Exercises: Repeating and Terminating Decimals

Work through each section in order. Write recurring decimals using a dot over the
repeating digit(s), and simplify fraction answers to lowest terms.

Grade 7·24 problems·~29 min·Uganda NCDC Primary 7 Mathematics·lesson·fractions-02

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Recall / Warm-Up

What does $\frac{3}{4}$ mean as a division?

$4 \div 3$

$3 \times 4$

$4 - 3$

$3 \div 4$

Continue the division $5 \div 8$ past the ones place by adding a decimal point and zeros to the dividend. What is $5 \div 8$ ?

Which decimal names the hundredths place with its digit?

$3.4\underline{5}6$ — the underlined digit is in the hundredths place

$3.\underline{4}56$ — the underlined digit is in the hundredths place

$3.45\underline{6}$ — the underlined digit is in the hundredths place

$\underline{3}.456$ — the underlined digit is in the hundredths place

Write $\frac{2}{5}$ as a decimal.

Write $\frac{1}{8}$ as a decimal.

Which decimal correctly shows $1 \div 3$ continued to three decimal places?

$0.3$ , because after one division step the answer is settled

$0.333$ , because the remainder 1 keeps returning and the division never ends

$0.3$ exactly, with no further digits needed

$0.33$ , because two threes are enough to show the pattern

Write $\frac{2}{11}$ as a decimal using dot notation over the repeating block.

Write $0.6$ as a fraction in lowest terms.

Write $0.125$ as a fraction in lowest terms.

$\frac{125}{100}$ , kept unsimplified since 100 is a familiar denominator

$\frac{125}{10}$ , using one zero for the whole number of digits shown

$\frac{1}{8}$ , because three decimal places give thousandths, $\frac{125}{1000}$ , which simplifies to $\frac{1}{8}$

$\frac{12}{100}$ , dropping the final digit before writing the denominator

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