Decimals: terminating and repeating

Advanced Math 6 · Unit 3 · decimals-terminating-repeating · Teacher edition

decimals-terminating-repeating

Name ______________________________Date ______________

1.
Write $\dfrac{7}{8}$ as a decimal.
Answer: ______________
2.
Which fraction has a terminating decimal?
1. (A)
  $\dfrac{1}{3}$
2. (B)
  $\dfrac{1}{6}$
3. (C)
  $\dfrac{1}{8}$
4. (D)
  $\dfrac{1}{9}$
3.
Compute $4.2 \times 0.35$ .
Answer: ______________
4.
Compute $7.2 \div 0.08$ .
Answer: ______________
5.
The decimal form of $\dfrac{3}{11}$ repeats. Enter the two-digit block that repeats.
Answer: ______________

Answer key — Decimals: terminating and repeating

1.
0.875decimals-terminating-repeating-01
$\frac{7}{8} = \frac{875}{1000} = \mathbf{0.875}$ . It terminates because $8 = 2^3$ has no primes other than $2$ and $5$ .
2.
(C)
$\dfrac{1}{8}$
decimals-terminating-repeating-02
$8 = 2^3$ , so $\frac{1}{8} = 0.125$ terminates. The others have a factor of $3$ in the denominator: $\frac{1}{3} = 0.\overline{3}$ , $\frac{1}{6} = 0.1\overline{6}$ , $\frac{1}{9} = 0.\overline{1}$ . Answer: $\mathbf{\frac{1}{8}}$ .
3.
1.47decimals-terminating-repeating-03
$42 \times 35 = 1470$ . Three decimal places: $1.470 = \mathbf{1.47}$ . Estimate check: $4 \times 0.35 = 1.4$ . ✓
4.
90decimals-terminating-repeating-04
$7.2 \div 0.08 = 720 \div 8 = \mathbf{90}$ . Sense check: $0.08$ is small, so the quotient should be much bigger than $7.2$ . ✓
5.
27decimals-terminating-repeating-05
$3 \div 11 = 0.2727\ldots = 0.\overline{27}$ . The repeating block is $\mathbf{27}$ . (Every $\frac{k}{11}$ has a two-digit block equal to $9k$ : $\frac{1}{11} = 0.\overline{09}$ , $\frac{2}{11} = 0.\overline{18}$ , $\frac{3}{11} = 0.\overline{27}$ .)