Find the value of each expression.

1. \(\frac{1}{3} \times \frac{1}{10}\)
2. \(\frac{1}{10} \times \frac{1}{10}\)
3. \(\frac{1}{10} \times \frac{1}{100}\)

1. Write a multiplication equation to represent the shaded region of the diagram.

   

2. What is the value of \(\frac{7}{10} \times \frac{5}{10}\)? Use the diagram if it is helpful.

   

1. What is the value of the digit 6 in 618,923?
2. How many times greater is the value of the digit 6 in 618,923 than the value of the digit 6 in 27,652?

Find the value of \(3,\!724 \div 7\). Explain or show your reasoning.

Find the value of each sum or difference.

1. What fraction of the whole square is shaded? Explain or show your reasoning.

   

2. What fraction of the whole square is shaded? Explain or show your reasoning.

   

1. Write a decimal number to represent how much of the square is shaded.

   

2. Shade the square to represent the decimal one hundred fifteen thousandths.

   

Write the decimal 0.418 as a fraction, in words, and in expanded form.

1. The gold nugget on the scale weighs 0.265 ounce. Name 2 different sets of 0.1-ounce, 0.01-ounce, and 0.001-ounce weights you can use to balance the nugget.

   

2. One gold nugget weighs 0.008 ounce. A second gold nugget weighs 0.8 ounce.

   • How many times as much as the first nugget does the second nugget weigh?
   • How many times as much as the second nugget does the first nugget weigh?

Noah threw the ball 4.89 yards.

1. Noah threw the ball farther than Lin. How far could Lin have thrown it?
2. Andre threw the ball farther than Noah but less than 4.9 yards. How far could Andre have thrown it? Explain or show your reasoning.

1. Label the tick marks. Use the number line to explain your reasoning.

   

2. Which is greater, 0.654 or 0.658? Explain or show your reasoning.

A \$5 gold coin weighs 8.359 grams.

1. Locate 8.359 on the number line.

   

2. A scale measures to the nearest 0.01 gram. What will the scale show for the weight of the coin? Explain or show your reasoning.

1. What is 0.374 rounded to the nearest hundredth? Explain or show your reasoning. Use the number line if it's helpful.

   

2. What is 9.893 rounded to the nearest tenth? To the nearest hundredth? Explain or show your reasoning.

List the decimals from least to greatest: 6.95, 6.895, 6.598, 6.985, 5.986

To the nearest hundredth of a mile per hour, a luge rider's top speed was 81.73 mph. What are some possible speeds to the thousandth of a mile per hour? Use the number line if it is helpful.

1. Jada has 3 doubloons. She knows that 2 have the same weight and 1 is heavier than the other 2. Jada also has a balance to compare the weights of coins. Explain or show how Jada can use the balance to figure out which doubloon is heavier and which 2 weigh the same.
2. What if Jada has 5 doubloons and knows that 4 have the same weight and 1 is heavier?

There are 2 packages of ground beef at the store. One package says it has 1 pound of beef. The second package says it has 0.97 pound of beef. Jada says that the 1-pound package has more beef. Do you agree? Explain or show your reasoning.