Write 0.006 as a fraction in simplest form.

Class 6DecimalsDecimals

A $\frac{6}{100}$
B $\frac{3}{50}$
C $\frac{6}{10}$
D $\frac{3}{500}$

Step-by-Step Solution

Three decimal places means denominator 1000, so

0.006 = \frac{6}{1000}

. Dividing top and bottom by 2 gives

\frac{3}{500}

. Counting only two places gives

\frac{6}{100}

, which is 0.06 — ten times too big.

Answer: D)

\frac{3}{500}

Key idea: Decimal ↔ fraction

**Decimal to fraction**: count the decimal places. Put the digits over 10, 100, 1000 accordingly. So 0.7 = 7/10. 0.43 = 43/100. 1.25 = 1 + 25/100 = 1 + 1/4 = 5/4.

**Fraction to decimal**: if the denominator is already 10, 100, 1000, …, just write the numerator with the right number of decimal places. 9/10 = 0.9. 27/100 = 0.27. For other fractions (e.g. 3/4), divide: 3 ÷ 4 = 0.75.

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