Write each decimal as a fraction

Write each decimal as a fraction: a. 3.0625 b. 0.78125

The correct answer and explanation is:

a) 3.0625 as a fraction

To convert 3.0625 into a fraction, follow these steps:

1. Separate the whole number from the decimal: The whole number is 3, and the decimal is 0.0625.
2. Convert the decimal part to a fraction:
   • 0.0625 can be written as 625/10000 because the decimal has four digits after the decimal point.
3. Simplify the fraction:
   • 625 and 10000 have a greatest common divisor (GCD) of 125. Divide both the numerator and denominator by 125:
   62510000=625÷12510000÷125=580\frac{625}{10000} = \frac{625 \div 125}{10000 \div 125} = \frac{5}{80}
   • The simplified fraction is 5/80, and dividing both the numerator and denominator by 5 gives:
   580=116\frac{5}{80} = \frac{1}{16}
4. Combine the whole number with the fraction:
   • The whole number 3 can be written as 3/1, and the fraction 0.0625 is 1/16.
   • Therefore, the complete fraction form is:
   3116or49163 \frac{1}{16} \quad \text{or} \quad \frac{49}{16}

b) 0.78125 as a fraction

To convert 0.78125 into a fraction, follow these steps:

1. Write the decimal as a fraction: 0.78125 has five digits after the decimal, so write it as: 78125100000\frac{78125}{100000}
2. Simplify the fraction:
   • The GCD of 78125 and 100000 is 15625. Divide both the numerator and denominator by 15625:
   78125100000=78125÷15625100000÷15625=564\frac{78125}{100000} = \frac{78125 \div 15625}{100000 \div 15625} = \frac{5}{64}

So, 0.78125 as a fraction is 5/64.

Conclusion

• 3.0625 = 49/16
• 0.78125 = 5/64