Number and Operations>Converting Between Decimal and Scientific Notation(TEKS.Math.8.2.C)
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Texas 8th Grade Math › Number and Operations>Converting Between Decimal and Scientific Notation(TEKS.Math.8.2.C)
A red blood cell has a diameter of about 0.000007 meters.
Express 0.000007 in scientific notation.
$7 \times 10^{-5}$
$0.7 \times 10^{-5}$
$7 \times 10^{-6}$
$7.0 \times 10^{-7}$
Explanation
Move the decimal right until the coefficient is between 1 and 10: 0.000007 → 7 (moved 6 places right), so the exponent is −6: $7 \times 10^{-6}$. A has an exponent off by one, B has a coefficient less than 1, and D corresponds to 0.0000007. Scientific notation makes tiny measurements easier to read and compare.
A sensor detects a radio wave with wavelength 0.000000125 meters.
Express 0.000000125 in scientific notation.
$12.5 \times 10^{-8}$
$0.125 \times 10^{-6}$
$1.25 \times 10^{-7}$
$1.25 \times 10^{7}$
Explanation
Move the decimal right until the coefficient is between 1 and 10: 0.000000125 → 1.25 (moved 7 places), so $1.25 \times 10^{-7}$. A has a coefficient greater than 10, B has a coefficient less than 1, and D uses the wrong sign. Scientific notation is standard for wavelengths and other scientific measurements.