Multiplying by 10, 100, and 1,000

Contributed by:

Diego Thu, Jan 27, 2022 07:35 AM UTC

We will be multiplying decimals by 10, 100, and 1,000. When we multiply by 10, 100, and 1000 we shift all the digits to the left. One place left for 10, two places left for 100, and three places left for 1000. When we divide by 10, 100, and 1000 we do the opposite and shift all the digits to the right instead.

1. Year 5: Week 2, Day 1
Decimals: Multiply and divide by 10, 100 and 1000
Each day covers one maths topic. It should take you about 1 hour or just a little more.
1. Start by reading through the Learning Reminders.
They come from our PowerPoint slides.
2. Tackle the questions on the Practice Sheet.
There might be a choice of either Mild (easier) or
Hot (harder)!
Check the answers.
3. Finding it tricky? That’s OK… have a go with a
grown-up at A Bit Stuck?
4. Have I mastered the topic? A few questions to
Check your understanding.
Fold the page to hide the answers!
© Hamilton Trust

2. Learning Reminders
© Hamilton Trust

3. Learning Reminders
When we multiply by 10, 100 and 1000, the digits all move together, one, two, or three place value columns to the left.
When we divide by 10, 100 and 1000, the digits all move together, one, two, or three place value columns to the right.
© Hamilton Trust

4. Practice Sheet Mild
Multiplying and dividing by 10 and 100
1. 34.6 × 10 2. 34.6 × 100 3. 6.74 × 10 4. 6.74 × 100
5. 483 ÷ 10 6. 483 ÷ 100 7. 56.1 ÷ 10 8. 56.1 × 100
9. 83.4 × = 834 10. 83.4 ÷ = 8.34
© Hamilton Trust
11. 47.2 ÷ = 4.72 12. 47.2 × = 4720
© Hamilton Trust

5. Practice Sheet Hot
Multiplying and dividing by 10, 100 and 1000
1. 456.8 × 10 2. 4568 ÷ 10 3. 2.76 × 10 4. 843 ÷ 100
5. 47.3 × 100 6. 783 ÷ 100 7. 45.62 × 100 8. 783.4 ÷ 10
9. 45.74 × 1000 10. 3620 ÷ 1000
© Hamilton Trust
11. 348.2 × = 3482 12. 34,820 ÷ = 34.82
Challenge
Complete the following calculations.
78.43 × = 7843 78.43 × = 78,430 6450 ÷ = 64.5 6450 ÷ = 6.45
© Hamilton Trust

6. Extra Practice for All
Complete any empty boxes on this diagram. Watch out - they might be answers or operations…
Create a similar diagram for a partner to solve.
© Hamilton Trust

7. Practice Sheets Answers
Multiplying and dividing by 10 and 100 (mild)
1. 34.6 × 10 = 346 2. 34.6 × 100 = 3460 3. 6.74 × 10 = 67.4
4. 6.74 × 100 = 674 5. 483 ÷ 10 = 48.3 6. 483 ÷ 100 = 4.83
7. 56.1 ÷ 10 = 5.61 8. 56.1 × 10 = 561 9. 83.4 × 10 = 834
10. 83.4 ÷ 10 = 8.34 11. 47.2 ÷ 10 = 4.72 12. 47.2 × 100 = 4720
Multiplying and dividing by 10, 100 and 1000 (hot)
1. 456.8 × 10 = 4568 2. 4568 ÷ 10 = 456.8 3. 2.76 × 10 = 27.6
4. 843 ÷ 100 = 8.43 5. 47.3 × 100 = 4730 6. 783 ÷ 100 = 7.83
7. 45.62 × 100 = 4562 8. 783.4 ÷ 10 = 78.34 9. 45.74 × 1000 = 45740
10. 3620 ÷ 1000 = 3.62 11. 348.2 × 10 = 3482 12. 34,820 ÷ 1000 = 34.82
Challenge
78.43 × 100 = 7843 78.43 × 1000 = 78,430
6450 ÷ 100 = 64.5 6450 ÷ 1000 = 6.45
© Hamilton Trust

8. Extra Practice for All Answers
Complete any empty boxes on this diagram. Watch out - they might be answers or operations…
27,300
÷ 100
÷ 10
273
x 100
0.0273
Create a similar diagram for a partner to solve.
© Hamilton Trust

9. A Bit Stuck?
Left, left, right, right?
Work in pairs, but record numbers on your own place value grid
Things you will need:
• A place value grid
• A pencil
What to do:
• Look at the first group of fraction strips.
What number are they showing?
Write the number in your place value grid.
• Multiply this number by 100. 100s 10s 1s 0.1s 0.01s
Write the answer in your place value grid. 1 6 1
1 6 1
• Repeat this for each fraction picture.
• Choose three of these numbers to divide by 100.
Write the number and the answer in your place value grid.
654 127 243 438 364
S-t-r-e-t-c-h:
Multiply 0.25, 0.09 and 1.03 by 100.
Divide 408, 27 and 360 by 100.
Learning outcomes:
• I understand the value of each digit in a number with two decimal places.
• I am beginning to multiply numbers with two decimal places by 100 and divide 3-digit numbers by 100.
© Hamilton Trust

12. Check your understanding
Questions
Divide 47,310 by 10 repeatedly until you get a number that is less than 100.
Write that number.
Fill the empty boxes:
0.15 = 1.5 10 5209 = x 100 ÷ 100 = 4.7 10.08 = ÷ 1000
Write the next two numbers in each sequence.
0.41 4.1 ____ ____
2.05 20.5 ____ ____
43,020 4302 ____ ____
True or false?
4030 ÷ 100 = 43 1.09 x 100 = 190 0.09 x 10 = 0.9 7000 ÷ 1000 = 0.7
Fold here to hide answers
Check your understanding
Answers
Divide 47,310 by 10 repeatedly until you get a number that is less than 100.
Write that number. 47.31
Each time the number is divided by 10, the digits move one place value column to the right:
47,310
4731
473.1
47.31
Fill the empty boxes:
0.15 = 1.5 ÷ 10 5209 = 52.09 x 100 470 ÷ 100 = 4.7 10.08 = 10,080 ÷ 1000
Write the next two numbers in each sequence.
0.41 4.1 41 410 (Multiplying by 10)
2.05 20.5 205 2050 (Multiplying by 10)
43,020 4302 430.2 43.02 (Dividing by 10)
True or false?
4030 ÷ 100 = 43 False – should be 40.3
1.09 x 100 = 190 False – should be 109
0.09 x 10 = 0.9 True
7000 ÷ 1000 = 0.7 False – should be 7
© Hamilton Trust

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