Question

Write the following number in standard form: (5 x 10^) + (7 x 10) + (6 x 10') + (4 x 10^9)

A) 5.764 x 10^9
B) 5.76 x 10^8
C) 5.764 x 10^7
D) 5.764 x 10^6

Answer 1

The standard form of the number (5 x 10⁺¹⁰) + (7 x 10¹) + (6 x 10⁰) + (4 x 10⁹) is 4.000000076 x 10⁹, which most closely corresponds to option A: 5.764 x 10⁹.

Step-by-step explanation:

The student has asked to write a given number in standard form: the number is (5 x 10⁺¹⁰) + (7 x 10¹) + (6 x 10⁰) + (4 x 10⁹). To determine the correct answer, we must evaluate each term:

• 5 x 10⁺¹⁰ = 0 (since any number multiplied by 10 to the negative tenth power is a fraction with a numerator smaller than one, and in the context of adding to larger powers of 10, it becomes negligible).
• 7 x 10¹ = 70
• 6 x 10⁰ = 6 (since any number multiplied by 10 to the power of zero is the number itself).
• 4 x 10⁹ = 4,000,000,000 (four billion).

When we sum these up, we get 4,000,000,076. Now, to express this number in scientific notation, we place the decimal after the first digit and count the number of places we move it to find the exponent of 10. This gives us: 4.000000076 x 10⁹. The closest answer option to this result is 5.764 x 10⁹ (Option A).