Grade 7 Math Practice Test: Converting Fractions to Terminating and Repeating Decimals

Divide 3 by 8: 3.000 ÷ 8 = 0.375, and the division ends because the remainder becomes 0. 0.38 just puts the digits 3 and 8 after the decimal point, and 2.667 is 8 ÷ 3.

5 ÷ 6 = 0.8 with remainder 2, and from then on every step leaves remainder 2 again, so the digit 3 repeats: 0.8333…. 1.2 is 6 ÷ 5, the division done the wrong way around.

20 = 2 · 2 · 5 has only 2s and 5s, and 7 ÷ 20 = 0.35 ends. 5/12 repeats (0.41666…) because 12 contains the factor 3, just like 3 and 9.

7 ÷ 4 = 1.75, and the negative sign stays, so the answer is −1.75. −0.57 comes from dividing 4 by 7, and 1.75 drops the sign.

4 ÷ 11 gives 0.36 with remainder 4, which is where it started, so the block 36 repeats: 0.363636…. 2.75 is 11 ÷ 4.

5 ÷ 8 = 0.625, and adding the whole number gives 1.625. 1.58 writes the digits of the fraction after the point, and 1.875 is 1 7/8.

As decimals: 5/8 = 0.625 and 2/3 = 0.666…. So the order is 0.6, 0.625, 0.66, 0.666…. 2/3 is slightly greater than 0.66, because its 6s go on forever.

When you divide by 7, every remainder is one of 0 to 6. The remainder is never 0 here, so after at most 6 steps a remainder repeats, and from that point the digits repeat too. Odd denominators like 5 or 25 give terminating decimals, so oddness is not the reason.

9 ÷ 16 = 0.5625, which terminates because 16 = 2 · 2 · 2 · 2. 1.778 is about 16 ÷ 9, the division the wrong way around.

−3/5 = −0.6. On a number line −0.6 lies to the right of −0.65, so it is the greater number. Thinking that 0.65 > 0.6 means −0.65 > −0.6 is the common trap with negatives.