Question

from
prefix
unit
to
prefix
unit
difference
in zeros/
decimal
places/steps
move decimal
left or right?
km
kilo
meters
m
no prefix
meters
3
right
mg
gg
ml
l
kj
mj
μs
ms
b
kb
cm
mm
cl
μl
problems

1. convert the following to grams (g):

before
converting
difference
in zeros/
decimal
places/steps
move to
left or
right?
after
converting
1.0 kg
g
2.5 kg
g
0.045 kg
g
100 mg
g
2,400 mg
g
adapted from http://www.morrowgalpern.ca/curriculum home.htm

Explanation:

Step1: Recall unit conversion factors

• \(1\space kg = 1000\space g\) (since kilo - means \(10^{3}\)), so the difference in decimal places is \(3\). When converting from \(kg\) to \(g\), we move the decimal to the right.
• \(1\space mg=10^{- 3}\space g\), so the difference in decimal places is \(3\). When converting from \(mg\) to \(g\), we move the decimal to the left.

Step2: Convert \(1.0\space kg\) to \(g\)

• Difference in decimal places: \(3\)
• Move to: right
• After converting: \(1.0\times10^{3}=1000\space g\)

Step3: Convert \(2.5\space kg\) to \(g\)

• Difference in decimal places: \(3\)
• Move to: right
• After converting: \(2.5\times10^{3} = 2500\space g\)

Step4: Convert \(0.045\space kg\) to \(g\)

• Difference in decimal places: \(3\)
• Move to: right
• After converting: \(0.045\times10^{3}=45\space g\)

Step5: Convert \(100\space mg\) to \(g\)

• Difference in decimal places: \(3\)
• Move to: left
• After converting: \(100\times10^{-3}=0.1\space g\)

Step6: Convert \(2400\space mg\) to \(g\)

• Difference in decimal places: \(3\)
• Move to: left
• After converting: \(2400\times10^{-3}=2.4\space g\)

Answer:

Before converting	Difference in zeros/decimal places/steps	Move to left or right?	After converting
\(2.5\space kg\)	\(3\)	right	\(2500\space g\)
\(0.045\space kg\)	\(3\)	right	\(45\space g\)
\(100\space mg\)	\(3\)	left	\(0.1\space g\)
\(2400\space mg\)	\(3\)	left	\(2.4\space g\)