Math

QuestionIdentify the larger unit in each pair: 1. mm vs km, 2. dm vs cm, 3. g vs dg, 4. cm vs mm, 5. Mg vs kg, 6. µg vs pg.

Studdy Solution

STEP 1

Assumptions1. We are comparing the magnitude of different metric units. . We understand the metric prefixes and their respective magnitudes.

STEP 2

We need to know the metric prefixes and their magnitudes. Here is a list for reference1. kilo- (k) = 10^ or1,0002. hecto- (h) = 10210^2 or100. deka- (da) = 10110^1 or104. base unit (meter, gram, liter, etc.) = 10010^0 or15. deci- (d) = 10110^{-1} or0.16. centi- (c) = 10210^{-2} or0.017. milli- (m) = 1010^{-} or0.0018. micro- (µ) = 10610^{-6} or0.0000019. nano- (n) = 10910^{-9} or0.00000000110. pico- (p) = 101210^{-12} or0.000000000001

STEP 3

Compare the units millimeter and kilometer.A millimeter is 10310^{-3} meters, and a kilometer is 10310^3 meters.Therefore, the kilometer is the larger unit.

STEP 4

Compare the units decimeter and centimeter.
A decimeter is 10110^{-1} meters, and a centimeter is 10210^{-2} meters.
Therefore, the decimeter is the larger unit.

STEP 5

Compare the units centimeter and millimeter.
A centimeter is 10210^{-2} meters, and a millimeter is 10310^{-3} meters.
Therefore, the centimeter is the larger unit.

STEP 6

Compare the units Megagram and kilogram.
A Megagram is 10610^6 grams, and a kilogram is 10310^3 grams.
Therefore, the Megagram is the larger unit.

STEP 7

Compare the units gram and decigram.
A gram is 10010^0 grams, and a decigram is 10110^{-1} grams.
Therefore, the gram is the larger unit.

STEP 8

Compare the units microgram and picogram.
A microgram is 10610^{-6} grams, and a picogram is 101210^{-12} grams.
Therefore, the microgram is the larger unit.
The larger units are kilometer, decimeter, centimeter, Megagram, gram, and microgram.

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