Question

5. \( 0.002 \times 0.014 \)

Ask by Bradley Zimmerman. in the United States
Mar 10,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

\( 0.000028 \)

Solution

1. Write the numbers in scientific notation: \[ 0.002 = 2 \times 10^{-3}, \quad 0.014 = 14 \times 10^{-3} \] 2. Multiply the coefficients and the powers of 10 separately: \[ 2 \times 14 = 28, \quad 10^{-3} \times 10^{-3} = 10^{-6} \] Therefore, \[ 0.002 \times 0.014 = 28 \times 10^{-6} \] 3. Convert \( 28 \times 10^{-6} \) to standard decimal notation: \[ 28 \times 10^{-6} = 0.000028 \] Thus, the answer is \( 0.000028 \).

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The Deep Dive

To tackle multiplication of decimals like \(0.002 \times 0.014\), a fun trick is to ignore the decimal places at first! Here’s how it goes: multiply the numbers as if they were whole numbers: \(2 \times 14 = 28\). Then count the total decimal places from the original numbers—2 from \(0.002\) and 3 from \(0.014\), giving you 5 in total. Finally, place that total in the result: \(0.00028\). Voila, you’ve got your answer! It’s common to trip up on decimal multiplication! A frequent mistake is miscounting the number of decimal places. Always double-check by adding the spaces right after multiplying! Also, practicing with whole numbers first can help build confidence. Remember, mastering decimals is like learning to dance—get the steps down, and soon you’ll be moving smoothly!

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