Identify the only prime number below. How do you know that the other numbers are composite numbers?

128

405

999

1579

Determine the prime factorization of each number.

235

Determine the prime factorization of each number.

1218

Determine the prime factorization of each number.

468

Determine the prime factorization of each number.

44 100

A square measures 72 cm by 72 cm.

a) Which of these rectangles can be used repeatedly to cover the square without any spaces or overlapping?

b) Determine two other rectangles with whole-number dimensions that can be used to cover the square.

c) How can you tell from the dimensions of a rectangle whether or not it will cover the square?

Kim keeps 0.9 of a 1.00 m rope. Shaun keeps 0.9 of Kim’s piece. Kent keeps 0.9 of Shaun’s piece. Charlene keeps 0.9 of Kent’s piece.

a) How long is Charlene’s piece of rope?

b) Explain how you can use powers of 0.9 to solve the problem.

c) How many more people need to be involved for the last person to have a piece of rope that is just under 0.5 m? Explain your reasoning.

The average human body contains about 40 L of water. What is the total amount of water contained in the 6.4 billion people in the world? Show each step in your solution. Express your answer in scientific notation.

Write each number in expanded form and in scientific notation.

a) 160 000

Write each number in expanded form and in scientific notation.

2 240 000

Write each number in expanded form and in scientific notation.

145 000 000

Write each number in expanded form and in scientific notation.

23 000 000 000

Explain how to estimate \sqrt{1659}.

Calculate.

\sqrt{35}

Calculate.

\sqrt{500}

Calculate.

\sqrt{169}

Calculate.

\sqrt{70}

The square root of a whole number is about 5.2. What is the number? Explain your reasoning.

Evaluate each expression. Use the rules for order of operations.

\displaystyle 5.5 + 3.5 \times 4.5

Evaluate each expression. Use the rules for order of operations.

\displaystyle (1 + 2.46) \div 2 + 3.5^2

Evaluate each expression. Use the rules for order of operations.

\displaystyle [(2.5+6.5 \times 2.3^2)-1.5]^2

Evaluate each expression. Use the rules for order of operations.

\displaystyle \sqrt{39} -3 \times 4.5 + 3.5^2

Derek wants to buy a cell phone. He wants to know which monthly plan is best if he uses the phone 8 h each month.

• Plan 150: Cost = \$20 + (time in minutes - 150) \times \$0.30

• Plan 400: Cost = \$40 + (time in minutes - 400) \times \$0.25

Calculate the cost of each plan for 8 h per month. Which plan is better for Derek?