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Zorluk: OrtaDecimals and Scientific Notation

A short-pulse laser emits a single pulse lasting 8.4×10−98.4 \times 10^{-9} seconds. A high-speed optical sensor completes one measurement cycle every 1.4×10−111.4 \times 10^{-11} seconds. How many measurement cycles does the sensor complete during the duration of a single laser pulse?

Cevap: 600 cycles

Cevap

600
Dividing the pulse duration (8.4×10−98.4 \times 10^{-9} seconds) by the sensor cycle time (1.4×10−111.4 \times 10^{-11} seconds) yields 8.41.4×10−9−(−11)=6×102=600\frac{8.4}{1.4} \times 10^{-9 - (-11)} = 6 \times 10^2 = 600 complete cycles.

Adım Adım Çözüm

1
Set up the division expression for the total number of cycles.
\frac{8.4 \times 10^{-9}\text{ seconds}}{1.4 \times 10^{-11}\text{ seconds}}
To find how many cycle intervals fit within the total pulse duration.
2
Divide the decimal coefficients.
8.41.4=6\frac{8.4}{1.4} = 6
Separating the numerical coefficients from the powers of ten.
3
Apply exponent rules to divide powers of 10.
10^{-9 - (-11)} = 10^{-9 + 11} = 10^2 = 100
Dividing powers with the same base requires subtracting the denominator exponent from the numerator exponent.
4
Combine results to find total cycles.
6×100=6006 \times 100 = 600
Multiplying coefficient quotient by the simplified power of ten.

Anahtar Kavram

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Decimals and Scientific Notation

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