Question

Fill in the blanks:
\[1kg{\text{ }} = \_\_\_\_\_\_\_\_\_dag{\text{ }}\].

Answer 1

Hint: In this question, we have to convert one unit of mass to another unit using the metric conversion. Here we will use the relation between different units of the basic quantity of mass and metric conversions to fill in the black with the correct multiplying factor or power of 10. While kg means kilogram and dag means dekagram, we need to establish the relation between these two measurements.

Complete step-by-step answer:
According to the question, we need to find the relation between kilogram (kg) and dekagram (dag).
Now as per the conversion table of mass we know:
\[\begin{array}{*{20}{l}}
  {10{\text{ }}milligram{\text{ }} = {\text{ }}1{\text{ }}centigram} \\
  {10{\text{ }}centigram{\text{ }} = {\text{ }}1{\text{ }}decigram} \\
  {10{\text{ }}decigram{\text{ }} = {\text{ }}1{\text{ gram}}} \\
  {10{\text{ gram }} = {\text{ }}1{\text{ }}dekagram} \\
  {10{\text{ }}dekagram{\text{ }} = {\text{ }}1{\text{ }}hectogram} \\
  {10{\text{ }}hectogram{\text{ }} = {\text{ }}1{\text{ }}kilogram}
\end{array}\]
So, from this table clearly:
\[10{\text{ }}dekagram{\text{ }} = {\text{ }}1{\text{ hectogram}}\]
And, $10hectogram = 1kilogram$
So, we can say that:
If, \[10{\text{ }}dekagram{\text{ }} = {\text{ }}1{\text{ hectogram}}\]
Then, we can rewrite it as \[1hectogram = 10dekagram\]
Now, if \[1hectogram = 10dekagram\]
Then, we can say that $10hectogram = 100dekagram$
Also, $10hectogram = 1kilogram$
So we can conclude that $1kilogram = 100dekagram$
That is, 1 kg = ….100….dag.
Hence, we will fill the blank with the multiplying factor of 100.

Note: Metric conversions mean, every unit is related with another by a multiplying factor of ${10^n}$ or ${10^{ - n}}$, where n is an integer. That is, every unit under the metric system is related to another unit by either higher multiple powers of 10 or lower multiple powers of 10. The metric conversion holds for all basic units – length, Mass, time etc. The relation stays the same across the units but the units change. For example for length we have the units as kilometer, millimeter etc.