Convert using dimensional analysis step by step: a) 35kg to g b) 7.2cm^2 to m^2 c) 81m^3 to km^3 d) 24.9 MJ to cJ e) 27.31 km/hr to m/s

Question

Please help. I don’t get the process to get the answer

Answer 1

Dimensional Analysis changes the units without changing the value.

It uses the Multiplicative Identity (that is 1). Any number multiplied by 1 remains the same.

For example:

Given: 1 = (12 inches) / ( 1 foot) = (1 foot) / (12 inches)

Question: How many inches is 3 feet?

3 feet

(3 feet) * 1

(3 feet) * ( (12 inches) / (1 foot) ) [note: use the one that allows units to cancel]

3 * 12 inches

36 inches

Let's do the one with a unit in the denominator:

27.31 km/hr to m/s

Given: 1 = ( 1 km ) / (1000 m) = ( 1000 m) / ( 1 km)

1 = (60 min) / (1 hr) = (1 hr) / (60 min)

1 = (60 sec) / (1 min) = (1 min) / (60 sec)

O.K. let's select formula that allows units to cancel.

27.31 km/hr

(27.31 km/hr) * 1

(27.31 km/hr) * ((1000m)/(1 km)) * ((1 hr)/(60 min)) * ((1 min)/(60 sec)) [carefully cancel units]

(27.31) * (1000/1)* (1/60) * (1/60) m/s

7.59 m/s

Note: You may split any lines so they will have a single multiplication -- until you understand the process.