# How do I add decimal expansions without a calculator

Really not sure how to go about the two questions here and I have not been able to find something similar like this online. Would appreciate anyones help on how to answer the two questions! Thank you in advance.

• the question tells you to do it by converting the decimals to fractions -- did you try that? – Matthew Towers Feb 10 '17 at 12:01
• yeah I got 64/99 + 94/99 but i`m not sure if thats correct. – Alan Piggott Feb 10 '17 at 12:09
• You can check if 94/99 is the same as.94949494... with the help of your calculator – Matthew Towers Feb 10 '17 at 12:50

When converting part a) to a fraction, you should get: $$\frac{67}{99}+\frac{94}{99}$$ If you divide by $99$, the digits on the numerator should repeat in the decimal form if the numerator is less than $100$ for positive integers.
Let me demonstrate why: $$\frac{67}{99}=\frac{67}{100}+\frac{67}{9900}=0.67+\frac{67}{9900}$$ We can continue this process: $$\frac{67}{9900}=\frac{67}{10000}+\frac{67}{990000}=0.0067+\frac{67}{990000}$$ $$\frac{67}{990000}=\frac{67}{1000000}+\frac{67}{99000000}=0.000067+\frac{67}{99000000}$$ Repeating this process infinitely gives: $$\frac{67}{99}=0.67+0.0067+0.000067\cdots=0.\dot{6}\dot{7}$$