High School

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What is the correct way to write [tex]$1,550,000,000$[/tex] in scientific notation?

A. [tex]$1.55 \times 10^9$[/tex]
B. [tex]$1.55 \times 10^{10}$[/tex]
C. [tex]$15.5 \times 10^8$[/tex]
D. [tex]$15.5 \times 10^9$[/tex]

Answer :

To write the number in scientific notation, we first note that in scientific notation a number is written as

[tex]$$
m \times 10^e,
$$[/tex]

where the mantissa [tex]\( m \)[/tex] satisfies [tex]\( 1 \leq m < 10 \)[/tex] and [tex]\( e \)[/tex] is an integer.

For the number

[tex]$$
1,\!550,\!000,\!000,
$$[/tex]

we determine how many places the decimal point must be moved to convert it into a number between 1 and 10. Moving the decimal point 9 places to the left gives

[tex]$$
1.55,
$$[/tex]

which is the mantissa.

Since we have moved the decimal point 9 places to the left, the exponent is [tex]\( 9 \)[/tex]. Therefore, the number in scientific notation is written as

[tex]$$
1.55 \times 10^9.
$$[/tex]

Thus, the correct answer is

[tex]$$
1.55 \times 10^9.
$$[/tex]

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