Metric Conversions

Metric Prefixes

• How many years are in a decade?

• How many legs does a centipede have?

• How many years are in a millennium?

• Is a megaphone larger than a phone?

• Does a microscope look at big or small things?

Metric prefixes (cont.)Metric prefix Symbol Value Scientific Notation

Mega- M 1,000,000 106

kilo- k 1,000 103

deci- d _1_10

10-1

centi- c _1_100

10-2

milli- m __1__1,000

10-3

micro- µ ____1____1,000,000

10-6

nano- n ______1______1,000,000,000

10-9

Conversion factors

Remember: The base unit can be meters, liters, grams, seconds, etc.

Conversion factor problems

Write a conversion factor for the relationship between:

• Mg and g 1 Mg = 1,000,000 g

• µL and L 1 L = 1,000,000 µL

• ns and s 1 s = 1,000,000,000 ns

• cm and m 1 m = 100 cm

Metric Conversion steps for a 1-conversion factor problem

1. Write ? unit that you are trying to get = Example: you want grams for your final answer,so you would write:

2. Then write what you are givenExample: you are given 15 Mg, so you wouldwrite:

Metric Conversion steps for a 1-conversion factor problem

3. Next write a multiplication sign and a lineExample:

4. Now determine which unit to place on the bottom. You want to put the unit that you are given on the bottom so that the given units will cancel out.

Example:

Metric Conversion steps for a 1-conversion factor problem

5. Then determine which unit to place on the top. You want to put the unit that you are trying to solve for on the top so that these units are in your final answer.

Example:

6. Now find the conversion factor. Look at the staircase.

Metric Conversion steps for a 1-conversion factor problem

7. Looking at the staircase, ask yourself… Which is bigger? Mg or g?

8. The unit that is bigger gets a 1 written in front of it.

9. In this case Mg is bigger than g. 10.So, the 1 is written in front of Mg.

Metric Conversion steps for a 1-conversion factor problem

11. Look at the staircase and find the conversion factor number that matches the relationship for Mega and grams.

Example: In this case, it is 1,000,00012. This number gets written in front of the unit

that is smaller (remember g is smaller than Mg). In this case it is written in front of g.

Metric Conversion steps for a 1-conversion factor problem

13. Make sure your units line up correctly and cancel out. If they do…

14. Then solve the problem by multiplying 15 by 1,000,000 and dividing by 1.

Sample Problem (1-conversion factor)

• Convert 48 cg to grams:

• Convert 0.159 dL to liters:

1-step vs. 2-step

• How do I know if it is a 1-step or a 2-step problem? Do both units have prefixes?

No Then it is a 1-step problemExample: µg and g

Yes Then it is a 2-step problemExample: µg and Mg

Metric Conversion steps for a 2-conversion factor problem

1. Write ? unit that you are trying to get = Example: you want milligrams for your finalanswer, so you would write:

2. Then write what you are givenExample: you are given 39 kg, so you wouldwrite:

Metric Conversion steps for a 2-conversion factor problem

3. Next write a multiplication sign and a lineExample:

4. Now determine which unit to place on the bottom. You want to put the unit that you are given on the bottom so that the given units will cancel out.

Example:

Metric Conversion steps for a 2-conversion factor problem

5. Then determine which unit to place on the top. You want to put the base unit on the top so that you are setup to add the second conversion factor.

Example: In this case, the base unit is grams because both mg and kg contain a g.

6. Now find the conversion factor. Look at the staircase.

Metric Conversion steps for a 2-conversion factor problem

7. Looking at the staircase, ask yourself… Which is bigger? kg or g?

8. The unit that is bigger gets a 1 written in front of it.

9. In this case kg is bigger than g. 10.So, the 1 is written in front of kg.

Metric Conversion steps for a 2-conversion factor problem

11. Look at the staircase and find the conversion factor number that matches the relationship for kilo and grams.

Example: In this case, it is 1,00012. This number gets written in front of the unit

that is smaller (remember g is smaller than kg). In this case it is written in front of g.

Metric Conversion steps for a 2-conversion factor problem

13. Now write the base unit on the bottom of the second conversion factor.

14. And write the unit that you are trying to solve for on the top.

Metric Conversion steps for a 2-conversion factor problem

15. Looking at the staircase, ask yourself… Which is bigger? mg or g?

16.The unit that is bigger gets a 1 written in front of it.

17.In this case g is bigger than mg. 18.So, the 1 is written in front of g.

Metric Conversion steps for a 2-conversion factor problem

19. Look at the staircase and find the conversion factor number that matches the relationship for milli and grams.

Example: In this case, it is 1,00020. This number gets written in front of the unit

that is smaller (remember mg is smaller than g). In this case it is written in front of mg.

Metric Conversion steps for a 2-conversion factor problem

21. Make sure your units line up correctly and cancel out. If they do…

22. Then solve by multiplying 39 by 1,000 and again by another 1,000 and then dividing by 1.

Sample Problem (2-conversion factors)

• Convert 256 dg to Mg:

• Convert 13.67 km to nm: