Joni has a box that has a mass of 67 dekagrams. She converts this to centigrams. Her work is shown below.

Question

67 dekagrams over 1,000 = 0.067 centigrams

Which statement explains Joni’s error? Use the metric table to help answer the question.

Metric Table
kilo-
hecto-
deka-
unit
deci-
centi-
milli-
1,000
100
10
1
0.1
0.01
0.001
Joni should have multiplied by 10,000.
Joni should have multiplied by 1,000.
Joni should have divided by 100.
Joni should have divided by 10,000.

Answer 1

To understand Joni's error, let's look at the conversion correctly. Joni's original mass was 67 dekagrams (dag).

1. The conversion from dekagrams to centigrams involves knowing the values in the metric table:

   • 1 dekagram (dag) = 10 grams (g)
   • 1 gram (g) = 100 centigrams (cg)

2. Therefore, to convert dekagrams to centigrams, you can multiply the mass in dekagrams by 10 (to get grams) and then multiply by 100 (to get centigrams):

   • 67 dag × 10 g/dag = 670 g
   • 670 g × 100 cg/g = 67,000 cg

So, the correct conversion is: \[ 67 , \text{dag} = 67,000 , \text{cg} \]

Joni incorrectly arrived at 0.067 centigrams by incorrectly dividing the mass instead of multiplying it correctly.

The statement that correctly identifies Joni's error is: Joni should have multiplied by 10,000.