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NCERT Solutions for Class 5th Maths Chapter 6 Filling the place value tables — Patterns in Multiplication by 10s and 100s

Book page 72–74 Updated on2026-09-19

Q1.
Let us revise multiplication by 10s and 100s. a) 4 × 10 = ___ b) 20 × 10 = ___ c) 10 × 40 = ___ d) 10 × 10 = 100 e) 20 × 50 = ___ f) 80 × 10 = ___ g) 3 × 100 = 100 × 3 = 300 h) 8 × 100 = ___ = ___ i) 10 × 100 = ___ = ___
Answer

Here are all the answers.

QuestionAnswerThink of it as
a) 4 × 10404 tens
b) 20 × 1020020 tens
c) 10 × 4040040 tens
d) 10 × 1010010 tens (given)
e) 20 × 501,0002 × 5 × 10 × 10 = 10 × 100
f) 80 × 1080080 tens
g) 3 × 100100 × 3 = 3003 hundreds (given)
h) 8 × 100100 × 8 = 8008 hundreds
i) 10 × 100100 × 10 = 1,00010 hundreds
To multiply by 10
Step 1. Take the number.
Step 2. Shift every digit one place to the left.
Step 3. Write 0 in the empty ones place.
Example: 4 → 40, 20 → 200, 80 → 800
Why the zero appears: Multiplying by 10 makes a number ten times bigger. A digit that was worth ones is now worth tens, and a digit that was worth tens is now worth hundreds. Every digit moves one house to the left, and the ones house is left empty — so we write 0 there to hold the place.
For 100, shift twice. 8 × 100: the 8 moves from the ones place to the hundreds place, and two zeros fill the gap — 800. For 1,000, shift three times.
Q2.
Find answers to the following questions. 100 × 90 = __,000; 400 × 10 = ___; 60 × 50 = ____; 30 × 20 = 600; 700 × 4 = _,_00; 10 × 45 = ____
Answer

All six answers, with the easy way to get each one.

QuestionBreak it upAnswer
100 × 901 × 9 × 100 × 10 = 9 × 1,0009,000
400 × 104 × 100 × 10 = 4 × 1,0004,000
60 × 506 × 5 × 10 × 10 = 30 × 1003,000
30 × 203 × 2 × 10 × 10 = 6 × 100600 (given)
700 × 47 × 4 × 100 = 28 × 1002,800
10 × 4545 tens450
60 × 50
Step 1. Set the zeros aside: 6 × 5 = 30
Step 2. Count the zeros you set aside: one from 60, one from 50, so two zeros.
Step 3. Put both zeros back: 3,000
Why this works: 60 is 6 × 10 and 50 is 5 × 10. Because we may multiply in any order, 6 × 10 × 5 × 10 can be rearranged as 6 × 5 × 10 × 10, which is 30 × 100 = 3,000.
Look out: the table on the same page asks for 700 × 8, while the bubble asks for 700 × 4. Both are worth doing: 700 × 4 = 2,800 and 700 × 8 = 5,600.
Q3.
How should we write 450 in the table below?
ProblemThHTO
10 × 45 =    
30 × 20 = 600
400 × 10 =    
700 × 8 =    
100 × 90 =9000
The place value table printed on page 73. Two rows are already filled in.
Answer

Write 4 in the hundreds column, 5 in the tens column and 0 in the ones column. The thousands column stays empty.

NumberThHTO
450450
  1. Read the number from the right. The last digit sits in the ones column. Here it is 0.
  2. Move left one column. That is tens. The digit there is 5, so 450 has 5 tens = 50.
  3. Move left again. That is hundreds. The digit there is 4, so 450 has 4 hundreds = 400.
  4. Check by adding. 400 + 50 + 0 = 450 ✓
Why the ones column needs a 0: If we left it blank we would only see 45, which is a completely different number. The 0 is a placeholder — it keeps the 4 and the 5 sitting in their correct houses.
Q4.
Fill in the table. Describe the pattern.
ProblemThHTO
10 × 45 =    
30 × 20 = 600
400 × 10 =    
700 × 8 =    
100 × 90 =9000
The place value table printed on page 73. Two rows are already filled in.
Answer

The completed table.

ProblemThHTOAnswer
10 × 45450450
30 × 20600600 (given)
400 × 1040004,000
700 × 856005,600
100 × 9090009,000 (given)
700 × 8
Step 1. 7 × 8 = 56
Step 2. 700 has two zeros, so put two zeros back.
Step 3. Answer = 5,600

The pattern: count the zeros in the two numbers you are multiplying, do the small multiplication first, then write that many zeros after it.

Why it happens: Each zero at the end of a number means it has been multiplied by 10 once more. Multiplying by 10 shifts every digit one place left and leaves a 0 behind. So the zeros simply queue up at the end of the answer.
Q5.
Fill in the tables. Describe the pattern. Discuss in class.
ProblemThHTO
60 × 50 =    
220 × 20 =    
11 × 300 =    
ProblemThHTO
80 × 90 =    
10 × 63 =    
40 × 12 =    
The two place value tables printed on page 73.
Answer

Both tables, completed.

ProblemThHTOAnswer
60 × 5030003,000
220 × 2044004,400
11 × 30033003,300
80 × 9072007,200
10 × 63630630
40 × 12480480
220 × 20
Step 1. Set the zeros aside: 22 × 2 = 44
Step 2. Zeros set aside: one from 220, one from 20 → two zeros
Step 3. Answer = 4,400

40 × 12
Step 1. 4 × 12 = 48
Step 2. One zero from 40
Step 3. Answer = 480
Why it happens: Every zero on the end is a hidden 10. 220 × 20 is really 22 × 10 × 2 × 10, and we may multiply in any order. So it is 22 × 2 first, giving 44, and then × 10 × 10, which pushes 44 two places to the left.
Sample answer for the class discussion: We saw that the answers all end in zeros, and the number of zeros equals the number of zeros in the question. 60 × 50 has two zeros in the question and two at the end of 3,000. But watch out — 60 × 50 = 3,000 has three zeros, because 6 × 5 = 30 already brings a zero of its own.
Q6.
What will happen if we multiply numbers by 1,000? 2 × 1,000 = ; 5 × 1,000 = ; 10 × 1,000 = ; 20 × 1,000 =
Answer

Every digit shifts three places to the left, and three zeros appear at the end.

2 × 1,000 = 2 thousand = 2,000
5 × 1,000 = 5 thousand = 5,000
10 × 1,000 = 10 thousand = 10,000
20 × 1,000 = 20 thousand = 20,000
TThThHTO 5 5000 5 jumps three houses to the left. Three zeros fill theempty houses.
Multiplying by 1,000 moves each digit three place values to the left.
Why three places: 1,000 is 10 × 10 × 10. Each 10 moves the digits one house left, so three tens move them three houses left.
Q7.
Let us fill in the table and observe the patterns.
ProblemTThThHTO
2 × 1,000 = 2000
5 × 1,000 = 5000
10 × 1,000 =10000
20 × 1,000 =20000
3 × 5,000 =     
8 × 3,000 =     
5 × 7,000 =     
The first table printed on page 74. The first four rows are already filled in.
Answer

The completed table.

ProblemTThThHTOAnswer
2 × 1,00020002,000 (given)
5 × 1,00050005,000 (given)
10 × 1,0001000010,000 (given)
20 × 1,0002000020,000 (given)
3 × 5,0001500015,000
8 × 3,0002400024,000
5 × 7,0003500035,000
8 × 3,000
Step 1. 8 × 3 = 24
Step 2. 3,000 has three zeros.
Step 3. Write 24 and add three zeros: 24,000
Read it aloud: 8 × 3 thousand = 24 thousand. Saying the word "thousand" out loud stops you from losing a zero.
Q8.
Fill in the table.
ProblemTThThHTO
20 × 100 =     
40 × 500 =     
60 × 300 =     
600 × 30 =     
80 × 900 =     
70 × 600 =     
5 × 7,000 =     
The second table printed on page 74.
Answer

The completed table.

ProblemSmall multiplicationZeros to addAnswer
20 × 1002 × 1 = 232,000
40 × 5004 × 5 = 20320,000
60 × 3006 × 3 = 18318,000
600 × 306 × 3 = 18318,000
80 × 9008 × 9 = 72372,000
70 × 6007 × 6 = 42342,000
5 × 7,0005 × 7 = 35335,000
Notice something lovely: 60 × 300 and 600 × 30 both give 18,000. The zeros just moved from one number to the other, and the total number of zeros stayed at three. That is the order rule at work again.
Check it yourself: Count the zeros in the question and the zeros in your answer. In 40 × 500 the question has three zeros, and 4 × 5 = 20 brings one more, so the answer 20,000 has four zeros in all.
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