Question

1. arrange the following numbers in ascending order (smallest first):

a 0.303, 0.33, 0.3, 0.03
b 7.07, 0.707, 0.700, 0.007
c 1.2, 1.02, 1.22, 1.002
d 8.6, 86, 0.86, 0.086
e 8.08, 808, 80.88, 808.8

Explanation:

Step1: Compare tenths place

For 0.03, 0.3, 0.303, 0.33: 0.03 has 0 in tenths, others have 3. So 0.03 is smallest. Then compare hundredths: 0.3 (0 in hundredths), 0.303 (0), 0.33 (3). So 0.3, 0.303, 0.33.

Step2: Order

0.03, 0.3, 0.303, 0.33

Step1: Compare ones place

For 0.007, 0.700, 0.707, 7.07: 0.007 (0), 0.700 (0), 0.707 (0), 7.07 (7). Then compare tenths: 0.007 (0), 0.700 (7), 0.707 (7). Then hundredths: 0.700 (0), 0.707 (7).

Step2: Order

0.007, 0.700, 0.707, 7.07

Step1: Compare hundredths place

For 1.002, 1.02, 1.2, 1.22: 1.002 (0), 1.02 (2), 1.2 (0), 1.22 (2). Then compare tenths: 1.002 (0), 1.02 (0); 1.2 (2), 1.22 (2).

Step2: Order

1.002, 1.02, 1.2, 1.22

Step1: Compare ones place

For 0.086, 0.86, 8.6, 86: 0.086 (0), 0.86 (0), 8.6 (8), 86 (8). Then compare tenths: 0.086 (0), 0.86 (8).

Step2: Order

0.086, 0.86, 8.6, 86

Step1: Compare ones place

For 8.08, 80.88, 808, 808.8: 8.08 (8), 80.88 (80), 808 (800), 808.8 (800).

Step2: Order

8.08, 80.88, 808, 808.8

Answer:

a. \( 0.03, 0.3, 0.303, 0.33 \)
b. \( 0.007, 0.700, 0.707, 7.07 \)
c. \( 1.002, 1.02, 1.2, 1.22 \)
d. \( 0.086, 0.86, 8.6, 86 \)
e. \( 8.08, 80.88, 808, 808.8 \)