write each number in scientific notation
3.68,000=6.8x10^4
4.7,000,000=7x10^6
5.30,500,000,000=3.05x10^10
6.73,280,000=7.328x10^7
All are Correct!!
1. To write 3.68,000 in scientific notation, we move the decimal point to the right until there is only one nonzero digit to the left of the decimal point. In this case, the decimal point should be moved 4 places to the right, giving us 6.8. The exponent will be positive since we moved the decimal point to the right, resulting in 10^4. Therefore, 3.68,000 can be written as 6.8 x 10^4.
2. To write 4.7,000,000 in scientific notation, we again need to move the decimal point until there is only one nonzero digit to the left of the decimal point. The decimal point should be moved 6 places to the right, giving us 7. The exponent will be positive since we moved the decimal point to the right, resulting in 10^6. Therefore, 4.7,000,000 can be written as 7 x 10^6.
3. To write 5.30,500,000,000 in scientific notation, we once again move the decimal point to the right until there is only one nonzero digit to the left of the decimal point. The decimal point should be moved 10 places to the right, giving us 3.05. The exponent will be positive since we moved the decimal point to the right, resulting in 10^10. Therefore, 5.30,500,000,000 can be written as 3.05 x 10^10.
4. To write 6.73,280,000 in scientific notation, we move the decimal point until there is only one nonzero digit to the left of the decimal point. The decimal point should be moved 7 places to the right, giving us 7.328. The exponent will be positive since we moved the decimal point to the right, resulting in 10^7. Therefore, 6.73,280,000 can be written as 7.328 x 10^7.
To write a number in scientific notation, follow these steps:
1. Identify the first nonzero digit in the number.
2. Count the number of digits from the first nonzero digit to the end of the number (including zeros if any).
3. Write the first nonzero digit, followed by a decimal point, and then write the remaining digits (including zeros if any) as a decimal number.
4. Multiply the decimal number obtained in step 3 by 10 raised to a power equal to the number of digits counted in step 2.
5. If the original number is greater than or equal to 10, then the exponent will be positive. If the original number is less than 1, then the exponent will be negative.
6. Write the decimal number obtained in step 4, multiplied by 10 raised to the power calculated in step 5, in the format a x 10^b.
Let's apply these steps to the given numbers:
1. 3.68,000:
- The first nonzero digit is 3.
- There are 5 digits from the first nonzero digit (3) to the end of the number (including zeros).
- The decimal number is 3.68.
- The power of 10 is 4 (since there are 4 digits from the first nonzero digit to the end of the number).
- The final scientific notation is 3.68 x 10^4.
2. 4.7,000,000:
- The first nonzero digit is 4.
- There are 7 digits from the first nonzero digit (4) to the end of the number (including zeros).
- The decimal number is 4.7.
- The power of 10 is 6 (since there are 6 digits from the first nonzero digit to the end of the number).
- The final scientific notation is 4.7 x 10^6.
3. 5.30,500,000,000:
- The first nonzero digit is 5.
- There are 11 digits from the first nonzero digit (5) to the end of the number (including zeros).
- The decimal number is 5.30.
- The power of 10 is 10 (since there are 10 digits from the first nonzero digit to the end of the number).
- The final scientific notation is 5.30 x 10^10.
4. 6.73,280,000:
- The first nonzero digit is 6.
- There are 7 digits from the first nonzero digit (6) to the end of the number (including zeros).
- The decimal number is 6.73.
- The power of 10 is 7 (since there are 7 digits from the first nonzero digit to the end of the number).
- The final scientific notation is 6.73 x 10^7.