Metric Prefixes

Metric Prefixes are “labels” that can be placed in front of base units. 

Metric Prefix Multipliers

Concept: Understanding Metric Prefixes

1m
Video Transcript

Now, what exactly is a metric prefix? Just understand it's kind of like a label that goes in front of what we call base units.
Now, what's a base unit? Good examples of base units are liters or seconds or grams or moles or minutes, these can be understood as base units and all a metric prefix is is a label that goes in front of that base unit, to describe what kind of base unit we're dealing with.
Here we're going to say we could have deciliters or kiloseconds or nanograms or millimoles or microminutes. The metric prefix is just a way of describing a change that's going on with that base unit, so they're just labels that go in front.

Concept: Using the Metric Prefix Chart

2m
Video Transcript

If we take a look here at this chart, this gives us a majority of the metric prefix that you're responsible for. Now there are some that go after pico and there are some that go after tera, but for the most part, professors will stick to this core group of metric prefixes.
What we're going to have to say here is, just remember, this is very important, one—is associated with the metric prefix, so one is associated with each one of this metric prefixes. What does that mean?
Let's say I had a picometer. Meter is the base. Pico is the metric prefix that goes in front of it. Since one is associated with my metric prefix, we're going to say 1 picometer is equal to, see right here, 10-12 meters. It's a way of setting things where you form a relationship between the metric prefix and the base.
Let's say I had kilo. So let's say I had kilograms and I wanted to go to grams, so we'd say that for every 1, because kilo is a metric prefix for every 1 kg, it is 103 grams, so that's what I mean by 1 is associated with the metric prefix. So remember that when we're doing these types of metric prefix conversions. 

Whenever using the metric prefix chart, remember that “1” is associated with the metric prefix. 

Example: Convert the following to the desired units. 

16.33 pm to m                                  172 GL to L 

4m

Example: Convert the following to the desired units.

0.73 cs to ns                          729 kg to mg

4m

Example: Convert the following to the desired units. 

453 cm3 to km3                 1.32 x 106  hm2  to  mm2

7m

Metric Prefixes Additional Practice Problems

4.934 mg/mL = _____ g/L 

Express your answer using four significant figures. 


4.934 mg/mL = ________ μg/mL 

Express your answer using four significant figures.

Watch Solution

Which metric prefix stands for 10-9?

a. centi-

b. milli-

c. pico-

d. micro-

e. nano-

Watch Solution

For light with a wavelength of 3.60 μm, calculate the corresponding wavenumber value.

Watch Solution

Which of the following sets of units is not in the order of increasing size?

a. mg < g < kg

b. uL < mL < L

c. ns < ms < s

d. mm < pm < cm

e. all of the above are in the correct order.

Watch Solution

How many milligrams of sodium sulfate are equivalent to 0.0562 kg?

a. 5.62 x 10-2 mg

b. 5.62 x 104 mg

c. 56.2 mg

d. 5.62 x 1010 mg

e. 5.62 x 107 mg

Watch Solution

Which of the following is the smallest mass?

a. 1000 g

b. 1000 ng

c. 1000 mg

d. 1000 kg

e. 1000 ug

Watch Solution

Which of the following is the largest mass?

a. 1000 g

b. 1000 ng

c. 1000 mg

d. 1000 kg

e. 1000 ug

Watch Solution

Which statemnent below is correct?

a. 100 mL = 1L

b. 10 mm = 1 cm

c. 150 g is greater than 0.150 kg

d. 1 microsecond =  106 seconds

e. all the above are correct

 

Watch Solution

One-thousandth of a micrometer is a?

a. picometer

b. meter

c. millimeter

d. nanometer

e. kilometer

 

Watch Solution

The mountain is 19, 341 feet tall. Convert this height to the  SI unit for length. To get you started, 1km = 3280.84 ft.

A) 5.8951 km

B) 6.3455 x 107 km

C) 5895.1 m

D) 6.3455 x 108 m

Watch Solution

The diameter of the nucleus of an atom is approximately 1 × 10 -15 m. If 1 nm is equal to 10 Ångstroms, what is the diameter of the nucleus in Ångstroms?

A) 1 × 10 -5 Å

B) 1 × 10 -7 Å

C) 1 × 10 -23 Å

D) 1 × 10 -8 Å

Watch Solution

Convert 5 μm to meters.

A) 5 × 10 -3 m

B) 5 × 10 -6 m

C) 5 × 10 -9 m

D) 5 × 10 6 m

Watch Solution

The mass of a proton is 1.67 × 10 -27 kg. What is the mass of a proton in nanograms?

A) 1.67 × 10 -12 ng

B) 1.67 × 10 -18 ng

C) 1.67 × 10 -15 ng

D) 1.67 × 10 -21 ng

Watch Solution

Convert 15 m3 to liters.

A) 1.5 L          

B) 1.5 × 10 2 L                  

C) 1.5 × 10 -2 L          

D) 1.5 × 10 4 L

Watch Solution

Convert 100 cm3 to m3.

A) 1 × 10 -43           

B) 1 × 10 83             

C) 1 × 10 43             

D) 1 × 10 0 3

Watch Solution

Convert 2.45 x 10-3 km to cm

Watch Solution

The dimensions of an ameoba are approximately 87 um. Express this length in Mm. 
a. 8.7 x 10-11 Mm
b. 8.7 x 1019 Mm
c. 8.7 x 107 Mm
d. 8.7 x 10-5 Mm
e. 8.7 x 10-14 Mm

Watch Solution

The radius of a helium atom 31.4 pm. What is the thickness in Gm?

a. 3.14 x 1022

b. 0.0314

c. 3.14 x 10 -17

d. 3.14 x 10 4

e. 3.14 x 10-20

Watch Solution

A number expressed to 10 -6 s, relate to which of the following units?

a. micro seconds

b. nano seconds

c. kilo seconds

d. milli seconds

e. giga seconds

Watch Solution

Perform the following unit conversions.

e. 4.48 lb to grams

Watch Solution

Express the quantity 556.2 X 10 -12 s in each unit. 

a. ms

b. ns

c. ps

d. fs

Watch Solution

Express the quantity 254,998 m in each unit.

a. km

b. Mm

c. mm

d. cm

Watch Solution

Complete the table:

2 .554 mg/mL =   ________g/L =   _______µg/mL 

Watch Solution

Complete the table:

c. 554 mK/s    _______K/s    _______µK/ms 

Watch Solution

Complete the table:

228 g/L =   _______g/mL  =  ______kg/ML

Watch Solution

Complete the table:

a. 355 km/s    _______cm/s    _______m/ms

Watch Solution

Complete the table: 

d. 3.345 kJ    _______J     _______mJ

Watch Solution

Complete the table: 

c. 122.355 s    _______ms    _______ks

Watch Solution

 Complete the table:

b. 515 km       _______dm     ________cm

Watch Solution

Complete the table: 

a. 1245 kg      1.245 X .10 6 g        1.245 X 10 9 mg

Watch Solution

Use scientific notation to express each quantity with only the base units (no prefix multipliers).

 133 Tg

Watch Solution

Use scientific notation to express each quantity with only the base units (no prefix multipliers).

b. 225 Mm

Watch Solution

Use prefix multipliers to express each measurement without any exponents.

d. 87.9 X 10 - 7

Watch Solution

Use prefix multipliers to express each measurement without any exponents.

c. 23.4 X 10 11

Watch Solution

Use prefix multipliers to express each measurement without any exponents.

b. 55.2 X 10 -10 s 

Watch Solution

Use prefix multipliers to express each measurement without any exponents.

a. 38.8 X 105 g

Watch Solution

Use the prefix multipliers to express each measurement without any exponents.

d. 3.5 X 106 L

Watch Solution

Use the prefix multipliers to express each measurement without any exponents.

c. 1.5 X 109

Watch Solution

Use the prefix multipliers to express each measurement without any exponents.

 22 X 10 -15

Watch Solution

Use the prefix multipliers to express each measurement without any exponents.

a. 1.2 x 10 - 9 m

Watch Solution

Total U.S. farmland occupies 954 million acres. How many square miles is this? (1 acre= 43,560ft2, 1 mile= 5280ft). Total U.S. land area is 3.537 million square miles. What percentage of U.S. land is farmland? 

Watch Solution

A bedroom has a volume of 115m3. What is its volume in: 

 cm3 

Watch Solution

A bedroom has a volume of 115m3. What is its volume in: 

b. dm3

Watch Solution

A house has an area of 195m 2. What is its area in:

b. dm2

Watch Solution

A house has an area of 195m 2. What is its area in:

a. km2

Watch Solution

 A gas can holds 5.0 gallons of gasoline. What is this quantity in cm 3

Watch Solution

A European automobile has a gas mileage of 17 km/L. What is the gas mileage in miles per gallon?

Watch Solution

Convert:

d. 815 yd to km

Watch Solution

Convert:

c. 1845 kg to lb

Watch Solution

Convert:

b. 116 ft to cm

Watch Solution

Convert:

a. 1.4 in to mm

Watch Solution

Convert:

d. 109 mm to in

Watch Solution

Convert:

c. 3.5 L to qt

Watch Solution

Convert:

b. 3.14 kg to g

Watch Solution

Convert:

a. 154 cm to in

Watch Solution

Convert 4.39 x 10-23 g to ng. 

a) 4.39x10-10 ng

b) 4.39x10-14 ng

c) 4.39x10-16 ng

d) 4.39x10-20 ng

Watch Solution

How many cm3 are contained in 3.77 × 104 mm3?

A) 3.77 × 104 cm3

B) 3.77 × 101 cm3

C) 3.77 × 10-10 cm3

D) 3.77 × 1020 cm3

E) 3.77 × 106 cm3

Watch Solution

How many kL does a 1.25 × 108 cL sample contain?

A) 1.25 × 103 kL

B) 1.25 × 1013 kL

C) 1.25 × 104 kL

D) 1.25 × 1012 kL

E) 1.25 × 102 kL

Watch Solution

How many mg does a 433 kg sample contain?

A) 4.33 × 10-4 mg

B) 4.33 × 107 mg

C) 4.33 × 10-3 mg

D) 4.33 × 106 mg

E) 4.33 × 108 mg

Watch Solution

The density of a substance if 3.400 g/mL. In SI units, the density is:

A. 3400 kg/m 3

B. 0.3400 kg/m 3

C. 3.4 kg/cm 3

D. 3.4 kg/m 3

E. 3.4 kg/L3

Watch Solution

The mass of a sample is 550 milligrams. Which of the following expresses that mass in nanograms?

A. 5.5 x 10 8 ng 

B. 5.5 x 10 6 ng 

C. 5.5 x 10 11 ng

D. 5.5 x 10 –6 ng

E. 5.5 x 10 –10 ng

Watch Solution

Express 327 kilometers in units of nanometers.

a. 3.27 x 10 12 nm

b. 3.27 x 10 11 nm

c. 3.27 x 10 –4 nm

d. 3.27 x 10 14 nm

Watch Solution

Which of the following does not equal 80 mL?

a. 8 x 10 -11 GL

b. 0.08 L

c. 8 x 10 -4 kL

d. 8 cL

e. 8 x 10 -7 nL

Watch Solution