Scientific Notation Online Practice

Question

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Question
A penny weighs 5.8×10−3
lb. How many pennies are in a pile of pennies that weighs 3.596×104
lb.? Write the answer in scientific notation.(1 point)
Responses

6.2×10−7
6.2 times 10 superscript negative 7 baseline

0.62×107
0.62 times 10 superscript 7 baseline

6.2×108
6.2 times 10 superscript 8 baseline

6.2×106

Answer 1

To determine how many pennies are in a pile that weighs \(3.596 \times 10^4\) lb, we need to divide the total weight of the pile by the weight of one penny.

1. Weight of one penny: \(5.8 \times 10^{-3}\) lb.
2. Total weight of the pile: \(3.596 \times 10^4\) lb.

To find the number of pennies, we divide the total weight by the weight of one penny:

\[ \text{Number of pennies} = \frac{3.596 \times 10^4 \text{ lb}}{5.8 \times 10^{-3} \text{ lb}} \]

This can be calculated as follows:

\[ = \frac{3.596}{5.8} \times \frac{10^4}{10^{-3}} \]

Calculating the numerical part:

\[ \frac{3.596}{5.8} \approx 0.620 \]

For the powers of ten:

\[ 10^{4 - (-3)} = 10^{4 + 3} = 10^7 \]

Now, putting these together:

\[ \text{Number of pennies} \approx 0.620 \times 10^7 \]

To express this in standard scientific notation, we adjust \(0.620\) to \(6.20\) (which is the correct adjustment in scientific notation, shifting the decimal point to the right by one position) and decrease the exponent by 1:

\[ = 6.20 \times 10^{6} \]

Thus, the number of pennies in the pile is:

\[ \boxed{6.2 \times 10^6} \]