Answer:
See below.
a) 560 mL= _0.56_L
b) 8.07 mg= _0.00807_g
c)0.789 kg=__789___g
d)5.2 mL =_5.2_cm^3
Step-by-step explanation:
NOTE: My original answer has more discussion, but exceeded the character limit. The discussion below answers the questions, but the attached pdf (MetricSystem) offers a greater perspective.
The key to the metric system is knowing the common conversion factors. See the attached table. You'll note that the system is based on prefixes to the unit of measure (length, mass, volume, energy, etc.) that describe 10^x orders of magnitude. This allows for efficient reporting and conversion of wildly differing unit values.
For example, an object with mass 1000 grams can be restated as 1 kg, since "k" represents kilograms. Kilo is 10^3 or 1,000. 1kg = 1x10^3 grams.
With the attached table, we can find the conversion factors necessary for making the requested conversions.
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a) 560 mL= ______L
The m in mL means "milli-". Milli means 0.001 or 1/1000 (one thousandth). So we can write 1000ml = 1L. Rearrange this to
( 1L/1000ml)
to form a conversion factor. A conversion factor can always be inverted, (1000ml/1L) since the numerator and denominator are equal to each other. E.g., (12in/1Ft) can be inverted to (1ft/12in). Both are valid conversion factors.
(560 mL)*( 1L/1000ml)= __0.56_L
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b) 8.07 mg= ______g
The same approach applies to mass.
1g = 1,000mg
The conversion factors become either (1g/1000mg) or (1000mg/1g)
(8.07 mg)*(1g/1000mg) = __0.00807_g
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c) 0.789 kg=_____g
From before, the conversion factors are either (1kg/1000g) or (1000g/1kg). I usually select the factor that allows me to multiply to eliminate the unwanted unit, which is this case would be (1000g/1kg).
(0.789 kg)*((1000g/1kg)=__789___g
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d)5.2 mL =__cm^3
This problems adds one dimension. We aren't told the relationship between cm^3 and ml. More information on base units in the metric system are included at the end. The base metric unit for volume is cubic meter (m^3), but the liter is most often the unit of choice. And liter is defined as 1,000 cm^3.
We want to convert ml to cm^3, so lets start with 1 L = 1,000 cm^3.
Once conversion factor would be (1,000 cm^3/1L). But to convert ml to cm^3, we need to relate ml and L. We know that 1L - 1000ml, so we can make (1L/1,000ml) a conversion factor.
Lets see if we have enough conversion factors to make the requested unit conversion.
5.2 mL =__cm^3
(5.2 mL)*(1L/1,000mL) =0.0052L
Now we can convert L to cm^3 from the (1,000 cm^3/1L) factor we found earlier.
(0.0052L)*(1,000 cm^3/1L) = 5.2 cm^3
5.2 mL =_5.2_cm^3