Metric to Metric Conversions

The essence of metric to metric conversions is recognizing the abbreviated base units.

Base Units: m (meter), L (liter), g (gram), s (seconds)

These are not all of the base units, but are the most common that you will encounter. Each base unit can have any of the prefixes listed in the chart below. As with any other prefix, the prefix means the same thing regardless of the abbreviated base unit it is attached to.

Giga (G)---------- it takes 10⁹ (billion) base units = 1 G

Mega (M)--------- it takes 10⁶ (million) base units = 1 M

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Kilo (K)----------- it takes 1000 base units = 1 K

Hecto (H)--------- it takes 100 base units = 1 H

Decka (Da)------- it takes 10 base units = 1 Da

Base Units: m, L, g, s

Deci (d)----------- it takes 1 base unit = 10 deci

Centi (c)---------- it takes 1 base unit = 100 centi

Milli (m)---------- it takes 1 base unit = 1000 milli

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Micro (m)--------- it takes 1 base unit = 10⁶ (million) micro

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Nano (n)---------- it takes 1 base unit = 10⁹ (billion) nano

There are two ways to work metric to metric conversions. The first way is to do the math by using the numerical conversion relationships listed in the chart above.

Ex: Convert 35 mg to g.

? g = 35 mg x 1 g = 0.000035 g

1,000,000 mg

The other way is to count the lines in the chart (every line except the one you start on), start from your given information and counting each line until you get to what you want to convert.

***Move Up the chart: Move decimal to the LEFT

***Move DOWN the chart: Move decimal to the RIGHT (remember RIGHT DOWN to the nitty gritty)

Ex: Convert 35 mg to g.

Begin at prefix m (micro) and count UP to g (gram). You counted UP six places, therefore you move your decimal to the LEFT six places. If your decimal is not shown, it is understood to be at the end of the number.

35. mg = 0.000035 g

Ex: Convert 0.26 ML to mL

Begin at prefix M (mega) and count DOWN to prefix m (milli). You counted DOWN nine places, therefore, you move your decimal to the RIGHT nine places. So, you will add seven zeros.

0.26 ML = 260,000,000. mL

PRACTICE PROBLEMS (and solutions) ON BACK

PRACTICE PROBLEMS

1) 170.4 m =______________ cm

2) 564 Dag =______________ g

3) 58 dg =______________ mg

4) 600 L =______________ KL

5) 0.0923 Km =______________ mm

6) 49 Hg =______________ g

7) 210 cL =______________ dL

8) 4.51 x 10³ mL =______________ mL

9) 45700 cg =______________ Kg

10) 24.6 KL =______________ mL

11) 82.4 nm =______________ mm

ANSWERS

1) 17040cm

2) 5640 g

3) 5800 mg

4) 0.600 KL

5) 92300 mm

6) 4900 g

7) 21.0 dL

8) 4.51 mL; write out 4.51 x 10³ mL = 4510 mL, the decimal is understood to be after the zero. Now count UP from the m prefix to the m (milli) prefix. You counted three places, so move the decimal to the LEFT three places = 4.51 mL

9) 0.457 Kg

10) 2.46 x 10¹⁰ mL or 24,600,000,000 mL

11) 0.0824 mm