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Question: How do you convert \( 1.8 \times {10^6} \) \( ng \) to \( dg \) ?...

How do you convert 1.8×1061.8 \times {10^6} ngng to dgdg ?

Explanation

Solution

11 nanograms of a substance is equal to 10−9{10^{ - 9}} grams of that substance. Similarly, 11 grams of any substance is equal to 1010 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 1.8×106ng1.8 \times {10^6}ng to gg .
We know that, 11 grams of a substance is equal to 109{10^9} nanograms of that substance.
109ng=1g{10^9}ng = 1g
Or, we can say that 11 nanograms of a substance is equal to 10−9{10^{ - 9}} grams of that substance,
1ng=10−9g1ng = {10^{ - 9}}g
On converting 1.8×106ng1.8 \times {10^6}ng to gg , we get,
1.8×106ng=1.8×106×10−9g1.8 \times {10^6}ng = 1.8 \times {10^6} \times {10^{ - 9}}g
=1.8×10−3g= 1.8 \times {10^{ - 3}}g
Hence, 1.8×106ng1.8 \times {10^6}ng is 1.8×10−3g1.8 \times {10^{ - 3}}g .
Now, we have to convert 1.8×10−3g1.8 \times {10^{ - 3}}g into dgdg .
We know that, 11 decigrams of any substance is equal to 0.10.1 decigrams of that substance.
1dg=0.1g1dg = 0.1g
Or, we can say that 11 grams of any substance is equal to 1010 decigrams of that substance.
1g=10dg1g = 10dg
On converting 1.8×10−3g1.8 \times {10^{ - 3}}g to dgdg , we get,
1.8×10−3g=1.8×10−3×10dg1.8 \times {10^{ - 3}}g = 1.8 \times {10^{ - 3}} \times 10dg
=1.8×10−2dg= 1.8 \times {10^{ - 2}}dg
Hence, we can say that 1.8×1061.8 \times {10^6} ngng is equal to 1.8×10−2dg1.8 \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 1010 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 0.0018dg0.0018dg. 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 1.8×10−2dg1.8 \times {10^{ - 2}}dg. Only use decimal form when you are asked to do so or if it is given in the question.