Anonymous
Anonymous asked in Science & MathematicsMathematics · 6 months ago

# Is it better to convert one unit to another at the beginning or end of solving a word problem?

say in math class you're given a word problem and they want the answer in kilograms but in the word problem, the unit is in grams. is it better to convert the grams to kilograms before solving the word problem or after solving it? thanks!

Relevance
• 6 months ago

YES!! Convert EVERYTHING to the same units before starting the question.

• Dr W
Lv 7
6 months ago

depends on the exact problem. My recommendation would be you learn and use factor label method. Setup 1 equation, verify it's correct, then run the calcs then repeat the calcs. The order of conversion doesn't really matter but for consistency, I recommend numerator first, then denominator.

I cover the math in my answer here

********

example #1

Little Jimmy weighed 44 lbs where 1lb = 454g. He ate a large pepperoni pizza of weight 33.8oz (where 16oz = 454g). And drank 32oz of water (128 liquid oz = 3780g). What was little Jimmy's new weight?

now I could do this

.. (1) convert 44lbs to g to kg

.. (2) convert 33.8oz to g to kg

.. (3) convert 32oz to g to kg

.. (4) add (1) + (2) + (3)

but... it's better to do this

.. [(44lb * (454g / lb) + 33.8oz * (454g / 16oz) + 32oz * (3780g / 128oz)] * (1kg / 1000g) = __ kg

just enter

.. (44 * 454 + 33.8 * 454 / 16 + 32 * 3780 / 128)/1000 =

in your calculator all at once.

********

example #2

little Jimmy weighed 44.0lbs. His miniature tesla weighed 40.5lbs what force was required to accelerate little Jimmy and his car from 0.00 to 6.00 mph (0.621mi = 1km) in 0.430 sec in newtons (1N = 1kgm/s²).. and.. F = m*a

then we could

.. (1) convert 44.0lbs to grams to kg

.. (2) convert 40.5lbs to grams to kg

.. (3) convert 6.00 miles/hr to km/hr to m/hr to m/min to m/sec

.. (4) divide (3) by 0.430sec to get m/sec²

.. (5) add (1) + (2) to get total mass

.. (6) multiply total mass from (5) by (4) to get kgm/s²

.. (7) convert kgm/s² to N

all in separate steps.

or you could do it all in grams, then convert to kg at the end... then to newtons.

both work.. but a better way is this

.. .... ... ... .. .... ... ... ... ... ... .. ... ... ... ... ... ... ... ... . . .6.00 mi.. .. .. . 1000m.. . 1hr.. . . . 1N

F = (44.0lbs+40.5lbs) * (454g/lb) * (1kg / 1000g) * --- --- --- --- ---- x --- --- --- x --- ---- x --- ---- =

.. ... .... ... ... ... .. .... .. ... ... ..... ... ... ... ... ... .. .......1 hr * 0.430sec... 0.621mi.. 3600s.. 1kgm/s²

.. = ___ N

and you calc it all at once like this

.. 84.5 * 454 / 1000 * 6 / 0.430 * 1000 / 0.621 / 3600 =

then you don't need to worry about any rounding errors or human errors (transposing numbers for example)

• 6 months ago

Most if the time I'll convert numbers at the end since it's just one number vs. initially when I may have multiple numbers to convert.

But if your initial values are different labels and they need to be the same for the math to work, then you'll have to do it upfront.

Depends on the question.

• Joe
Lv 7
6 months ago

As Bill said: either way will work.

If you've got several "inputs" in grams, and you have to produce only one numeric answer in kilograms, keep everything in grams until the end. That way, you only have a single conversion to do, instead of several.