Question

using division to write fractions as decimals - item 52313
calculators cannot display repeating decimals. calculators always round.
yuris calculator displays decimals to 5 places. he uses his calculator to find the
decimal equivalent for each of the fractions below.
for each number, choose what his calculator will display as the decimal equivalent.
then choose whether or not this is the exact decimal equivalent.
1/9
calculator display for 1/9
is this the exact decimal equivalent?
7/9
calculator display for 7/9
is this the exact decimal equivalent?
1/10

Explanation:

Step1: Analyze $\frac{1}{9}$

To find the decimal of $\frac{1}{9}$, we do the division: $1\div9 = 0.11111\cdots$ (repeating decimal). The calculator displays to 5 decimal places, so it will show $0.11111$. Since $\frac{1}{9}$ is a repeating decimal ($0.\overline{1}$), the 5 - place decimal is a rounded (or truncated) value, not the exact equivalent.

Step2: Analyze $\frac{7}{9}$

For $\frac{7}{9}$, perform the division: $7\div9 = 0.77777\cdots$ (repeating decimal). The calculator, showing 5 decimal places, will display $0.77777$. As $\frac{7}{9}=0.\overline{7}$, the 5 - place decimal is not the exact equivalent.

Step3: Analyze $\frac{1}{10}$

For $\frac{1}{10}$, the division is $1\div10 = 0.1$. The calculator displays to 5 decimal places, so it will show $0.10000$. Since $\frac{1}{10}=0.1$, this is the exact decimal equivalent (when written to 5 decimal places, it's just $0.10000$ which is equal to $0.1$).

Answer:

• For $\frac{1}{9}$: Calculator display is $0.11111$, Is this exact? No.
• For $\frac{7}{9}$: Calculator display is $0.77777$, Is this exact? No.
• For $\frac{1}{10}$: Calculator display is $0.10000$, Is this exact? Yes.