Question

write an equivalency statement relating nanograms and dekagrams. reference \powers of ten\ by clicking on the \chemistry resources\ link at the top - left of the page.

• write a 1 in front of the larger unit
• determine the power of 10 for each prefix
• subtract the small power of 10 from the large power of 10

1 x 10^1-(-9)=10

• write the power of 10 calculated above in front of the smaller unit. enter the number in standard scientific notation if the number is too large.
• make sure to enter the power into the blank in the \e\ form. for example, if your power is 10^5 enter 1e5 into the blank.
• write the larger unit on the left of the equal sign and smaller unit on the right.
• if you need the greek letter mu, copy and paste the symbol below
• μ

Explanation:

Step1: Identify prefix powers

The prefix "deka -" has a power of \(10^{1}\) and "nano -" has a power of \(10^{-9}\).

Step2: Calculate the difference

We subtract the power of the smaller - unit prefix from the power of the larger - unit prefix. So, \(1-(-9)=1 + 9=10\).

Step3: Write the equivalency statement

The larger unit is dekagram (dag) and the smaller unit is nanogram (ng). The equivalency statement is \(1\ dag=1\times10^{10}\ ng\) or in the given "E" form \(1\ dag = 1e10\ ng\).

Answer:

\(1\ dag = 1e10\ ng\)