to write:

\[ 0.3 \; \color{red}{\textbf{G}}\textbf{W} \]

Substitute G (Giga) by its factor and evaluate:

\[ 0.3 \times \color{red}{1,000,000,000} \textbf{ W} \]

Solution to Example 12

\[ \text{Using the table above, the factor corresponding to the prefix} \quad \color{red}{\textbf{Tera}} = 1,000,000,000,000 = 10^{12} \]

Use the symbol T for Tera and the symbol W for Watts to write:

\[ 1.3 \; \color{red}{\textbf{T}}\textbf{W} \]

Substitute T (Tera) by its factor and evaluate:

\[ 1.3 \times \color{red}{1,000,000,000,000} \textbf{ W} \]

Solutions to the Above Exercises

Part A: Convert to meters (m)

1. \( 0.02 \text{ Mm} \) to meters

   \[ 0.02 \text{ Mm} = 0.02 \times 1,000,000 \text{ m} \]
   \[ 0.02 \text{ Mm} = 20,000 \text{ m} \]



2. \( 234 \text{ dam} \) to meters

   \[ 234 \text{ dam} = 234 \times 10 \text{ m} \]
   \[ 234 \text{ dam} = 2340 \text{ m} \]



3. \( 1200 \text{ pm} \) to meters

   \[ 1200 \text{ pm} = 1200 \times 0.000000000001 \text{ m} \]
   \[ 1200 \text{ pm} = 0.0000000012 \text{ m} \]



4. \( 205 \text{ nm} \) to meters

   \[ 205 \text{ nm} = 205 \times 0.000000001 \text{ m} \]
   \[ 205 \text{ nm} = 0.000000205 \text{ m} \]



5. \( 0.002 \text{ cm} \) to meters

   \[ 0.002 \text{ cm} = 0.002 \times 0.01 \text{ m} \]
   \[ 0.002 \text{ cm} = 0.00002 \text{ m} \]



6. \( 1.002 \text{ hm} \) to meters

   \[ 1.002 \text{ hm} = 1.002 \times 100 \text{ m} \]
   \[ 1.002 \text{ hm} = 100.2 \text{ m} \]



7. \( 0.005 \text{ Gm} \) to meters

   \[ 0.005 \text{ Gm} = 0.005 \times 1,000,000,000 \text{ m} \]
   \[ 0.005 \text{ Gm} = 5,000,000 \text{ m} \]



8. \( 1.34 \; \mu\text{m} \) to meters

   \[ 1.34 \; \mu\text{m} = 1.34 \times 0.000001 \text{ m} \]
   \[ 1.34 \; \mu\text{m} = 0.00000134 \text{ m} \]



9. \( 23000 \; \text{mm} \) to meters

   \[ 23000 \; \text{mm} = 23000 \times 0.001 \text{ m} \]
   \[ 23000 \; \text{mm} = 23 \text{ m} \]



10. \( 1.003 \; \text{dm} \) to meters

    \[ 1.003 \; \text{dm} = 1.003 \times 0.1 \text{ m} \]
    \[ 1.003 \; \text{dm} = 0.1003 \text{ m} \]



11. \( 0.02 \; \text{km} \) to meters

    \[ 0.02 \; \text{km} = 0.02 \times 1000 \text{ m} \]
    \[ 0.02 \; \text{km} = 20 \text{ m} \]



12. \( 0.01 \text{ Tm} \) to meters

    \[ 0.01 \text{ Tm} = 0.01 \times 1,000,000,000,000 \text{ m} \]
    \[ 0.01 \text{ Tm} = 10,000,000,000 \text{ m} \]

Part B: Convert to grams (g)

1. \( 0.003 \text{ Tg} \) to grams

   \[ 0.003 \text{ Tg} = 0.003 \times 1,000,000,000,000 \text{ g} \]
   \[ 0.003 \text{ Tg} = 3,000,000,000 \text{ g} \]



2. \( 0.3 \; \text{dg} \) to grams

   \[ 0.3 \; \text{dg} = 0.3 \times 0.1 \text{ g} \]
   \[ 0.3 \; \text{dg} = 0.03 \text{ g} \]



3. \( 1.2 \; \text{kg} \) to grams

   \[ 1.2 \; \text{kg} = 1.2 \times 1000 \text{ g} \]
   \[ 1.2 \; \text{kg} = 1200 \text{ g} \]



4. \( 1000 \; \mu\text{g} \) to grams

   \[ 1000 \; \mu\text{g} = 1000 \times 0.000001 \text{ g} \]
   \[ 1000 \; \mu\text{g} = 0.001 \text{ g} \]



5. \( 0.056 \text{ Mg} \) to grams

   \[ 0.056 \text{ Mg} = 0.056 \times 1,000,000 \text{ g} \]
   \[ 0.056 \text{ Mg} = 56,000 \text{ g} \]



6. \( 2.3 \text{ dag} \) to grams

   \[ 2.3 \text{ dag} = 2.3 \times 10 \text{ g} \]
   \[ 2.3 \text{ dag} = 23 \text{ g} \]



7. \( 102.4 \text{ cg} \) to grams

   \[ 102.4 \text{ cg} = 102.4 \times 0.01 \text{ g} \]
   \[ 102.4 \text{ cg} = 1.024 \text{ g} \]



8. \( 20.2 \text{ hg} \) to grams

   \[ 20.2 \text{ hg} = 20.2 \times 100 \text{ g} \]
   \[ 20.2 \text{ hg} = 2020 \text{ g} \]



9. \( 0.001 \text{ Gg} \) to grams

   \[ 0.001 \text{ Gg} = 0.001 \times 1,000,000,000 \text{ g} \]
   \[ 0.001 \text{ Gg} = 1,000,000 \text{ g} \]



10. \( 1100 \text{ pg} \) to grams

    \[ 1100 \text{ pg} = 1100 \times 0.000000000001 \text{ g} \]
    \[ 1100 \text{ pg} = 0.0000000011 \text{ g} \]



11. \( 9000 \text{ ng} \) to grams

    \[ 9000 \text{ ng} = 9000 \times 0.000000001 \text{ g} \]
    \[ 9000 \text{ ng} = 0.000009 \text{ g} \]



12. \( 23000 \; \text{mg} \) to grams

    \[ 23000 \; \text{mg} = 23000 \times 0.001 \text{ g} \]
    \[ 23000 \; \text{mg} = 23 \text{ g} \]

Part C: Convert to liters (L)

1. \( 200 \; \text{mL} \) to liters

   \[ 200 \; \text{mL} = 200 \times 0.001 \text{ L} \]
   \[ 200 \; \text{mL} = 0.2 \text{ L} \]



2. \( 0.005 \text{ TL} \) to liters

   \[ 0.005 \text{ TL} = 0.005 \times 1,000,000,000,000 \text{ L} \]
   \[ 0.005 \text{ TL} = 5,000,000,000 \text{ L} \]



3. \( 1.4 \text{ hL} \) to liters

   \[ 1.4 \text{ hL} = 1.4 \times 100 \text{ L} \]
   \[ 1.4 \text{ hL} = 140 \text{ L} \]



4. \( 0.00002 \text{ GL} \) to liters

   \[ 0.00002 \text{ GL} = 0.00002 \times 1,000,000,000 \text{ L} \]
   \[ 0.00002 \text{ GL} = 20,000 \text{ L} \]



5. \( 440000 \text{ pL} \) to liters

   \[ 440000 \text{ pL} = 440000 \times 0.000000000001 \text{ L} \]
   \[ 440000 \text{ pL} = 0.00000044 \text{ L} \]



6. \( 500 \text{ nL} \) to liters

   \[ 500 \text{ nL} = 500 \times 0.000000001 \text{ L} \]
   \[ 500 \text{ nL} = 0.0000005 \text{ L} \]



7. \( 0.007 \text{ ML} \) to liters

   \[ 0.007 \text{ ML} = 0.007 \times 1,000,000 \text{ L} \]
   \[ 0.007 \text{ ML} = 7000 \text{ L} \]



8. \( 1.06 \text{ daL} \) to liters

   \[ 1.06 \text{ daL} = 1.06 \times 10 \text{ L} \]
   \[ 1.06 \text{ daL} = 10.6 \text{ L} \]



9. \( 203.6 \text{ cL} \) to liters

   \[ 203.6 \text{ cL} = 203.6 \times 0.01 \text{ L} \]
   \[ 203.6 \text{ cL} = 2.036 \text{ L} \]



10. \( 0.02 \; \text{dL} \) to liters

    \[ 0.02 \; \text{dL} = 0.02 \times 0.1 \text{ L} \]
    \[ 0.02 \; \text{dL} = 0.002 \text{ L} \]



11. \( 10.1 \; \text{kL} \) to liters

    \[ 10.1 \; \text{kL} = 10.1 \times 1000 \text{ L} \]
    \[ 10.1 \; \text{kL} = 10100 \text{ L} \]



12. \( 100 \; \mu\text{L} \) to liters

    \[ 100 \; \mu\text{l} = 100 \times 0.000001 \text{ L} \]
    \[ 100 \; \mu\text{L} = 0.0001 \text{ L} \]