Question

the number 4,570,000 can be expressed using scientific notation as ______.

a.) \\(45.7 \times 10^{-5}\\)

b.) \\(4.57 \times 10^{6}\\)

c.) \\(457 \times 10^{4}\\)

d.) \\(0.457 \times 10^{-7}\\)

Explanation:

Identify the standard form value

The given number is \(4,570,000\).

Determine the decimal shift for scientific notation

To write a number in scientific notation \(a \times 10^n\), the coefficient \(a\) must satisfy \(1 \le |a| < 10\).
Placing the decimal point after the first non-zero digit gives \(4.57\).
Counting the number of places the decimal point moves from the end of \(4,570,000.\) to \(4.570000\):
The decimal point shifts \(6\) places to the left.

Formulate the scientific notation expression

Since the decimal shifted \(6\) places to the left to make the number smaller, we multiply by \(10^6\) to keep the value equivalent:

$$4,570,000 = 4.57 \times 10^6$$

This matches option (b).

Answer:

• a.) \(45.7 \times 10^{-5}\)
• b.) \(4.57 \times 10^6\) (Correct answer)
• c.) \(457 \times 10^4\)
• d.) \(0.457 \times 10^{-7}\)