Section A: Practice Problems Numbers to Thousandths

Section Summary

Details

In this section, we represented decimals to the thousandths place.

Diagram, square. Length and width, 1.

The shaded region of the diagram represents 0.542. The 5 shaded rows are each a tenth or 0.1, the 4 shaded small squares are each a hundredth or 0.01, and the 2 shaded tiny rectangles are each a thousandth or 0.001. The decimal 0.542 can be represented in other ways

  • five hundred forty-two thousandths

We can also locate 0.542 on a number line.

Number line. Scale, 54 hundredths to 55 hundredths, by thousandths. Point at five hundred 42 thousandths.

The number line shows that 0.542 is closer to 0.54 than to 0.55 so 0.542 rounded to the nearest hundredth is 0.54.

Problem 1 (Pre-Unit)

Find the value of each expression.

Problem 2 (Pre-Unit)

  1. Write a multiplication equation shown by the shaded region of the diagram.

    Diagram, square. Length and width, 1. Partitioned into 10 rows of 10 of the same size squares. 36 squares shaded. 

  2. What is the value of ? Use the grid if it is helpful.

    Diagram, square. Length and width, 1. Partitioned into 10 rows of 10 of the same size squares. No squares shaded. 

Problem 3 (Pre-Unit)

Find the value of . Use the diagram if it is helpful.

Diagram, rectangle partitioned vertically and horizontally into 4 rectangles.

Problem 4 (Pre-Unit)

  1. What is the value of the 6 in 618,923?

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

Problem 5 (Pre-Unit)

Find the value of . Explain or show your reasoning.

Problem 6 (Pre-Unit)

Find the value of each sum or difference.

  1. Add. 13 thousand, 8 hundred, 17, minus, 6 thousand, 5 hundred, forty 4, equals.
  2. Subtract. eight thousand, seven hundred, ninety three, minus, four thousand six hundred, seventy five, equals.

Problem 7 (Lesson 1)

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

    Diagram, square. Length and width, 1. Partitioned into 10 rows of 10 of the same size squares. 1 square shaded.

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

    Diagram, square. Length and width, 1. Partitioned into 10 rows of 10 of the same size squares. Top left square partitioned into 10 rows. 1 row shaded.

Problem 8 (Lesson 2)

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

    Diagram, square. Length and width, 1. Partitioned into 10 rows of 10 of the same size squares. 66 squares shaded. 

  2. Shade one hundred fifteen thousandths of the square.

    Diagram, square. Length and width, 1. Partitioned into 10 rows of 10 of the same size squares. No squares shaded. 

Problem 9 (Lesson 3)

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

Problem 10 (Lesson 4)

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

    Scale, tilted left-side down, right-side up. Left side, gold nuggets. Right side, nothing.

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

    • 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?

Problem 11 (Lesson 5)

Noah threw the frisbee 4.89 yards.

  1. Noah threw the frisbee farther than Lin. How far could Lin have thrown the frisbee?

  2. Andre threw the frisbee farther than Noah but less than 4.9 yards. How far could Andre have thrown the frisbee? Explain your reasoning.

Problem 12 (Lesson 6)

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

    Number line. Eleven evenly spaced tick marks. First tick mark, 65 hundredths. Last tick mark, 66 hundredths.

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

Problem 13 (Lesson 7)

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.

Problem 14 (Lesson 8)

  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? What about to the nearest hundredth? Draw a number line if it is helpful.

Problem 15 (Lesson 9)

List the decimals from least to greatest:

  1. 6.95

  2. 6.895

  3. 6.598

  4. 6.985

  5. 5.986

Problem 16 (Lesson 10)

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.

Number line. Scale, 81 and 72 hundredths to 81 and 74 hundredths, by hundredths.

Problem 17 (Exploration)

  1. Jada has 3 doubloons. She knows that two of them have the same weight and one of them is heavier than the other two. Jada also has a balance which she can use to compare the weights of coins. Explain or show how Jada can use the balance to figure out which doubloon is heavier and which two are the same weight.

  2. What if Jada has 5 doubloons and knows that 4 of them have the same weight and one of them is heavier?

Problem 18 (Exploration)

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