Lesson missions show an expertise of multiplication by powers of 10Demonstrate an knowledge of division by powers of 10Learn exactly how to develop a metric conversion prefix chartLearn how to convert in between metric systems of measurement

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In our critical lesson, we learned just how to convert in between U.S. Customary systems of measurement. In this lesson, we will certainly learn just how to convert in between metric systems of measurement. Most people in the U.S. Are not acquainted with the metric system. This have the right to make metric switch a bit difficult at first. As soon as the ax is learned, the procedure becomes a little bit simpler. Metric System basic Units load (Mass) Volume length
In ours table above, we deserve to see the straightforward units for the metric system. These devices are: meter - provided for lengthgram - supplied for weight (mass)liter - supplied for volume once we work with U.S. Units, we are often converting between different unit names. This units room chosen based on the size of what"s being described. As an example, expect we had 14,000 pounds the rice. Us could more easily speak we had actually 7 lots of rice because 2000 pounds=1 ton. When we work with the metric system, things space a lot of easier. Rather of having various unit names, prefixes are added to the prior of the basic unit to scale up or down. These prefixes are based on powers the 10: Metric Prefixes Prefix an interpretation
basic unit1
deci1/10 or 0.1
centi1/100 or 0.01
milli1/1000 or 0.001
We can place a prefix in front of the simple unit to range up or down: 1 kilometer=1000 meters1 dekagram=10 grams1 centiliter=0.01 liters4 hectograms=400 grams hecto method 100, 4 hectograms tells united state we have 4 x 100 or 400 grams 9 centimeters=0.09 meters centi way 0.01, 9 centimeters tells us we have 9 x 0.01 or 0.09 meter How deserve to we adjust 6000 grams (g) into kilograms (kg)? us could collection up a unit fraction and carry out the multiplication: $$6000 extgcdot frac1 extkg1000 extg$$ our unwanted systems (g) will cancel and we can simplify: $$ equirecancelcancel60006 cancel extgcdot frac1 extkgcancel1000cancel extg=6 extkg$$ over there is an easier method to employ when working with the metric system. Remind from our lesson top top multiplying decimal that us can conveniently multiply a number by 10 or a power of 10 by relocating the decimal point one ar to the appropriate for every zero in the strength of 10. Additionally, us learned in our splitting decimals great that us can quickly divide a number by 10 or a strength of 10 by relocating the decimal suggest one ar to the left for each zero in the strength of 10. In our example above, us realize the relationship is such the for every 1000 grams we have actually 1 kilogram. For this reason to change between the two, we have the right to divide 6000 by 1000 or relocate the decimal suggest in 6000. Three areas to the left (since there space 3 zeros in 1000): 6000. » 6. » 6 This tells us 6000 grams is equal to 6 kilograms.

Metric Prefix Chart

We can use a prefix chart to do metric conversion an extremely simple. Once we change between metric units, us are essentially just multiplying or dividing by the appropriate power the 10. Each time we move right top top the prefix chart us are separating by 10 and also each time we move left we space multiplying by 10. The prefix chart enables us to match the movement on the chart with the activity of the decimal point in the number. Let"s look at a sample prefix chart:

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frequently we usage "King Henry died Unexpectedly Drinking coco Milk" to remember the prefix chart: King » kiloHenry » hectoDied » dekaUnexpectedly » unit (gram, meter, liter)Drinking » deciChocolate » centiMilk » milli In our over example, we went indigenous 6000 grams come kilograms. Us would identify kilo and also our basic unit gram top top the prefix chart:
because we are relocating from the straightforward unit (gram) to kilogram, we will certainly be separating by 1000 or relocating 3 places left on our prefix chart:
once we match this movement in our number 6000, we end up v 6. This is just how we quickly adjust between 6000 grams and also 6 kilograms. Let"s watch at some examples. Instance 1: adjust 47 centimeters to hectometers. Let"s look in ~ our metric prefix chart:
We have the right to see that relocating from centi come hecto on our prefix chart provides us a movement of 4 devices left. We will enhance this movement with our number: 47. » 0.0047 47 centimeters=0.0047 hectometers. Instance 2: change 3.905 dekaliters come deciliters. Let"s look in ~ our metric prefix chart:
We deserve to see that moving from deka come deci on ours prefix chart offers us a activity of 2 systems right. Us will enhance this movement with our number: 3.905 » 390.5 3.905 dekaliters=390.5 deciliters example 3: adjust 0.591 kilograms come centigrams.

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Let"s look in ~ our metric prefix chart:
We can see that relocating from kilo to centi on our prefix chart provides us a motion of 5 devices right. We will complement this movement with ours number: 0.591 » 59,100 0.591 kilograms=59,100 centigrams skills Check: