Question

How do you convert $ 1.8 \times {10^6} $ $ ng $ to $ dg $ ?

Answer 1

Hint: $ 1 $ nanograms of a substance is equal to $ {10^{ - 9}} $ grams of that substance. Similarly, $ 1 $ grams of any substance is equal to $ 10 $ decigram of that substance. Use this conversion scheme to solve the question. First, change the given value from nanograms to grams using the conversion method of units. After getting the value in grams, just convert it into decigrams.

Complete step by step solution:
First, let’s convert $ 1.8 \times {10^6}ng $ to $ g $ .
We know that, $ 1 $ grams of a substance is equal to $ {10^9} $ nanograms of that substance.
 $ {10^9}ng = 1g $
Or, we can say that $ 1 $ nanograms of a substance is equal to $ {10^{ - 9}} $ grams of that substance,
 $ 1ng = {10^{ - 9}}g $
On converting $ 1.8 \times {10^6}ng $ to $ g $ , we get,
 $ 1.8 \times {10^6}ng = 1.8 \times {10^6} \times {10^{ - 9}}g $
 $ = 1.8 \times {10^{ - 3}}g $
Hence, $ 1.8 \times {10^6}ng $ is $ 1.8 \times {10^{ - 3}}g $ .
Now, we have to convert $ 1.8 \times {10^{ - 3}}g $ into $ dg $ .
We know that, $ 1 $ decigrams of any substance is equal to $ 0.1 $ decigrams of that substance.
 $ 1dg = 0.1g $
Or, we can say that $ 1 $ grams of any substance is equal to $ 10 $ decigrams of that substance.
 $ 1g = 10dg $
On converting $ 1.8 \times {10^{ - 3}}g $ to $ dg $ , we get,
 $ 1.8 \times {10^{ - 3}}g = 1.8 \times {10^{ - 3}} \times 10dg $
 $ = 1.8 \times {10^{ - 2}}dg $
Hence, we can say that $ 1.8 \times {10^6} $ $ ng $ is equal to $ 1.8 \times {10^{ - 2}}dg $.

Note:
Remember the conversion scheme of nanograms to grams and grams to decigrams carefully. Also, while doing the conversion, pay close attention to powers of $ 10 $ as well as its exponent operations. Do not forget to write the units while doing the calculation and while writing the results.
The result of the above question can also be written as $ 0.0018dg $. But, refrain from doing so as the question is given in the scientific form, so, try to use the scientific form of your result which is $ 1.8 \times {10^{ - 2}}dg $. Only use decimal form when you are asked to do so or if it is given in the question.