Sure, let's convert the speed of light from its standard decimal notation into scientific notation step by step.
Step 1: Identify the number given.
The speed of light is given as [tex]\( 299,500,000 \)[/tex] meters per second.
Step 2: Understand scientific notation.
Scientific notation has the form [tex]\( a \times 10^b \)[/tex], where:
- [tex]\( a \)[/tex] is a number greater than or equal to 1 but less than 10.
- [tex]\( b \)[/tex] is an integer.
Step 3: Convert the given number.
- To convert [tex]\( 299,500,000 \)[/tex] into scientific notation, we want to express it as a product of a number [tex]\( a \)[/tex] and a power of ten [tex]\( 10^b \)[/tex].
- We move the decimal point in 299,500,000 to the left until only one non-zero digit remains to the left of the decimal point.
Step 4: Moving the decimal point.
- Start with 299,500,000. Place the decimal after the first non-zero digit: [tex]\( 2.99500000 \)[/tex].
- We moved the decimal point 8 places to the left.
Step 5: Determine the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex].
- [tex]\( a \)[/tex] is the coefficient, which is [tex]\( 2.995 \)[/tex].
- [tex]\( b \)[/tex] is the exponent, which indicates how many places we moved the decimal point. Here, we moved the decimal point 8 places to the left.
Thus, in scientific notation, the speed of light is written as:
[tex]\[ 2.995 \times 10^8 \][/tex]
So, [tex]\( a = 2.995 \)[/tex] and [tex]\( b = 8 \)[/tex].
