Question
Maria wanted to bring back 5 million grains of sand from her trip to the beach. Each grain of sand weighs approximately 6.7×10−7 kg. How heavy is the bag of sand that Maria brings home?(1 point)ResponsesMultiply 5,000,000(6.7×10−7)=(5×106)⋅(6.7×10−7)=(5⋅6.7)(106+7)=33.5×1013=3.35×1014 kgMultiply 5 comma 000 comma 000 times open paren 6 point 7 times 10 to the negative 7 power close paren is equal to open paren 5 times 10 to the 6th power close paren times open paren 6 point 7 times 10 to the negative 7 power close paren is equal to open paren 5 times 6 point 7 close paren times open paren 10 raised to the 6 plus 7 power close paren is equal to 33 point 5 times 10 to the 13th power is equal to 3 point 3 5 times 10 to the 14th power kgMultiply 5(6.7×10−7) = 33.5×10−7=3.35×10−6 kgMultiply 5(6.7×10−7) = 33.5×10−7=3.35×10−6 kgMultiply 5,000,000(6.7×10−7)=(5×106)⋅(6.7×10−7)=(5⋅6.7)(106+(−7))=33.5×10−1=3.35 kgMultiply 5 comma 000 comma 000 times open paren 6 point 7 times 10 to the negative 7 power close paren is equal to open paren 5 times 10 to the 6th power close paren times open paren 6 point 7 times 10 to the negative 7 power close paren is equal to open paren 5 times 6 point 7 close paren times open paren 10 raised to the 6 plus negative 7 power close paren is equal to 33 point 5 times 10 inverse is equal to 3 point 3 5 kgDivide 5,000,0006.7×10−7=5×1066.7×10−7=(56.7)×106+(−7)=0.74×10−1=0.074 kgDivide the fraction with numerator 5 comma 000 comma 000 and denominator 6 point 7 times 10 to the negative 7 power is equal to the fraction with numerator 5 times 10 to the 6th power and denominator 6 point 7 times 10 to the negative 7 power is equal to open paren 5 over 6 point 7 close paren times 10 raised to the 6 plus negative 7 power is equal to 0 point 7 4 times 10 inverse is equal to 0 point 0 7 4 kg
Answers
GPT-4o mini
To calculate the total weight of the 5 million grains of sand that Maria wanted to bring back, we can use the formula:
\[
\text{Total weight} = (\text{Number of grains}) \times (\text{Weight of each grain})
\]
We know:
- Number of grains = \(5,000,000\) grains = \(5 \times 10^6\)
- Weight of each grain = \(6.7 \times 10^{-7}\) kg
Now, we can multiply these two values:
\[
\text{Total weight} = (5 \times 10^6) \times (6.7 \times 10^{-7})
\]
Using the property of exponents, we can separate the multiplication:
\[
= (5 \times 6.7) \times (10^6 \times 10^{-7})
\]
Calculating \(5 \times 6.7\):
\[
5 \times 6.7 = 33.5
\]
Calculating \(10^6 \times 10^{-7}\):
\[
10^6 \times 10^{-7} = 10^{6 - 7} = 10^{-1}
\]
Putting it all together:
\[
\text{Total weight} = 33.5 \times 10^{-1} \text{ kg} = 3.35 \text{ kg}
\]
Thus, the correct weight of the bag of sand that Maria brings home is:
**3.35 kg**
\[
\text{Total weight} = (\text{Number of grains}) \times (\text{Weight of each grain})
\]
We know:
- Number of grains = \(5,000,000\) grains = \(5 \times 10^6\)
- Weight of each grain = \(6.7 \times 10^{-7}\) kg
Now, we can multiply these two values:
\[
\text{Total weight} = (5 \times 10^6) \times (6.7 \times 10^{-7})
\]
Using the property of exponents, we can separate the multiplication:
\[
= (5 \times 6.7) \times (10^6 \times 10^{-7})
\]
Calculating \(5 \times 6.7\):
\[
5 \times 6.7 = 33.5
\]
Calculating \(10^6 \times 10^{-7}\):
\[
10^6 \times 10^{-7} = 10^{6 - 7} = 10^{-1}
\]
Putting it all together:
\[
\text{Total weight} = 33.5 \times 10^{-1} \text{ kg} = 3.35 \text{ kg}
\]
Thus, the correct weight of the bag of sand that Maria brings home is:
**3.35 kg**