Steps to Write Decimals as Fractions

Warm Up Can you write problems 1 and 4 as fractions? Explain your steps. When you have a terminating decimal, you need to say the decimal properly so that you can hear the decimal place value, and write it like a fraction. You cannot say “point” in your answer; you need to say the decimal place value that ends in “ths”. Then reduce the fraction, if possible. 1.222 is read as “one AND two hundred twenty two thousandths”. 43.76676 is read as “forty-three AND seventy-six thousand six hundred seventy-six hundred thousandths”.

If you have a hard time figuring out how to say the place value, can you think of another way to determine what the denominator is in your un-reduced fraction? Look at the number of decimal places used in the original number and the number of zeroes in the denominator of the fraction. 1.222 is read as “one AND two hundred twenty two thousandths. 43.76676 is read as “forty-three AND seventy-six thousand six hundred seventy-six hundred thousandths.

When you have a repeating decimal there are different steps

You can think of the steps in a slightly different way, too. Let the given decimal be equal to x. See what repeats. You need to get an equation with what repeats just to the left of the decimal point. You need to get a second equation with what repeats just to the right of the decimal point, too. Subtract the equations so that you have no numbers after the decimal point in the answer Solve for x. Let x = 0.171717 17 repeats Multiply x = 0.171717 on both sides by 100 to get the first 17 just to the left of the decimal point. You now have 100 x = 17.1717 for first new equation Your first equation has the 17 just to the right of the decimal point, so you do not need to change it. Keep the original equation x = 0.171717 Now subtract the two equations 100 x = 17.171717 - 1 x - 0.171717 99 x = 17. ÷ 99 ÷99 1 x = 17/99

You can think of the steps in a slightly different way, too. Let the given decimal be equal to x. See what repeats. You need to get an equation with what repeats just to the left of the decimal point. You need to get a second equation with what repeats just to the right of the decimal point, too. Subtract the equations so that you have no numbers after the decimal point in the answer Solve for x. Let x = 0.41666 6 repeats Multiply x = 0.41666 on both sides by 1000 to get the first 6 just to the left of the decimal point. You now have 1000 x = 416.66 for first new equation Multiply x = 0.41666 on both sides by 100 to get the repeating part just to the right of the decimal point. You now have 100 x = 41.666 for second new equation Now subtract the two equations 1000 x = 416.666 - 100 x - 41.666 900 x = 375 ÷ 900 ÷900 1 x = 375/900 which reduces to 15/35 = 5/12

Do you notice anything? In these problems, every number to the right of the decimal point repeats. Look at what is repeating, and the number in the denominator. What is the connection? Your denominator will have as many 9s as the the number of digits repeating in the decimal.