Grade 8 Math Number Sense and Operations Scientific notation

What is the scientific notation for the number 5,600,000?

Answer explanation

To express 5,600,000 in scientific notation, we write it as 5.6 multiplied by 10 raised to the power of 6, since the decimal moves 6 places to the left. Thus, the correct answer is 5.6 × 10^6.

• 0.00345

• 0.0345

• 0.345

• 3.45

Answer explanation

To express 3.45 × 10^{-3} in standard form, move the decimal point three places to the left, resulting in 0.00345. Thus, the correct answer is 0.00345.

• 789

• 7,890

• 78,900

• 789,000

Answer explanation

To convert 7.89 × 10^4 to standard form, multiply 7.89 by 10,000. This gives 78,900, making it the correct choice. The other options are incorrect as they do not represent the same value.

Convert the number 0.00052 to scientific notation.

Answer explanation

To convert 0.00052 to scientific notation, move the decimal point 4 places to the right, giving 5.2. Thus, it becomes 5.2 × 10^{-4}, which is the correct choice.

Answer explanation

To find the product of (2 × 10^3) × (3 × 10^2), multiply the coefficients: 2 × 3 = 6, and add the exponents: 3 + 2 = 5. Thus, the result is 6 × 10^5, which matches the correct answer.

Answer explanation

To simplify (4 × 10^5) ÷ (2 × 10^2), divide the coefficients: 4 ÷ 2 = 2. For the powers of ten, subtract the exponents: 10^5 ÷ 10^2 = 10^(5-2) = 10^3. Thus, the result is 2 × 10^3.

Which of the following numbers is written in scientific notation?

• 0.45

• 45

• 0.091

• 0.0091

• 0.00091

• 0.000091

Answer explanation

To convert $9.1 \times 10^{-2}$ to decimal, move the decimal point two places to the left, resulting in 0.091. Thus, the correct answer is 0.091.

Answer explanation

To find the sum, add the coefficients: 3 + 2 = 5. Since both terms are multiplied by 10^4, the result is 5 × 10^4. Thus, the correct answer is 5 × 10^4.

Convert the number 1,230,000 to scientific notation.

Answer explanation

To convert 1,230,000 to scientific notation, we express it as 1.23 multiplied by 10 raised to the power of 6, since the decimal moves 6 places to the left. Thus, the correct answer is 1.23 \times 10^6.