The image presents six problems. Problems 13, 14, and 15 require converting numbers to scientific notation. Problems 16, 17, and 18 require converting numbers from scientific notation to standard form.
2025/4/7
1. Problem Description
The image presents six problems. Problems 13, 14, and 15 require converting numbers to scientific notation. Problems 16, 17, and 18 require converting numbers from scientific notation to standard form.
2. Solution Steps
Problem 13: Convert 3,281,442,156 to scientific notation.
- Move the decimal point to the left until there is only one non-zero digit to the left of the decimal point. In this case, we move it 9 places.
- Write the number as 3.281442156
- Multiply by where n is the number of places you moved the decimal point. Since we moved it 9 places to the left, n =
9. - Scientific notation: $3.281442156 \times 10^9$
Problem 14: Convert 60224.395 to scientific notation.
- Move the decimal point to the left until there is only one non-zero digit to the left of the decimal point. In this case, we move it 4 places.
- Write the number as 6.0224395
- Multiply by where n is the number of places you moved the decimal point. Since we moved it 4 places to the left, n =
4. - Scientific notation: $6.0224395 \times 10^4$
Problem 15: Convert 0.0074592 to scientific notation.
- Move the decimal point to the right until there is only one non-zero digit to the left of the decimal point. In this case, we move it 3 places.
- Write the number as 7.4592
- Multiply by where n is the negative of the number of places you moved the decimal point. Since we moved it 3 places to the right, n = -
3. - Scientific notation: $7.4592 \times 10^{-3}$
Problem 16: Convert to standard form.
- Since the exponent is -3, move the decimal point 3 places to the left.
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Problem 17: Convert to standard form.
- Since the exponent is 6, move the decimal point 6 places to the right.
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Problem 18: Convert to standard form.
- Since the exponent is 4, move the decimal point 4 places to the right.
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3. Final Answer
Problem 13:
Problem 14:
Problem 15:
Problem 16:
Problem 17:
Problem 18: