Use the Prefix multiplier table to do the following Lonversion A. 1Gg = µg • exponent Value for G = • exponent Value for µ = • Answer = 1x10______(Put exponent in blank) B. 35ng = dg • exponent value for n = • exponent value for d = • Answer = 3.5 x 10______(Put exponent in black)
The Correct Answer and Explanation is:
Let’s break down the conversions step-by-step using the prefix multipliers and their respective exponent values.
A. Convert 1 Gg to µg
We know:
- Gg (gigagram) is 10910^9109 grams (G = 9).
- µg (microgram) is 10−610^{-6}10−6 grams (µ = -6).
To convert 1 Gg to µg, we use the relationship: 1 Gg=1×109 g1 \, \text{Gg} = 1 \times 10^9 \, \text{g}1Gg=1×109g
Now, we convert grams to micrograms (µg): 1 g=1×106 µg1 \, \text{g} = 1 \times 10^6 \, \text{µg}1g=1×106µg
So, to convert 1 Gg to µg, we multiply by 109×10610^9 \times 10^6109×106: 1 Gg=1×109+6 µg=1×1015 µg1 \, \text{Gg} = 1 \times 10^{9 + 6} \, \text{µg} = 1 \times 10^{15} \, \text{µg}1Gg=1×109+6µg=1×1015µg
Thus, the conversion for 1 Gg to µg is:
- Exponent value for G = 9
- Exponent value for µ = -6
- Answer = 1 × 10^15
B. Convert 35 ng to dg
We know:
- ng (nanogram) is 10−910^{-9}10−9 grams (n = -9).
- dg (decigram) is 10−110^{-1}10−1 grams (d = -1).
To convert 35 ng to dg, we use the relationship: 35 ng=35×10−9 g35 \, \text{ng} = 35 \times 10^{-9} \, \text{g}35ng=35×10−9g
Now, we convert grams to decigrams (dg): 1 g=10 dg1 \, \text{g} = 10 \, \text{dg}1g=10dg
To convert ng to dg, we multiply by 10−9×10110^{-9} \times 10^110−9×101: 35 ng=35×10−9+1 dg=35×10−8 dg35 \, \text{ng} = 35 \times 10^{-9 + 1} \, \text{dg} = 35 \times 10^{-8} \, \text{dg}35ng=35×10−9+1dg=35×10−8dg
Thus, the conversion for 35 ng to dg is:
- Exponent value for n = -9
- Exponent value for d = -1
- Answer = 3.5 × 10^{-7}
Summary of the answers:
A) 1 Gg = 1 × 10^15 µg
B) 35 ng = 3.5 × 10^-7 dg
