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Question

Without finding the value of each expression below, determine the fewest number of zeroes needed to write the value of each expression. Then, put the expressions in order based on the fewest number of zeroes required to write the value, from least to greatest.
7,820x10^2 36x10^2 459x10^1 15,000x10^1

Answer 1

To determine the fewest number of zeroes needed to write the value of each expression, we will simplify each expression to its standard form and count the zeros:

1. \(7,820 \times 10^2\):

   • \(7,820 \times 10^2 = 782,000\)
   • Number of zeros: 3

2. \(36 \times 10^2\):

   • \(36 \times 10^2 = 3,600\)
   • Number of zeros: 2

3. \(459 \times 10^1\):

   • \(459 \times 10^1 = 4,590\)
   • Number of zeros: 1

4. \(15,000 \times 10^1\):

   • \(15,000 \times 10^1 = 150,000\)
   • Number of zeros: 5

Now, we can put the expressions in order based on the fewest number of zeros, from least to greatest:

• \(459 \times 10^1\) - 1 zero
• \(36 \times 10^2\) - 2 zeros
• \(7,820 \times 10^2\) - 3 zeros
• \(15,000 \times 10^1\) - 5 zeros

Final Order:

1. \(459 \times 10^1\)
2. \(36 \times 10^2\)
3. \(7,820 \times 10^2\)
4. \(15,000 \times 10^1\)