To write the number [tex]\( 8.501 \times 10^5 \)[/tex] in ordinary notation, follow these steps:
1. Understand Scientific Notation:
- Scientific notation expresses numbers as a product of two factors: a coefficient (a number typically between 1 and 10) and 10 raised to an exponent.
- Here, the number is [tex]\( 8.501 \)[/tex], and the exponent is [tex]\( 5 \)[/tex]. This means the coefficient ([tex]\( 8.501 \)[/tex]) is multiplied by [tex]\( 10 \)[/tex] raised to the power of [tex]\( 5 \)[/tex].
2. Multiply by [tex]\( 10^5 \)[/tex]:
- The exponent [tex]\( 5 \)[/tex] signifies that we need to multiply [tex]\( 8.501 \)[/tex] by [tex]\( 10 \)[/tex] five times.
- Each multiplication by [tex]\( 10 \)[/tex] shifts the decimal point one place to the right.
3. Shift the Decimal Point:
- Start with [tex]\( 8.501 \)[/tex] (where the decimal point is initially between the 8 and 5).
- Shift the decimal point 5 places to the right:
- Shifting once: 85.01
- Shifting twice: 850.1
- Shifting thrice: 8501.0
- Shifting four times: 85010.0
- Shifting five times: 850100.0
4. Result:
- After shifting the decimal point five places to the right, the result is [tex]\( 850100.0 \)[/tex].
Therefore, [tex]\( 8.501 \times 10^5 \)[/tex] in ordinary notation is [tex]\( 850100.0 \)[/tex].
