What is the product of 7.5 ×10^(4) and 2.9 ×10^(4) expressed in scientific notation? Answer:

Multiply Coefficients: Multiply the coefficients (7.5 and 2.9) together. Calculation: 7.5 × 2.9Add Exponents: Add the exponents (since the bases are the same and we are multiplying). Calculation: 10^4 × 10^4 = 10^(4+4) = 10^8Combine in Scientific Notation: Combine the results from Step 1 and Step 2 to express the product in scientific notation. Calculation: (7.5 × 2.9) × 10^8Perform Multiplication: Perform the multiplication from Step 1. Calculation: 7.5 × 2.9 = 21.75Adjust Coefficient: Write the final answer in scientific notation. Calculation: 21.75 × 10^8 However, the coefficient 21.75 is not between 1 and 10, so we need to adjust it to fit the scientific notation format.Adjust to Scientific Notation: Adjust the coefficient to be between 1 and 10 and adjust the exponent accordingly. Calculation: 21.75 can be written as 2.175 × 10^1 (since 21.75 = 2.175 × 10).Combine Adjusted Coefficient: Combine the adjusted coefficient with the exponent from Step 5. Calculation: 2.175 × 10^1 × 10^8 = 2.175 × 10^(1+8) = 2.175 × 10^9

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Math Problems

Grade 8

Convert between standard and scientific notation

Full solution

Q. What is the product of

7.5 \times 10^{4}

and

2.9 \times 10^{4}

expressed in scientific notation?

\newline

Answer:

Multiply Coefficients: Multiply the coefficients ( $7.5$ and $2.9$ ) together. $\newline$ Calculation: $7.5 \times 2.9$
Add Exponents: Add the exponents (since the bases are the same and we are multiplying). $\newline$ Calculation: $10^4 \times 10^4 = 10^{4+4} = 10^8$
Combine in Scientific Notation: Combine the results from Step $1$ and Step $2$ to express the product in scientific notation. $\newline$ Calculation: $(7.5 \times 2.9) \times 10^8$
Perform Multiplication: Perform the multiplication from Step $1$ . $\newline$ Calculation: $7.5 \times 2.9 = 21.75$
Adjust Coefficient: Write the final answer in scientific notation. $\newline$ Calculation: $21.75 \times 10^8$ $\newline$ However, the coefficient $21.75$ is not between $1$ and $10$ , so we need to adjust it to fit the scientific notation format.
Adjust to Scientific Notation: Adjust the coefficient to be between $1$ and $10$ and adjust the exponent accordingly. $\newline$ Calculation: $21.75$ can be written as $2.175 \times 10^1$ (since $21.75 = 2.175 \times 10$ ).
Combine Adjusted Coefficient: Combine the adjusted coefficient with the exponent from Step $5$ . $\newline$ Calculation: $2.175 \times 10^1 \times 10^8 = 2.175 \times 10^{1+8} = 2.175 \times 10^9$