Express the quantity 556.2×10 −12 s in each unit. a. ms b. ns c. ps d. fs

Hi everyone here we have a question. I'm telling us to convert 742.8 times 10 to the negative seconds into each of the given units. So first we have to kill a second. So one kill a second Equals 10 to the third seconds. So we have 742 . times 10 to the negative 12 seconds. Times one kill a second Over 10 to the 3rd 2nd. And our seconds are going to cancel out giving us 7. to 8 times 10 to the negative 13 kill O seconds. We have nana seconds. One nana second equals 10 to the negative ninth seconds. So we have 742.8 times 10 to the negative 12 2nd times one nanosecond Over 10 to the - seconds. And our second will cancel out, giving us 0.74 to eight nanoseconds. We have microseconds. One microsecond Equals 10 to the -6 seconds. So 742.8 times 10 to the negative 12 seconds times one Microsecond over 10 to the negative six seconds equals 7.4 to 8 times 10 to the negative fourth microseconds, We have one time to second equals to the negative 15 seconds. So you have 742.8 times to the negative 12 seconds, Times 1, 5th of 2nd Over 10 to the negative seconds and our second will cancel out and that equals 7.4 to 8 times 10 to the 5th. 5th seconds. And these are our final answers. Thank you for watching bye.

Ch.1 - Matter, Measurement & Problem Solving

Tro - Chemistry: A Molecular Approach 4th Edition

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Tro 4th Edition

Ch.1 - Matter, Measurement & Problem Solving

Problem 62

Chapter 1, Problem 62

Express the quantity 556.2×10⁻¹² s in each unit. a. ms b. ns c. ps d. fs

Verified step by step guidance

Identify the original unit and the target units. The original unit is seconds (s), and the target units are milliseconds (ms), nanoseconds (ns), picoseconds (ps), and femtoseconds (fs).

Understand the conversion factors between the units: 1 ms = 10^-3 s, 1 ns = 10^-9 s, 1 ps = 10^-12 s, 1 fs = 10^-15 s.

Convert the given time from seconds to milliseconds (ms) by multiplying the given time by 10^3 (since 1 ms = 10^-3 s).

Convert the given time from seconds to nanoseconds (ns) by multiplying the given time by 10^9 (since 1 ns = 10^-9 s).

Convert the given time from seconds to picoseconds (ps) and femtoseconds (fs) by multiplying the given time by 10^12 and 10^15 respectively.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small in a more manageable form. It is written as a product of a number between 1 and 10 and a power of ten. For example, 556.2 * 10^-12 seconds can be expressed as 5.562 * 10^-10 seconds, which simplifies calculations and comparisons.

Unit Conversion

Unit conversion involves changing a quantity expressed in one unit to another unit while maintaining the same value. In this case, converting seconds to milliseconds (ms), nanoseconds (ns), picoseconds (ps), and femtoseconds (fs) requires knowing the relationships between these units: 1 ms = 10^-3 s, 1 ns = 10^-9 s, 1 ps = 10^-12 s, and 1 fs = 10^-15 s.

Time Units

Time units are standardized measures used to quantify time intervals. Common time units include seconds (s), milliseconds (ms), nanoseconds (ns), picoseconds (ps), and femtoseconds (fs). Understanding the scale of these units is crucial for converting between them, as they differ by factors of ten, with each subsequent unit being a thousand times smaller than the previous one.