Convert the following numbers into standard notation: 12) 8.65 x 10-1 13) 9.11 x 103 14) 5.40 x 101 15) 1.76 x 100 16) 7.4 x 10-5
The Correct Answer and Explanation is:
Answers in Standard Notation:
- 8.65 × 10⁻¹ = 0.865
- 9.11 × 10³ = 9110
- 5.40 × 10¹ = 54.0
- 1.76 × 10⁰ = 1.76
- 7.4 × 10⁻⁵ = 0.000074
Explanation
Scientific notation expresses very large or very small numbers using powers of ten. Converting from scientific to standard notation involves moving the decimal point based on the exponent.
A positive exponent on 10 means the decimal moves to the right. For example, in 9.11 × 10³, the exponent is 3. This indicates moving the decimal three places to the right, turning 9.11 into 9110.
A negative exponent on 10 signals a move to the left. In 8.65 × 10⁻¹, the exponent is –1, so the decimal shifts one position to the left, producing 0.865.
The number 5.40 × 10¹ has an exponent of 1, shifting the decimal one place to the right. The result is 54.0, where the trailing zero shows that the tenths place holds value.
In 1.76 × 10⁰, the exponent is 0. Any number to the power of zero equals 1, so the decimal remains unchanged. Thus, the number stays as 1.76.
For 7.4 × 10⁻⁵, the exponent of –5 requires the decimal to move five positions to the left. Zeros are used to fill in the empty places: starting with 7.4, the result becomes 0.000074.
This process relies on understanding place value. Positive exponents expand numbers by increasing place value, while negative exponents shrink them, making them fractions of 1. Scientific notation offers a concise way to handle extreme values, especially useful in scientific and engineering calculations where precision and readability are key.
