Maria wanted to bring back 5 million grains of sand from her trip to the beach.

Question

Each grain of sand weighs approximately 6.7×10
−7
kg. How heavy is the bag of sand that Maria brings home? (1 point)

Multiply
5,000,000(6.7×10
−7
)=(5×10
6
)⋅(6.7×10
−7
)=(5⋅6.7)(10
6+(−7)
)=33.5×10
−1
=3.35kg

Divide $
\frac{5,000,000}{6.7 \times 10^{-7}} = \frac{5 \times 10^6}{6.7 \times 10^{-7}} = (\frac{5}{6.7}) \times 10^{6 - (-7)} = 0.74 \times 10^1 = 0.74 kg$

Multiply 5(6.7×10
−7
)=33.5×10
−7
=3.35×10
−6
kg

Multiply
5,000,000(6.7×10
−7
)=(5×10
6
)⋅(6.7×10
−7
)=(5⋅6.7)(10
6+(−7)
)=33.5×10
−1
kg

Answer 1

To calculate the weight of the bag of sand that Maria brings home, we can follow the correct steps using the provided values:

1. Understanding the Problem:

   • Maria wants to bring back 5 million grains of sand, which is \( 5,000,000 \) grains.
   • Each grain of sand weighs approximately \( 6.7 \times 10^{-7} \) kg.

2. Calculating the Total Weight:

   • We can use multiplication to find the total weight: \[ \text{Total weight} = \text{number of grains} \times \text{weight of each grain} \] \[ \text{Total weight} = 5,000,000 \times (6.7 \times 10^{-7}) \]
   • We can express \( 5,000,000 \) in scientific notation: \[ 5,000,000 = 5 \times 10^6 \]
   • Now, we substitute this into the equation: \[ \text{Total weight} = (5 \times 10^6) \times (6.7 \times 10^{-7}) \]
   • This can be simplified as follows: \[ \text{Total weight} = (5 \times 6.7) \times (10^{6 + (-7)}) = 33.5 \times 10^{-1} \]

3. Converting to Standard Form:

   • \( 33.5 \times 10^{-1} \) can be simplified to: \[ 3.35 \times 10^{0} , \text{kg} = 3.35 , \text{kg} \]

So, the total weight of the bag of sand that Maria brings home is 3.35 kg.