Multiplying by Powers of 10
What is the trick to multiplying by a whole number or decimal power of 10?
When you multiply by a whole number power of 10 the decimal point moves to the right (based on the number of zeros, or the exponent). WHen you multiply by a decimal power of ten the decimal point moves to the left based on how many digits are after your decimal point.
0.29 × 31=
8.99
How do you know how many decimal places your product should contain?
Count the total number of decimal places in the factors being multiplied.
True or false? The product of 7.3 and 0.6 is 43.8.
False
True or False 0.09 × 1,000 = 9. Show your work
False
True or false?
6.2 x 10 = 62
True!
29 × 3.1=
89.9
Which problems will have two decimal places in the product?
A) 5 × 0.89
B) 7.4 × 10
C) 5.31 × 100
D) 6.1 × 3
E) 3.2 × 4.3
A, C, E
True or false? The product of 1.5 and 2.8 is 4.2.
True
True or false?
a. The product of 1.5 and 2.8 is 4.2.
b. The product of 7.3 and 0.6 is 43.8.
c. The product of 0.09 and 0.7 is 6.3.
d. The product of 0.79 and 1.5 is 1.185.
a) True
b) False
c) False
d) True
Which direction does your decimal point move when you multiply by a whole number power of 10, and why?
The decimal point moves to the right because you are finding, 10, 100, or 1,000 etc... groups of the other factor, so your product will be greater than the factor you started with. Moving the decimal to the right increases the value of the factor.
How would you multiply using a quick picture 3 x 0.08? Show ALL steps.
We group the 20 hundredths to 2 tenths. We are left with 20 tenths and seven hundredths
Final Answer: 0.27 (in picture form)
Joaquin lives 0.3 mile from Keith. Layla lives 0.4 times as far from Keith as Joaquin. How many decimal places should the product contain?
2 decimal places
Trevor is reading a book for a book report. Last week, he read 35 pages of the book. This week, he read 2.5 times as many pages as he read last week. How many pages of the book has Trevor read this week? Show your work.
87.5 pages
The cost of admission to the Baytown Zoo is $10.50 for each senior citizen, $15.75 for each adult, and $8.25 for each child. A family of 2 adults and 1 child plan to spend the day at the Baytown Zoo.
Part A: How much does admission for the family cost?
Part B: Describe another way you could solve the problem.
Part C:What if 2 more tickets for admission are purchased? If the two additional tickets cost $16.50, determine what type of tickets the family purchases. Explain how you can determine the answer without calculating.
A: $39.75
B:I could add the cost of the three tickets. $15.75 + $15.75 + $8.25 = $39.75
C:
Two additional children’s tickets are purchased. Possible explanation: Since senior citizen tickets cost about $10 each, then 2 tickets would cost about $20, which is too much. Adult tickets cost about $16 each, so 2 adult tickets would cost about $32, which is too much. Children’s tickets cost about $8, and 2 tickets would be about $16 which is correct.
Nicole is making 1,000 bows for people who donate to the library book sale. She needs a piece of ribbon that is 0.75 meter long for each bow. How many meters of ribbon does Nicole need to make the bows?
750 meters of ribbon
Tenley is making a square frame for her painting. She is using 4 pieces of wood that are each 2.75 feet long. How much wood will Tenley use to make the frame?
11 feet
Explain how an estimate can help you to place the decimal point when multiplying 3.9 × 5.3.
Estimating 4 x 5= 20 lets me know that my answer should be close to 20, so after I remove my decimla points and calculate my whole number multiplication and see that the product is 2067, I know that my decimal point belongs between 0 and 6 so the product is 20.67. If the decimal point were anywhere else, the actual answer wouldn't be close to 20.
Jonah drives his car to and from work. The total length of the trip to and from work is 19.2 miles. In August, Jonah worked 21 days. How many miles in all did Jonah drive to and from work that month?
403.2 miles in August
At a tailor shop, it costs $6.79 to shorten a pair of pants and 4 times as much to mend a dress. Choose the answer that correctly completes the statement. It would cost Lisa _____ shorten one pair of pants and mend one dress.
$33.95
Omar is making a scale model of the Statue of Liberty for a report on New York City. The Statue of Liberty is 305 feet tall measuring from the ground to the tip of the torch. If the model is 1/100 the actual size of the Statue of Liberty, how tall is the model?
3.05 feet tall
Sophia exchanged 1,000 U.S. dollars for the South African currency, which is called the rand. The exchange rate was 7.15 rand to $1.
Part A :How many South African rand did Sophia get?
Part B: Sophia spent 6,274 rand on her trip. She exchanged the rand she had left for U.S. dollars. The exchange rate was 1 rand to $0.14. How many U.S. dollars did Sophia get? Support your answer using specific information from the problem.
A: 7,150 Rand
B: $122.64; Possible explanation: I subtracted 7,150 −6,274 = 876 rand to find the number of rand left. If the exchange rate was 1 rand to $0.14, for every 1 rand Sophia exchanged, she received $0.14. So, 876 × $0.14 = $122.64
Brianna is getting materials for a chemistry experiment. Her teacher gives her a container that has 0.15 liter of a liquid in it. Brianna needs to use 0.4 of this liquid for the experiment. Kyle thinks Brianna will use 0.060 liters for the experiment. Kayla thinks she will use 0.06 liters. Who is right?
They are both right. If you look at the factors you can assume the product will have 3 decimal places. Kyle's answer shows this. However, the 0 in the thousandths place does not hold any value, so you can write the answer as 0.06 liters, so both Kyle and Kayla are correct.
Melinda, Zachary, and Heather went to the mall to shop for school supplies. Melinda spent $14.25 on her supplies. Zachary spent $2.30 more than Melinda spent. Heather spent 2 times as much money as Zachary spent. How much did Heather spend on school supplies?
$33.10
Mr. Evans is paid $9.20 per hour for the first 40 hours he works in a week. He is paid 1.5 times that rate for each hour after that. Last week, Mr. Evans worked 42.25 hours. He says he earned $388.70 last week. Do you agree?
I do not agree because the earnings for 40 hours are $9.20 × 40 = $368.
$9.20 × 1.5 = $13.80, which is the rate for each hour over 40. $13.80 × 2.25 = $31.05. I added $31.05 + $368 = $399.05. $399.05 > $388.70.