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Part B - Write this large number in scientific notation.

Determine the values of [tex]\(m\)[/tex] and [tex]\(n\)[/tex] when the following average distance from the Sun to the Earth is written in scientific notation:

[tex]\[150,000,000,000 \text{ ml}\][/tex]

Enter [tex]\(m\)[/tex] and [tex]\(n\)[/tex], separated by commas.

Sagot :

GinnyAnsweridn
To write the large number 150,000,000,000 in scientific notation, we need to express it in the form:
[tex]\[ m \times 10^n \][/tex]
where [tex]\( m \)[/tex] is a number greater than or equal to 1 and less than 10, and [tex]\( n \)[/tex] is an integer.

Given the number 150,000,000,000, let's follow these steps:

1. Identify the significant figures in the number. Here the significant figures are 1.5.

2. Determine the power of 10 needed to represent the original number. To do this, count how many places you need to move the decimal point to the left to get a number between 1 and 10.
- Starting with 150,000,000,000, the decimal point is after the last zero.
- Move the decimal point 11 places to the left to get 1.5 (since there are 11 digits following the initial digit 1).

Thus, the number [tex]\( 150,000,000,000 \)[/tex] can be written in scientific notation as:

[tex]\[ 1.5 \times 10^{11} \][/tex]

Therefore, the values are:
[tex]\[ m = 1.5, \quad n = 11 \][/tex]

So, when the average distance from the Sun to the Earth is written in scientific notation, the correct values for [tex]\( ml \)[/tex] and [tex]\( nl \)[/tex] are:

[tex]\[ 1.5, \, 11 \][/tex]
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