Turn a repeating decimal into a fraction
Grade 8 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.
Bo copies a repeating decimal into a notebook. The figure subtracts the lines to cancel the repeat. In simplest form, what fraction is x?
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Strip of the digits: 0.[2] [2] [2] ... Lines: x = 0.222... and 10x = 2.222.... Subtract: 10x - x = 2.
Esme sees a repeating decimal on a robot's screen. The figure subtracts the lines to cancel the repeat. In simplest form, what fraction is x?
Number line with a tick at every tenth and a mark at 0.222…. Strip of the digits: 0.[2] [2] [2] … Lines: x = 0.222… and 10x = 2.222…. Subtract: 10x − x = 2. Number line with a tick at every tenth and a mark at 0.222…. Strip of the digits: 0.[2] [2] [2] … Lines: x = 0.222… and 10x = 2.222…. Subtract: 10x − x = 2. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.222... Jun finds a repeating decimal in a math book. The figure subtracts the lines to cancel the repeat. In simplest form, what fraction is x?
Number line with a tick at every tenth and a mark at 0.4545…. Strip of the digits: 0.[45] [45] … Lines: x = 0.4545… and 100x = 45.4545…. Subtract: 100x − x = 45. Number line with a tick at every tenth and a mark at 0.4545…. Strip of the digits: 0.[45] [45] … Lines: x = 0.4545… and 100x = 45.4545…. Subtract: 100x − x = 45. 0.[45] [45] ... 0.4545.... x = 0.4545.... 100x = 45.4545.... Subtract: 100x - x = 45. Luz checks a repeating decimal on a quiz card. The figure subtracts the lines to cancel the repeat. In simplest form, what fraction is x?
Number line with a tick at every tenth and a mark at 0.8181…. Strip of the digits: 0.[81] [81] … Lines: x = 0.8181… and 100x = 81.8181…. Subtract: 100x − x = 81. Number line with a tick at every tenth and a mark at 0.8181…. Strip of the digits: 0.[81] [81] … Lines: x = 0.8181… and 100x = 81.8181…. Subtract: 100x − x = 81. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Strip of the digits: 0.[81] [81] ... x = 0.8181... and 100x = 81.8181.... Subtract: 100x - x = 81. Milo puts a repeating decimal on a poster. The figure subtracts the lines to cancel the repeat. In simplest form, what fraction is x?
Number line with a tick at every tenth and a mark at 0.1212…. Strip of the digits: 0.[12] [12] … Lines: x = 0.1212… and 100x = 12.1212…. Subtract: 100x − x = 12. Number line with a tick at every tenth and a mark at 0.1212…. Strip of the digits: 0.[12] [12] … Lines: x = 0.1212… and 100x = 12.1212…. Subtract: 100x − x = 12. 0 0.1 0.2 0.1212... 0.[12] [12] ... x = 0.1212... 100x = 12.1212... Subtract: 100x - x = 12. Noah reads a repeating decimal on a phone. The block has 1 digit, so the figure slides the point 1 digit. In simplest form, what fraction is x?
Number line with a tick at every tenth and a mark at 0.888…. Strip of the digits: 0.[8] [8] [8] … Lines: x = 0.888… and 10x = 8.888…. Number line with a tick at every tenth and a mark at 0.888…. Strip of the digits: 0.[8] [8] [8] … Lines: x = 0.888… and 10x = 8.888…. Number line 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.888.... 0. 8 8 8 ... x = 0.888... 10x = 8.888.... Strip of the digits: 0.[36] [36] ... Lines: x = 0.3636... and 100x = 36.3636.... Pia notes a repeating decimal for a puzzle. The block has 2 digits, so the figure slides the point 2 digits. In simplest form, what fraction is x?
Number line with a tick at every tenth and a mark at 0.3636…. Strip of the digits: 0.[36] [36] … Lines: x = 0.3636… and 100x = 36.3636…. Number line with a tick at every tenth and a mark at 0.3636…. Strip of the digits: 0.[36] [36] … Lines: x = 0.3636… and 100x = 36.3636…. 0 0.1 0.2 0.3 0.4 0.5 Tala tests a repeating decimal in a math game. The block has 2 digits, so the figure slides the point 2 digits. In simplest form, what fraction is x?
Number line with a tick at every tenth and a mark at 0.5454…. Strip of the digits: 0.[54] [54] … Lines: x = 0.5454… and 100x = 54.5454…. Number line with a tick at every tenth and a mark at 0.5454…. Strip of the digits: 0.[54] [54] … Lines: x = 0.5454… and 100x = 54.5454…. x = 0.5454... 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Strip of the digits: 0.[54] [54] ... 0. 54 54 ... 100x = 54.5454.... Zee reads a repeating decimal on a quiz. The block has 2 digits, so the figure slides the point 2 digits. In simplest form, what fraction is x?
Number line with a tick at every tenth and a mark at 0.6363…. Strip of the digits: 0.[63] [63] … Lines: x = 0.6363… and 100x = 63.6363…. Number line with a tick at every tenth and a mark at 0.6363…. Strip of the digits: 0.[63] [63] … Lines: x = 0.6363… and 100x = 63.6363…. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Strip of the digits: 0.[63] [63] ... Lines: x = 0.6363... and 100x = 63.6363.... Strip of the digits: 0.[21] [21] ... Lines: x = 0.2121... and 100x = 21.2121.... Bo finds a repeating decimal on a worksheet. The block has 2 digits, so the figure slides the point 2 digits. In simplest form, what fraction is x?
Number line with a tick at every tenth and a mark at 0.2121…. Strip of the digits: 0.[21] [21] … Lines: x = 0.2121… and 100x = 21.2121…. Number line with a tick at every tenth and a mark at 0.2121…. Strip of the digits: 0.[21] [21] … Lines: x = 0.2121… and 100x = 21.2121…. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1