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Analyzing and Communicating Scientific Information: Mastery Test

Type the correct answer in each box. Use numerals instead of words.

The speed of light in a vacuum is approximately 299,500,000 meters per second. In scientific notation, we can write this number as [tex]a \times 10^b[/tex], where [tex]a = [/tex] ______ and [tex]b = [/tex] ______.



Answer :

GinnyAnswer
Sure, let's translate the given speed of light in a vacuum, which is approximately [tex]\( 299,500,000 \)[/tex] meters per second, into scientific notation. Here's the step-by-step process for converting this number:

1. Identify the Coefficient [tex]\( a \)[/tex]:
- In scientific notation, the number is written in the form [tex]\( a \times 10^b \)[/tex], where [tex]\( 1 \leq a < 10 \)[/tex].
- Move the decimal point so that there is only one non-zero digit to the left of the decimal point.
- For [tex]\( 299,500,000 \)[/tex], if you move the decimal point 8 places to the left, it becomes [tex]\( 2.995 \)[/tex].

2. Determine the Exponent [tex]\( b \)[/tex]:
- Count the number of places you move the decimal point to convert the original number into the coefficient [tex]\( a \)[/tex]. This count gives the exponent [tex]\( b \)[/tex].
- For [tex]\( 299,500,000 \)[/tex], you moved the decimal point 8 places to the left, so [tex]\( b = 8 \)[/tex].

Thus, when writing [tex]\( 299,500,000 \)[/tex] in scientific notation, it becomes:

[tex]\[ 2.995 \times 10^8 \][/tex]

So, the values for [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are:
[tex]\[ a = 2.995 \][/tex]
[tex]\[ b = 8 \][/tex]

Therefore, the speed of light in scientific notation is [tex]\( 2.995 \times 10^8 \)[/tex] meters per second.

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