Without using a calculator: Find the decimal representation of each of the following fractions: 1/5¼1/3 2/53/102/7 1/94/253/100 5/95/77/8
Decimals as rational numbers Some decimal numbers are rational numbers: but some are not. A decimal is a rational number if it can be written as a fraction with integer numerator and denominator. Those are decimals that either terminate (end) or have a repeating block of digits. Repeating decimals: 7.6666…; 0.727272… Terminating decimals: 4.8; 9.00001; 0.75
Irrational numbers A number that is not rational is called irrational. A decimal like 3.5655655565555655556… is not rational because although there is a pattern, it does not repeat. It is an irrational number. Compare this to 3.556556556556556556… It is rational because 556 repeats. It is a rational number.
Comparing Decimals When are decimals equal? 3.56 = 3.56000000 But, 3.056 ≠ 3.560. To see why, examine the place values. 3.056 = 3 + 0.1 + 5.01 + 6.001 3.560 = 3 + 5.1 + 6.01 + 0.001 Think of units, rods, flats, and cubes.
Ways to compare decimals Write them as fractions and compare the fractions as we did in the last section. Use base-10 blocks. Use a number line. Line up the place values.