Multiplying Whole Numbers by Power of 10s
These are the numbers found above base numbers that tell the mathematician how many times the base is to be used as a factor.
What are exponents?
These are strategies for breaking down multidigit multiplication problems into smaller parts. List one or more strategies.
What are partial products, place value sections, or the rows method.
0.6 x 101
0.6 x 102
0.6 x 103
Solve each expression then describe the pattern.
6
60
600
Each product is 10 times larger than the previous one.
9.4 x 3
4.7 x 8
12.1 x 5
Solve each expression and provide an estimate to prove your answer is reasonable.
28.2 -> Estimate could be 10 x 3 = 30
37.6 -> Estimate could be 5 x 8 = 40
60.5 -> Estimate could be 12 x 5 = 60
Mrs. Serafin is taking the class on a field trip to volunteer at the Hopelink Food Bank in Bellevue. Each student is asked to pack 220 cans per hour. If 23 students pack for one hour many cans will the class pack together? Show your work.
220 x 23 = 5,060 cans
4 x 10 x 10 x 10
Use an exponent to rewrite the repeated multiplication problem above then solve.
4 x 103 = 4,000
40 x 30
20 x 50
70 x 70
Solve these expressions and describe a pattern you see.
1,200
1,000
1,400
The number of zeros in the answer is related to the number of zeros in the factors combined with the product of the basic (nonzero) factors.
0.07 x 102
0.09 x 102
0.05 x 102Solve each expression and describe the relationship between the products and the factors.
7
9
5
We multiplied each decimal by 100 and found that the products were similar to the decimal factor. The product was the decimal factor with the place value moved two times to the right making our answer larger.
6 x 0.03 = 6 x 3 x ___
5 x 0.07 = 5 x 7 x ___
Fill in the blank so that each side of the equation is equal to the other.
.01
.01
Mrs. Serafin is preparing a cooking demonstration for the class to promote healthy eating and needs help making some measurements. Each group will receive 25.8 grams of powder for their soup. If there are four groups receiving powder, how much powder in total is needed for the whole class? Show your work and provide an estimate to prove your answer is reasonable.
25.8 grams x 4 groups = 103.2 grams
Estimate could be 25 x 4 = 100
49 x 102
Rewrite the expression as repeated multiplication then solve.
49 x 10 x 10 = 490
39 x 100
72 x 98
12 x 84
Solve the expressions and provide an estimate to prove your answer is reasonable.
3,900 (Estimate could be 40 x 100 = 4,000)
7,056 (Estimate could be 70 x 100 = 7,000)
1,008 (Estimate could be 10 x 80 = 800)
Estimates may vary.
0.043 x 103
0.012 x 103
Rewrite each expression as repeated multiplication then solve.
0.012 x 10 x 10 x 10 = 12
9.9 x 0.12
6.2 x 5.8
4.7 x 33
Solve for each and describe how to setup and solve each expression.
1.188
35.96
155.1
Do not line up the decimals, add decimals as the last step considering how many numbers appear to the right of the decimals in the factors.
We've decided as an end of year class reward to go see a movie at Lincoln Square in Bellevue. Each ticket will cost $7.48 and there will be 24 people attending. How much money will we need to raise in total to afford the trip to the movies? Show your work and provide an estimate to prove your answer is reasonable.
$7.48 x 24 = $179.52
Estimate could be 7 x 24 =168
37 x 103
65 x 103
91 x 103
Solve all three expressions, then describe a pattern you see among the products.
37,000
65,000
91,000
There were three total zeroes in the factors and products. (Answers may vary)
7,212 x 42
3,333 x 11
Solve these expressions and provide an estimate to prove your answer is reasonable.
302,904 (Estimate could be 7,000 x 40 = 280,000)
36,663 (Estimate could be 3,000 x 10 = 30,000)
Estimates may vary.
7.41 x ___ = 7,410
4.85 x ___ = 485
Fill in the blank with a power of ten and an exponent.
103
102
42.1 x 8.9
11.7 x 5.05
Solve each expression and provide an estimate to prove your answer is reasonable.
374.69 -> Estimate could be 40 x 9 = 360
59.085 -> Estimate could be 11 x 5 = 55
Wyatt is looking for his first summer job as a newspaper delivery boy. The Seattle Times says he will make $12.50 an hour and will work for 2 hours each morning of the week. If Wyatt works all 7 days of the week, how much will he make? Show your work.
$12.50 x 2 hours = $25
$25 x 7 days = $175
721 x 104
942 x 104
Solve these expressions then rewrite the problems using repeated multiplication.
721 x 10 x 10 x 10 x 10 = 7,210,000
942 x 10 x 10 x 10 x 10 = 9,420,000
94 x 47
81 x 55
Solve each expression using either partial products, place value sections, or rows methods.
4,418
4,455
Models may vary.
Write a word problem (that makes sense in a real world situation!) using the factors .05 and 102 then solve.
Example: Alexa and Rohan are selling lemonade for $0.05 per cup. They sell 100 cups in a day, how much money did they make? $5.00
7.9 x 1.2
Create a word problem that includes this expression, it must make sense in a real life situation then solve.
I am building a chicken coop in my backyard and I want to know the area that it will cover. One side is 7.9 feet while the other side is 1.2 feet. What is the area?
9.48 feet2 (Square Feet)
After watching the landing of the Mars rover InSight earlier this year some of us wondered how far away Mars was from Earth. If we know that the average distance from Earth to the Moon is about 380,000 km and that Mars is more than 150 times further away, about how far is Mars from Earth? Show your work.
380,000 x 150 = 57,000,000 km