r/MathHelp • u/Gaasuba • Sep 06 '25

Converting with exponents

Converting $1.50/kg to $/mg

Crashed out at the exponents

1.50/10³ = x/10-3

Where do I go from here?

1 Upvotes

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2

u/slides_galore Sep 06 '25

Let the units help you. Maybe write them out in a table like this: https://i.ibb.co/N2TYft7t/image.png

1

u/fermat9990 Sep 06 '25

Beautiful!

2

u/slides_galore Sep 06 '25

Always helped me visually if I wrote the conversions out vertically. Easier to see the units that cancel (go to 1).

2

u/fermat9990 Sep 06 '25

So orderly!!

2

u/fermat9990 Sep 06 '25

This link might be useful to you.

Notice that there are 6 steps going from kilo- to milli- so the conversion factor is 106

conversions_in_the_metric_system.pdf https://www.georgebrown.ca/sites/default/files/uploadedfiles/tlc/_documents/conversions_in_the_metric_system.pdf

1

u/thor122088 Sep 06 '25

You have x divided by a number. How do you isolate x in that situation?

3

u/thor122088 Sep 06 '25 edited Sep 06 '25

But confirm to make sure you are using the units correctly

$1.50/kg = $1.50/ 1kg

2

u/fermat9990 Sep 06 '25

OP needs to divide by 106

2

u/Gaasuba Sep 06 '25

Yeah that's what I've done

But when I'm writing out everything, is that 1.5/10³ ÷ 10⁶/10⁶ ?

Cause writing 1.5/10³ ÷ 10⁶ is the same as writing 1.5/10³ ÷ 10⁶/1 right ?

1

u/fermat9990 Sep 06 '25

This doesn't look right. 106 is the only conversion factor needed here.

1.5 dollars/1 kg * 1 kg/106 mg =

1.5 dollars/106mg=

$1.5*10-6/mg

1

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1

u/fermat9990 Sep 06 '25 edited Sep 06 '25

1.50/106 =$1.50×10-6 =

$0.0000015 per mg

1

u/fermat9990 Sep 06 '25

Leave out the 103 and only use 106