Q1.
In each group, identify the longest and the shortest lengths. Mark each length on the scale. (a) 3/10, 3/100, 33/100 (b) 3 1/10, 30/10, 1 3/10 (c) 45/100, 54/100, 5/10, 4/10 (d) 3 6/10, 3 6/100, 3 6/10 6/100 (e) 8/10 2/100, 9/100, 1 8/100 (f) 7 3/10 5/100, 7 5/10, 7 41/100 (g) 65/10 15/100, 5 87/100, 5 7/100
Answer
Write every length in hundredths (or as a decimal) and then compare like whole numbers.
| Group | Values in decimal form | Longest | Shortest |
|---|---|---|---|
| (a) | 0.30, 0.03, 0.33 | 33⁄100 | 3⁄100 |
| (b) | 3.1, 3.0, 1.3 | 3 1⁄10 | 1 3⁄10 |
| (c) | 0.45, 0.54, 0.50, 0.40 | 54⁄100 | 4⁄10 |
| (d) | 3.60, 3.06, 3.66 | 3 6⁄10 6⁄100 | 3 6⁄100 |
| (e) | 0.82, 0.09, 1.08 | 1 8⁄100 | 9⁄100 |
| (f) | 7.35, 7.50, 7.41 | 7 5⁄10 | 7 3⁄10 5⁄100 |
| (g) | 6.65, 5.87, 5.07 | 65⁄10 15⁄100 | 5 7⁄100 |
Marking them on the scale. Count small divisions from the labelled mark:
- (a) scale 0 to 1: 3⁄100 is the 3rd small mark, 3⁄10 the 30th, 33⁄100 the 33rd.
- (b) scale 0 to 10: mark 1.3, 3.0 and 3.1.
- (c) scale 0 to 1: mark 0.40, 0.45, 0.50 and 0.54.
- (d) scale 30⁄10 to 40⁄10: 3.06 sits just after 3.0, 3.60 on the 36⁄10 mark, 3.66 six small marks later.
- (f) scale 68⁄10 to 78⁄10: mark 7.35, 7.41 and 7.50.
Why it happens: once all the lengths are converted to the same small unit, the comparison is ordinary counting. In (d) the trap is 3 6⁄10 = 3.60 against 3 6⁄100 = 3.06 — the 6 is worth ten times more in the first one.
Check it yourself: two of the printed scales are too short for their own group — in (e) the scale runs only from 0 to 1, so 1 8⁄100 falls just beyond its right end, and in (g) the scale starts at 57⁄10, so 5 7⁄100 falls before its left end. Extend the scale a little in your notebook and then mark them.