Comparing Decimals Using Place Value: Up to Thousandths

Comparing Decimals Using Place Value: Up to Thousandths exercise

• What does the digit '4' represent in the decimal number 3.48?

  Hints

  The digit is directly to the right of the decimal point.

  Each position to the right of the decimal point represents a fraction of ten, with the first position being tenths, and the second hundredths.

  Imagine a similar number like 7.12.

  The 1 represents one tenth.

  Use this to help you find the value of 4 in 3.48.

  Solution

  The digit 4 in the decimal number 3.48 represents 4 tenths, or 0.4.

• Why is 1.5 greater than 1.49 when comparing their place values?

  Hints

  Look at the first digit after the decimal point in each number.

  How do these digits compare?

  Consider what the value of 1.5 would be if it was written with an extra zero to match the number of decimal places in 1.49.

  What does this tell you about its size relative to 1.49?

  Compare the two numbers.

  Solution

  1.5 is greater than 1.49 because when comparing decimals, the digits are compared place by place from left to right.

  In the tenths place, 1.5 has a 5 whereas 1.49 has an 4.

  Since 5 is greater than 4, 1.5 is greater than 1.49.

• If you were to compare 0.701 and 0.72, which decimal would be greater and why?

  Hints

  Add an extra zero to the end of 0.72 to compare it directly with 0.701.

  Does this change the way you compare the two decimals?

  What are the values in the hundredths place for each decimal?

  Solution

  0.72 is greater than 0.701 because in the hundredths place, 0.72 has a 2 while 0.701 has a 0, and since the hundredths place is the first place where they differ, the number with the higher digit in this place—0.72— is the greater decimal.

  1: Align the decimals to compare them directly. Write them as 0.720 and 0.701 to make it easier to compare.

  2: Compare the tenths place. Both numbers have 7 in the tenths place, so we move to the next position.

  3: Compare the hundredths place. 0.72 has a 2 in the hundredths place, whereas 0.701 has a 0. Since 2 is greater than 0, 0.72 is greater than 0.701.

  4: The thousandths place comparison is unnecessary in this context because the hundredths place already determined the greater value.

• Compare the decimal numbers 0.392, 0.398, and 0.39.

  Hints

  Check each decimal place starting from the tenths to the thousandths.

  Where do you find the first difference among the digits?

  Consider the significance of the thousandths place in deciding the largest number when the tenths and hundredths are the same for all numbers.

  Consider adding a zero to the end of 0.39 to make it 0.390, which helps in directly comparing it with 0.392 and 0.398 in terms of the thousandths place.

  Solution

  In order from smallest to largest, the numbers are 0.39, 0.392, and 0.398.

  Look at the Tenths Place: All the numbers have 3 in the tenths place, so they are the same here.

  Check the Hundredths Place: They all have 9 in the hundredths place too, so we still can't decide which is bigger.

  Move to the Thousandths Place: Here we see the difference! 0.39 doesn't have a thousandths place, so it's like 0.390. 0.392 has 2, and 0.398 has 8.

  Find the Biggest and Smallest: Since 0 is less than 2, and 2 is less than 8, we know 0.39 is the smallest, 0.392 is in the middle, and 0.398 is the biggest.

• Which glass has more juice?

  Hints

  Remember, a higher number in the rightmost place you compare means a larger overall decimal value.

  Compare the thousandths place.

  Does the digit in glass A or glass B have a higher value?

  Focus on the last digit of each decimal, as the first two digits are the same.

  Solution

  Glass B has more juice.

  Compare the Tenths Place: Look at the tenths digit of each decimal. Both 0.256 and 0.259 have 2 in the tenths place.

  Compare the Hundredths Place: Both decimals have 5 in the hundredths place, so we still need to find a difference.

  Compare the Thousandths Place: The thousandths place shows 6 for glass A and 9 for glass B.

  Determine the Larger Amount: Since 9 is greater than 6, glass B has more juice.

• Apply your knowledge of comparing place value to compare numbers between zero and one.

  Hints

  Look at the last digit (thousandths place) of each decimal rate to determine which one is highest, as the tenths and hundredths places are the same for all options.

  Remember, even a small difference in the rightmost decimal place can determine which option allows for a greater flow rate.

  Focus on comparing these smallest differences.

  Solution

  The setting with 0.627 liters per minute will provide the most water flow over one minute.

  Identify Decimal Places: Look at each number to recognize the digits in the tenths, hundredths, and thousandths places.

  Compare the Tenths Place: All three settings have 6 in the tenths place, so no difference here.

  Compare the Hundredths Place: The hundredths digits are 2 for 0.622, 2 for 0.625, and 2 for 0.627, so they are the same up to this point.

  Compare the Thousandths Place: 0.622 has 2, 0.625 has 5, and 0.627 has 7. The setting with 7 in the thousandths place, which is 0.627, provides the most flow rate as it is the highest number in the smallest place value compared.