Math Basics for Physics Review

What is the correct scientific Notation for the following value:

34500000000

• 34.5 X 10⁹

• 3.45 X 10^-10

• 3.45 X 10¹⁰

• 34.5 X 10^-9

Answer explanation

The scientific notation for 34500000000 is done by shifting the decimal point to the left until we get a number between 1 and 10. So we shift 10 places to the left to get 3.45. Hence, the correct answer is 3.45 X 10^10.

What is the correct scientific Notation for the following value:

.0672000

• 6.72 X 10⁵

• 6.72 X 10^-2

• 6.72 X 10²

• 6.72 X 10^-7

What is the correct Standard Notation for the following scientific value:

9.876 x 10⁵

• 987600

• .987600

• .00009876

• 98760

Answer explanation

The question asks for the standard notation of the scientific value 9.876 x 10^5. In standard notation, this value is represented by moving the decimal point five places to the right, resulting in the correct answer 987600.

Solve the following:

(4.2 x 10²) + (8.88 x 10⁴)

• 8.922 x 10⁴

• 3.73 x 10¹⁰

• 1.3 x 10⁶

• 8.9 x 10²

Answer explanation

The question is asking to add (4.2 x 10^2) and (8.88 x 10^4). When we perform the addition, the result is 8.922 x 10^4 which is the correct answer. This is because the larger exponent determines the overall scale of the result. So, despite adding a smaller number to a larger one, the result is roughly the size of the larger number.

Solve the following:

(3.48 × 10³ )(9.8 × 10⁴ )

• 2.69 x 10⁵

• 4.6 x 10²

• 3.41 x 10⁸

Solve the following:

1.91 x 10³ ÷ 5.0 x 10^-4

• 3.82 x 10⁶

• 2.22 x 10^-12

• 6.23 x 10⁸

Answer explanation

The question asks us to divide 1.91 x 10^3 by 5.0 x 10^-4. When dividing numbers in scientific notation, we divide the coefficients and subtract the exponents. Thus, 1.91 ÷ 5 = 0.382, and 3 - -4 = 7. But, to keep only one digit before the decimal in the coefficient, we adjust it to 3.82 and the exponent to 6. Hence, the correct answer is 3.82 x 10^6.

Solve the following:

(4.0 x 10⁴)÷ (3.63 x 10^-4)

• 2.64 x 10⁴

• 1.10 x 10⁸

• 5.36 x 10¹²

Solve the following:

(7.0 x 10³) + (8.20 x 10²)

• 7.82 x 10⁹

• 7.82 x 10³

• 7.82 x 10⁵

Solve the following:

(9.0 x 10²) – (5.54 x 10⁴)

• -5.5 x 10^-7

• -5.88 x 10⁶

• -5.5 x 10⁴

Convert 32g to mg

• 3.2 x 10⁴

• 3.2 x 10²

• 3.2 x 10^-4