Convert 4.5 x 104+ 6.45 x 105 to decimal form
The Correct Answer and Explanation is:
Correct Answer:
4.5 × 10⁴ = 45,000
6.45 × 10⁵ = 645,000
Total: 45,000 + 645,000 = 690,000
Explanation:
To convert numbers expressed in scientific notation into decimal form, each coefficient is multiplied by a power of ten. The exponent on the ten determines how many places the decimal point moves.
For the first number, 4.5 × 10⁴, the exponent is 4. This means the decimal point in 4.5 must shift four positions to the right. Moving the point turns 4.5 into 45,000. This can be thought of as adding four zeros to shift the digits accordingly:
4.5 → 45.0 → 450.0 → 4,500.0 → 45,000
Next, 6.45 × 10⁵ has an exponent of 5, indicating the decimal point in 6.45 must move five places to the right. This gives:
6.45 → 64.5 → 645.0 → 6,450.0 → 64,500.0 → 645,000
After converting both numbers to decimal form, addition becomes straightforward. Start with 45,000 and add 645,000. Adding these yields:
645,000 + 45,000 = 690,000
Scientific notation is often used to simplify the expression of very large or very small numbers. It allows easier manipulation during multiplication or division, especially in scientific or engineering contexts. However, when the goal involves basic arithmetic such as addition or subtraction, converting to decimal form avoids confusion and aligns digits based on place value.
Decimal form also offers clarity when presenting final answers in real-world applications like finances, measurements, or population figures. Maintaining place value integrity is essential during such conversions and calculations, especially when exponents differ.
