NCERT Solutions for Class 5th Maths Chapter 10 2 3 4 5 6 7 8 9 0, and the numbers 11 and 1001 — Let Us Do — Find symmetry in the digits
Book page 1381 Updated on2026-09-19
Q1.
Find symmetry in the digits. 1 2 3 4 5 6 7 8 9 0 — Which digit(s) have reflection symmetry? ___________________________
Answer
0, 1, 3 and 8.
Test each digit the way you tested the letters: draw a line on it and fold. Use the shapes exactly as they are printed in your book — there the digit 1 is a plain straight bar, with no flag and no foot.
The digit 2 is shown for comparison — no fold works on it.
Digit
Line of symmetry?
Which line
0
Yes
upright and flat
1 (a bar)
Yes
upright and flat
2
No
—
3
Yes
flat (horizontal)
4
No
—
5
No
—
6
No
—
7
No
—
8
Yes
upright and flat
9
No
—
Why 3 has only a flat line: The top curve of 3 and the bottom curve of 3 are the same. Fold it across and they land on each other. But the left side of 3 is open while the right side is round, so an upright fold does not work.
Check it yourself: Hold a small mirror upright, touching the flat line of a 3. Look into it. You see a 3 again. Now hold the mirror upright along the middle of a 3 — you get a strange shape, not a 3.
Q2.
Which digit(s) have rotational symmetry? ___________________________
Answer
0, 1 and 8 — each of them looks the same after a 1/2 turn.
1, 8 and 0 are unchanged when the paper is turned upside down.
1 upside down → 1 ✓ 8 upside down → 8 ✓ 0 upside down → 0 ✓ 6 upside down → 9 ✗ (it changes into a different digit) 9 upside down → 6 ✗
Why 6 and 9 do not count: Rotational symmetry means the shape must look like itself again. A 6 turned half way round becomes a 9. That is a different digit, so 6 has no rotational symmetry on its own.
Try This: Write 1, 8 and 0 boldly on a card. Turn the card upside down and hold it up. Your friends will not be able to tell that you turned it.
Q3.
Which digit(s) have both rotational and reflection symmetries? ________
Why 3 is left out: 3 folds neatly along a flat line, so it has reflection symmetry. But turn a 3 upside down and you get a shape like a backwards E — not a 3. So it has no rotational symmetry.
Did you know? There is no digit here with rotational symmetry but no line of symmetry. Among the letters, though, N is exactly like that.
Q4.
Now, let us look at the following numbers: 11 , 1001. Do these have (a) rotational symmetry, (b) reflection symmetry or (c) both symmetries?
Answer
(c) Both symmetries. Both 11 and 1001 have reflection symmetry and rotational symmetry.
Remember, in the book each 1 is a plain bar and each 0 is a smooth oval.
Both numbers read the same in a mirror and the same upside down.
Test 1 — the folding test (reflection):
Fold 11 down the middle, between the two bars. The left bar lands on the right bar. ✓
Fold 11 across the middle. Each bar folds onto itself. ✓
Fold 1001 down the middle, between the two zeros. The left 1 lands on the right 1, the left 0 on the right 0. ✓
Fold 1001 across the middle. Every digit folds onto itself. ✓
Test 2 — the turning test (rotational):
Turn 11 by a half turn → the bars stay bars → reads 11 ✓ Turn 1001 by a half turn → 1 stays 1, 0 stays 0, and the order flips → reads 1001 ✓
Why the flipping does not spoil it: A half turn reverses the order of the digits. In 1001 the order reversed is 1‑0‑0‑1 — the very same number. Numbers that read the same forwards and backwards are called palindromes, and that is why 1001 survives the turn.
Q5.
Give examples of 2-, 3-, and 4-digit numbers which have rotational symmetry, reflection symmetry, or both.
Answer
Here are examples of each kind. First remember which digits can be used.
For a flat (horizontal) line of symmetry, use only 0, 1, 3, 8. Each of these folds across on its own, and the order of digits stays as it is.
For an upright (vertical) line of symmetry, use only 0, 1, 8, and the number must read the same backwards.
For a 1/2 turn, use 0, 1, 8 (which stay the same) and the pair 6, 9 (which swap), and the number must still read the same after the order is reversed.
69 turned a half turn: 6 → 9 and 9 → 6, and the order flips So 69 → 69 ✓ rotational symmetry
318 folded along a flat line: 3 → 3, 1 → 1, 8 → 8, order unchanged So 318 → 318 ✓ reflection symmetry (flat line)
Why the order flips for turning but not for folding across: A half turn moves the number end over end, so the last digit arrives first. Folding along a flat line only flips each digit up and down; the digits stay in their places.
Try This: Write 1691 on a slip of paper and turn it upside down. It still says 1691. Now try 1961 — it becomes 1961 too? Check carefully and you will see it does not. Only some arrangements work.