A penny weighs 5.8×10−3

Question

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

6.2×106
6.2 times 10 superscript 6 baseline

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

Answer 1

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

The weight of one penny is \( 5.8 \times 10^{-3} \) lb.

So, we calculate:

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

First, rearranging gives us:

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

To divide these numbers, we first divide the coefficients and subtract the exponents:

1. Divide the coefficients: \[ \frac{3.596}{5.8} \approx 0.620 \]

2. Subtract the exponents: \[ 10^4 \div 10^{-3} = 10^{4 - (-3)} = 10^{4 + 3} = 10^7 \]

Putting this together:

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

Now, to express \( 0.620 \) in proper scientific notation, we can write it as \( 6.20 \times 10^{-1} \), and then combine this with \( 10^7 \):

\[ 0.620 \times 10^7 = (6.20 \times 10^{-1}) \times 10^7 = 6.20 \times 10^{6} \]

Thus, rounding to two significant figures:

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

So the answer is:

6.2×10⁶