Convert 7.11 x 10-4 to microseconds. Use only the metric system.
Answer (2)
To convert 7.11 × 1 0 − 4 seconds to microseconds, we use the conversion ratio where 1 microsecond equals 1 0 − 6 seconds. The calculation simplifies to 711 microseconds. Hence, 7.11 × 1 0 − 4 seconds is equal to 711 microseconds.
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Recall that 1 microsecond = 1 0 − 6 seconds.
Divide the given value in seconds by 1 0 − 6 to convert to microseconds: 7.11 × 1 0 − 4 /1 0 − 6 .
Simplify the expression: 7.11 × 1 0 − 4 + 6 = 7.11 × 1 0 2 .
Calculate the final value: 7.11 × 100 = 711 microseconds. Therefore, the answer is 711 .
Explanation
Understanding the Problem We are asked to convert 7.11 × 1 0 − 4 seconds to microseconds using the metric system.
Recalling Metric Prefixes First, let's recall the relationship between seconds and microseconds. The prefix 'micro' means one millionth, so 1 microsecond is equal to 1 0 − 6 seconds.
Setting up the Conversion To convert seconds to microseconds, we need to divide the given value in seconds by the number of seconds in a microsecond, which is 1 0 − 6 seconds. So, we will perform the following calculation: 1 0 − 6 seconds/microsecond 7.11 × 1 0 − 4 seconds
Simplifying the Expression Now, let's simplify the expression: 7.11 × 1 0 − 4 ÷ 1 0 − 6 = 7.11 × 1 0 − 6 1 0 − 4 = 7.11 × 1 0 − 4 − ( − 6 ) = 7.11 × 1 0 − 4 + 6 = 7.11 × 1 0 2
Final Calculation 7.11 × 1 0 2 = 7.11 × 100 = 711 Therefore, 7.11 × 1 0 − 4 seconds is equal to 711 microseconds.
Stating the Answer So, 7.11 × 1 0 − 4 seconds is equal to 711 microseconds.
Examples
Imagine you are working with high-speed photography, and you need to measure the duration of a very short event, like the popping of a balloon. The camera records the event in seconds, but to analyze the data precisely, you need to convert the time to microseconds because the events happen so quickly. Converting between seconds and microseconds allows you to understand and analyze these rapid processes more effectively.
