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 both conversions step by step using the prefix multipliers:
A. 1 Gg to µg
- Prefix for Gg (gigagram):
- 1 Gg = 1×1091 \times 10^91×109 grams (Gg = 10^9 g).
- Prefix for µg (microgram):
- 1 µg = 1×10−61 \times 10^{-6}1×10−6 grams (µg = 10−610^{-6}10−6 g).
To convert from Gg to µg:
1 Gg = 1×1091 \times 10^91×109 grams
Now, convert grams to micrograms:
1×109 g×(106 μg1 g)=1×1015 μg1 \times 10^9 \, \text{g} \times \left( \frac{10^6 \, \mu\text{g}}{1 \, \text{g}} \right) = 1 \times 10^{15} \, \mu\text{g}1×109g×(1g106μg)=1×1015μg
Answer:
1 Gg = 1×10151 \times 10^{15}1×1015 µg
- Exponent Value for G: 9
- Exponent Value for µ: -6
- Final Answer: 1×10151 \times 10^{15}1×1015
B. 35 ng to dg
- Prefix for ng (nanogram):
- 1 ng = 1×10−91 \times 10^{-9}1×10−9 grams (ng = 10−910^{-9}10−9 g).
- Prefix for dg (decigram):
- 1 dg = 1×10−11 \times 10^{-1}1×10−1 grams (dg = 10−110^{-1}10−1 g).
To convert from ng to dg:
1 ng = 1×10−91 \times 10^{-9}1×10−9 grams
Now, convert grams to decigrams:
1×10−9 g×(10−1 dg1 g)=1×10−10 dg1 \times 10^{-9} \, \text{g} \times \left( \frac{10^{-1} \, \text{dg}}{1 \, \text{g}} \right) = 1 \times 10^{-10} \, \text{dg}1×10−9g×(1g10−1dg)=1×10−10dg
For 35 ng:
35×10−9 g×(10−1 dg1 g)=3.5×10−10 dg35 \times 10^{-9} \, \text{g} \times \left( \frac{10^{-1} \, \text{dg}}{1 \, \text{g}} \right) = 3.5 \times 10^{-10} \, \text{dg}35×10−9g×(1g10−1dg)=3.5×10−10dg
Answer:
35 ng = 3.5×10−103.5 \times 10^{-10}3.5×10−10 dg
- Exponent Value for n: -9
- Exponent Value for d: -1
- Final Answer: 3.5×10−103.5 \times 10^{-10}3.5×10−10
Summary:
- A: 1 Gg = 1×10151 \times 10^{15}1×1015 µg
Exponent value for G = 9
Exponent value for µ = -6 - B: 35 ng = 3.5×10−103.5 \times 10^{-10}3.5×10−10 dg
Exponent value for n = -9
Exponent value for d = -1
