Lemonade Stand Batches: Powers of 10 Patterns
0 / 13Lemonade Stand Batches: Powers of 10 Patterns
Make big batches and pour small cups by multiplying and dividing by powers of 10.
Powers of 10 at the stand
An exponent tells how many times 10 is used as a factor. For example, 10² = 10 × 10.
1.
The stand counts its paper cups with powers of 10. Write each power of 10 as a whole number.
10² =
10⁵ =
2.
Kai writes 10 × 10 × 10 × 10 to show the number of cups in a giant stack. Which is equal to 10 × 10 × 10 × 10?
Big batches and small cups
Multiply or divide. Think about how far each digit shifts in the place value chart.
3.
One pitcher holds 1.75 liters of lemonade. Kai fills 10 pitchers.
1.75 × 10 = liters
4.
One lemon costs $0.48. Imani buys 100 lemons.
0.48 × 100 = $
5.
One scoop of sugar has a mass of 0.012 kilogram. The stand uses 10³ scoops this summer.
0.012 × 10³ = kilograms
6.
The stand makes 36 liters of lemonade. Kai pours it equally into 100 cups.
36 ÷ 100 = liter in each cup
7.
A bag of 10² ice cubes has a mass of 2.5 kilograms. Each ice cube has the same mass.
2.5 ÷ 10² = kilogram for each ice cube
8.
Each jug of lemonade uses 0.6 cup of lemon juice. For the school fair, the stand uses 60 cups of lemon juice. Write the number of jugs they make.
0.6 × = 60
9.
Lemonade spilled on the recipe card. Write the missing exponent in the small box.
4.07 × 10 = 4,070
Spot the pattern
Look for patterns in the zeros and in where the decimal point goes.
10.
Complete the pattern.
520 ÷ 10 =
520 ÷ 100 =
520 ÷ 1,000 =
520 ÷ 10⁴ =
11.
Dana says 3.5 × 10 = 3.50 because you put a zero at the end when you multiply by 10. What is the correct product, and why?
12.
Think about each answer. Which way does the decimal point move, and how many places? Sort each problem.
13.
Imani says 0.4 × 10³ must have 3 zeros in the answer because 10³ has 3 zeros. Find 0.4 × 10³. Is Imani right? Explain.