Scientific Understanding

**What sections should I know before attempting to learn this section?**

—> Introduction to Problem Solving

**What about more advanced metric unit conversions?**

We want to use the units and ratios we discussed in the previous section as mathematical tools for conversions. I will show you how to do one example problem of each of the three ratio techniques. Keep the unit prefixes table open as you are following the problems below.

**VIDEO Advanced Unit Conversions Solving Demonstrated Example 1: **If you have 1200 ng how many kg is that? (using only the base to decimal ratio)

**Step 1:**

What numbers and units does the question give you?

Answer: 1200 ng

**Step ****2****:**

What units does the question ask for?

Answer: kg

**Step ****3****:**

How do we start laying out the problem?

Answer: Put the numbers and units given by the question first.

1200 ng | |||

1 |

**Step ****4****:**

What comes next?

Answer: The units of the answer.

1200 ng | kg | ||

1 |

**Step ****5****:**

What is the first ratio I put between them?

Answer: 0.000 000 001 g / 1 ng, start with units.

1200 ng | g | kg | |

ng |

**Step ****6****:**

Fill in the numbers and cross out units

1200 ng | 0.000 000 001 g | kg | |

1 ng |

**Step ****7****:**

What is the second ratio?

Answer: 1000 g / 1 kg, start with units.

1200 ng | 0.000 000 001 g | kg | kg |

1 ng | g |

**Step ****8****:**

Fill in the numbers and cross out units

1200 ng | 0.000 000 001 g | 1 kg = | kg |

1 ng | 1000 g |

**Step ****9****:**

How do I complete the math?

Answer: (1200 * 0.000 000 001) / 1000 = 0.000 000 0012

1200 | 0.000 000 001 | 1 kg = | kg |

1 | 1000 |

**Step ****10****:**

COMPLETE ANSWER: 0.000 000 0012 kg or 1.2 * 10-9 kg

**VIDEO Advanced Unit Conversions Solving Demonstrated Example 2: **If you have 134 cm how many Mm is that? (using only the power of 10 ratio)

**Step 1:**

What numbers and units does the question give you?

Answer: 134 cm

**Step ****2****:**

What units does the question ask for?

Answer: Mm

**Step ****3****:**

How do we start laying out the problem?

Answer: Put the numbers and units given by the question first.

134 cm | |||

1 |

**Step ****4****:**

What comes next?

Answer: The units of the answer.

134 cm | Mm | ||

1 |

**Step ****5****:**

What is the first ratio I put between them?

Answer: 10^{-2} m / 1 cm, start with units.

134 cm | m | Mm | |

cm |

**Step ****6****:**

Fill in the numbers and cross out units.

134 cm | 10^{-2} m |
Mm | |

1 cm |

**Step ****7****:**

What is the second ratio?

Answer: 10^{6} m / 1 Mm, start with units.

134 cm | 10^{-2} m |
Mm | Mm |

1 cm | m |

**Step ****8****:**

Fill in the numbers and cross out units.

134 cm | 10^{-2} m |
1 Mm | Mm |

1 cm | 10^{6} m |

**Step ****9****:**

How do I complete the math?

Answer: (134 * 10^{-2}) / 10^{6} = 0.000 00134

134 | 10^{-2} |
1 Mm = | Mm |

1 | 10^{6} |

**Step ****10****:**

COMPLETE ANSWER: 0.000 00134 Mm or 1.34 * 10^{-6} Mm

**VIDEO Advanced Unit Conversions Solving Demonstrated Example 3: **If you have 369GL then how many pL is that? (using only the common ratio)

**Step 1:**

What numbers and units does the question give you?

Answer: 369GL

**Step ****2****:**

What units does the question ask for?

Answer: pL

**Step ****3****:**

How do we start laying out the problem?

Answer: Put the numbers and units given by the question first.

369 GL | |||

1 |

**Step ****4****:**

What comes next?

Answer: The units of the answer.

369 GL | pL | ||

1 |

**Step ****5****:**

What is the first ratio I put between them?

Answer: 1 000 000 000 L / 1 GL, start with units.

369 GL | L | pL | |

GL |

**Step ****6****:**

Fill in the numbers and cross out units.

369 GL | 1 000 000 000 L | pL | |

1 GL |

**Step ****7****:**

What is the second ratio?

Answer: 1 000 000 000 000 pL / 1 L, start with units.

369 GL | 1 000 000 000 L | pL | pL |

1 GL | L |

**Step ****8****:**

Fill in the numbers and cross out units.

369 GL | 1 000 000 000 L | 1 000 000 000 000 pL = | pL |

1 GL | 1 L |

**Step ****9****:**

How do I complete the math?

Answer: (369 * 1 000 000 000 * 1 000 000 000 000) = 3.69 *10^{23}

369 | 1 000 000 000 | 1 000 000 000 000 pL= | pL |

1 | 1 |

**Step ****10****:**

COMPLETE ANSWER: 3.69 * 10^{23} pL

**PRACTICE PROBLEMS**: Give the final answer for these questions. Use unit prefixes table if you need.

If you have 15 dag how many cg is that?

Answer: 15000 cg

If you have 27 um how many cm is that?

Answer: 0.0027 cm

How many kilograms are in 49 dg?

Answer: 0.0049 kg

How many megameters are in 98 hm?

Answer: 0.0098 hm

**When you finish the lesson, try out the metrics and conversions worksheet.**