Multiplying with powers of ten, area models and partial products
Week 6 · Multiplying with powers of ten, area models and partial products · 3 lessons
1
Shifting digits: multiplying by powers of ten
Discover Mathematics P5: Term 1, Unit 3, Lessons 1–4
GoalMultiply a number by 10, 100, 1,000 and 10,000 by shifting its digits, and use the pattern with multiples of ten.
New words
power of ten · a number made by multiplying 10 by itself: 10, 100 (10 × 10), 1,000 (10 × 10 × 10)product · the answer to a multiplicationshift · to move every digit to another place
Explanation
The numbers 10, 100, 1,000 and 10,000 are powers of ten. When you multiply by a power of ten, every digit shifts to the left, one place for each zero of the power, and zeros fill the empty places on the right. So 45 × 10 = 450, 45 × 100 = 4,500 and 45 × 1,000 = 45,000. The digits 4 and 5 stay together; only their places change. This helps with multiples of ten too. To work out 40 × 300, multiply the non-zero digits, 4 × 3 = 12, then write all the zeros that were in the two factors: one zero and two zeros make three zeros, so 40 × 300 = 12,000. Be careful when the digit product ends in a zero: 50 × 60 = 3,000, because 5 × 6 = 30 and then two more zeros are added.
Number
Ten thousands
Thousands
Hundreds
Tens
Ones
45
4
5
45 × 10 = 450
4
5
0
45 × 100 = 4,500
4
5
0
0
45 × 1,000 = 45,000
4
5
0
0
0
Worked examples
A school buys 100 boxes with 24 pencils in each box. 24 × 100 = 2,400. The digits 2 and 4 move two places left, because 100 has two zeros. The school buys 2,400 pencils.
★Remember
Multiply the digits that are not zeros, then put back ALL the zeros.
Work out 40 × 300. Multiply the non-zero digits: 4 × 3 = 12. Count the zeros in both factors: 1 + 2 = 3. Write 12 followed by 3 zeros: 12,000. So 40 × 300 = 12,000.
A factory packs 10,000 pencils in each container and fills 35 containers. 35 × 10,000 = 350,000 pencils. Also 6,500 × 10,000 = 65,000,000: the digits move four places left; the two zeros that were already there and four new zeros make six zeros, so we write 65 followed by six zeros.
Class activity
Zero machine. Write a number such as 38 on a card. Roll a die to choose 10, 100 or 1,000 (1–2 means 10, 3–4 means 100, 5–6 means 1,000). The child says and writes the product. Then try numbers with zeros, like 70 × 400, and say how many zeros the answer has.
Practice
1
Work out 36 × 100.
3,600.
2
Work out 7,800 × 10.
78,000.
3
Work out 50 × 400.
5 × 4 = 20, then three zeros: 20,000.
4
Work out 600 × 5,000. How many zeros does the product have?
6 × 5 = 30, then 2 + 3 = 5 zeros: 3,000,000. The product has 6 zeros.
5
A bakery uses 250 g of flour for one batch. How many grams are used in 100 batches? How many kilograms is that?
