Name: Mr Judd’s Solutions Section: Metric Conversions
Metric Conversions Worksheet I
T tera- 1 000 000 000 000 1012
G giga- 1 000 000 000 109 M mega- 1 000 000 106 k kilo- 1 000 103 These are the metric units. h hecto- 100 102 The letter in the first column 1
Going table up the movethe decimalto theleft D deka 10 10 is used as the prefix before the unit. Some common NO PREFIX ( UNIT) 1 100 types of units are: grams (g), meters (m), liters (L), d deci 0.1 10-1 joules (J), seconds (s), c centi- 0.01 10-2 and bytes (B). m milli- 0.001 10-3 -6 μ micro- 0.000001 10
Goingtable the down movethe decimalto theright n nano- 0.000000001 10-9
When working in the metric system it is helpful to use a “metric map.” This metric map will enable you to successfully convert your units.
Units Liters Tera Giga Mega Kilo Hecto Deka Meters deci centi milli micro nano Grams Joules Seconds Bytes
indicates that there is a difference of three steps/decimal places/zeros to get from one prefix to the next. indicates that there is a difference of only one step/decimal place/zero to get from one prefix to the next.
EXAMPLES
1.0 kg = ? mg
1.0 kg = 1 000 000 mg
Kilo Hecto Deka Unit deci centi milli
Grams
2.3 cm = ? m
2.3 cm = 0.023 m (unit) is going to the left on the “map”; therefore move the decimal two places to the left
Kilo Hecto Deka Unit deci centi milli
Meters From To Difference Move decimal in zeros/ left or right? prefix unit prefix unit decimal places/steps
km kilo Meters m no prefix Meters 3 right
Mg mega grams Gg giga grams 3 left
mL milli Litres L no prefix Litres 3 left
kJ kilo Joules mJ milli Joules 6 right
μs micro seconds ms milli seconds 3 left
B no prefix bytes kB kilo bytes 3 left
cm centi metre mm milli metre 1 right
cL centi Litres μL micro Litres 4 right
PROBLEMS
1. Convert the following to grams (g):
Difference Move to Before in zeros/ After left or converting decimal converting places/steps right?
1.0 kg 3 right 1000. g
2.5 kg 3 right 2500. g
0.045 kg 3 right 45.0 g
100 mg 3 left 0.1 g
2400 mg 3 left 2.4 g 2. Convert the following to meters (m):
Difference Move to Before in zeros/ After left or converting decimal converting places/steps right?
4 mm 3 left 0.004 m
15.6 km 3 right 15600. m
0.005 Mm 6 right 5000. m
1,000,000 μm 6 left 1. m
2400 mm 3 left 2.4 m
3. Convert the following to kiloliters (kL):
Difference Move to Before in zeros/ After left or converting decimal converting places/steps right?
1600 L 3 left 1.6 kL
2050 cL 5 left 0.0205 kL
5000 mL 6 left 0.005 kL
0.15 kL 1.5 hL 1 left
0.003 µL 9 left 0.000000000003kL Name: Mr Judd’s Solutions Section: Metric Conversions
Metric Conversions Worksheet II
1. Convert the following to km:
1600.0 m = 1.6 km 2050 cm = 0.0205 km 1.033 Mm = 1033 km
245 565 mm = 0.245565 km 20099 m = 20.099 km 499 m = 0.499 km
2. Convert the following:
10.034 mJ = 1.0034 cJ 36.45 cL = 364500 μL
0.05 cm = 0.5 mm 1024 B = 1.024 kB
0.0325 kJ = 3250 cJ 1202.5 mL = 1.2025 L
0.42101 Gg = 421.01Mg 25.5 km = 25500 m
0.12907 cm = 1.2907 mm 756 900 μs = 756.9 ms
5600.4 Ms = 5.6004 Gs 268 000 cm = 2.68 km Name: Mr Judd’s Solutions Section: Metric Conversions
Metric Conversions Worksheet III
Convert the following:
0.0075 Gm = 7500 km 0.00091 TL = 910 ML
0.00046 ks = 46 cs 244475.3 μs = 0.002444753 hs
4096 MB = 4.096 GB 210 hm = 0.021 cm
0.0002 μg = 0.0000002 mg 448.5 cg = 4.485 g
0.00034 μL = 0.0000000034 cL 2103.55 s = 2.10355 ks
11120.33 ng = 0.001112033 cg 0.0000012 GL = 120000 cL
Word Problems 1. The distance from your home to the airport is 0.0000075 Gm. How far is this in km?
0.0000075 Gm = 7.5 km
2. There are 10 computers in the computer lab that each have 20 GB hard drives. How many bytes (B) of disk space do we have in the computer lab in total.
10 × 20 GB = 200 GB 200 GB = 200 000 000 000 B
3. A challenge: convert 100125368477004 ng to Teragrams. 100125368477004 ng = 0.000000100125368477004Tg.
G M k m µ n Giga Mega kilo “None” milli micro nano
109 106 103 100 10-3 10-6 10-9
102 101 10-1 10-2 hecto deca deci centi h da d c
When converting from one metric prefix to another, you move the decimal place the same direction as the conversion moves along the above decimal line. You move the decimal place the same number of places as the difference between the two indices.
Example 1 Convert 1200000 mg into kg.
This conversion is to the left of the decimal line, from 10-3 to 103, representing a change of 106 or 6 decimal place moves to the left.
∴ 1200000 mg = 1.2 kg