Physics

Physics

Problem

Convert 3.2 km3.2\,\text{km} to metres and write the answer in scientific notation. a) 3.2×10−3 m3.2\times10^{-3}\,\text{m} b) 3.2×102 m3.2\times10^{2}\,\text{m} c) 3.2×103 m3.2\times10^{3}\,\text{m} d) 32×103 m32\times10^{3}\,\text{m}
Intuitive explanation

Unit conversion is about multiplying by a fraction that equals 1—here, using the fact that 1 km = 1000 m. The key insight is that scientific notation requires a number between 1 and 10 multiplied by a power of 10, so after you convert to metres, you'll need to shift the decimal point to the right place and express the result as a coefficient times 10n10^n.

Intuitive explanation

Unit conversion is about multiplying by a fraction that equals 1—here, using the fact that 1 km = 1000 m. The key insight is that scientific notation requires a number between 1 and 10 multiplied by a power of 10, so after you convert to metres, you'll need to shift the decimal point to the right place and express the result as a coefficient times 10n10^n.

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