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Diagnostic Assessment - Maths ACSF Level 5

The Earth is 146,000,000 kilometers from the Sun. What is this number in scientific notation?

Select the correct answer:

A. [tex]\(0.146 \times 10^9\)[/tex]
B. [tex]\(1.46 \times 10^{-8}\)[/tex]
C. [tex]\(14.6 \times 10^6\)[/tex]
D. [tex]\(1.46 \times 10^8\)[/tex]

Sagot :

GinnyAnsweridn
Sure, let's go through the detailed steps to convert 146,000,000 kilometers into scientific notation.

1. Identify the significant figures:
The number you're provided with is 146,000,000. The significant figures here are 1, 4, and 6.

2. Place the decimal point:
To convert to scientific notation, we need to place the decimal point after the first significant figure. In this case, it should be placed after 1, so we get 1.46.

3. Count the number of places the decimal point has moved:
Originally, the decimal point is at the end of the number (although it's not shown, it is implied). When we move the decimal point from the end of the number (146,000,000) to after the first digit (1.46), we count the number of places moved.

Count the digits excluding trailing zeros:
146,000,000 (There are 8 places between the original decimal point and after the 1.)

4. Express the number in scientific notation:
Since we moved the decimal point 8 places to the left, we multiply 1.46 by 10 raised to the power of 8. Therefore, 146,000,000 in scientific notation is written as [tex]\( 1.46 \times 10^8 \)[/tex].

The correct answer is:
[tex]\[ 1.46 \times 10^8 \][/tex]

So, you should select:
1.46 x 10^8
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