Detailed Solutions to Practice #1

If you had difficulty with any of the items in this practice, read the detailed solutions given on this page. You can either scroll through all the solutions or select the specific one you wish to view.

I want to view the detailed solution to (click on the one you want to view):

1. Write each of the following numerically.
   Item 1a: two hundred and sixty-seven thousandths is 200.067.
   In this solution we demonstrate how this is determined using the steps outlined in the unit.
   1. Look at the ending of the statement. See if it indicates there will be a decimal.
      The statement ends in thousandths, so there is a decimal in this number.

   2. Look to see if there is an 'and' in the statement. If there is an 'and', then there is a whole number to the left of the decimal. Write this number out and add a decimal on the end. If there is no 'and', move on to step 3.
      The statement in front of the 'and' is two hundred. We write this as: 200.

   3. Now note the ending, which represents the decimal place in which the decimal will end. Mark out some blanks for each place that will be filled to the right of the decimal.

      The statement ends in thousandths. This means that the last place occupied will be three places to the right of the decimal

   4. Look at the number that appears after the decimal, and write it out so that the last digit appears in the last place marked off in step 3.

      The number that appears after the decimal is sixty-seven thousandths. This means that the number 67 is placed after the decimal so that its last digit, a 7, is in the thousandths place.

   5. If there are any spaces between the decimal and the number to the right of the decimal, add zeros as place holders.

      In the diagram above, we can see that the tenths place is still empty. This means we need to add a zero as a place holder.
      After adding the correct number of place holders we find the number two hundred and sixty-seven thousandths written as a number is shown on the right.	200.067

   Item 1b: eight thousand twenty-four and five hundred twenty-three millionths is 8,024.000523.
   In this solution we demonstrate how this is determined using the steps outlined in the unit.

   1. Look at the ending of the statement. See if it indicates there will be a decimal.
      The ending of millionths indicates that there is a decimal here, so we move on to step 2.

   2. Look to see if there is an 'and' in the statement. If there is an 'and', then there is a whole number to the left of the decimal. Write this number out, and add a decimal on the end. If there is no 'and', move on to step 3.
      There is an and in the statement, so there is a whole number to the right of the decimal. This number is eight thousand twenty-four so is written as: 8,024.

   3. Now note the ending, which represents the decimal place in which the decimal will end. Mark out some blanks for each place that will be filled to the right of the decimal.

      The ending here is millionths. This means that the last place is six places to the right of the decimal.

   4. Looking at the number that appears after the decimal, write it out so that the last digit appears in the last place marked off in step 3.

      The number given to the right of the decimal is five hundred twenty-three, or 523. We write this out so that the 3 is in the millionths place.

   5. If there are any spaces between the decimal and the number to the right of the decimal, add zeros as place holders.
      If we look at the diagram above, we see that we need three place holders between the decimal point and the 523. After adding these, we get the number: 8,025.000523
      
   
   
2. Write out each decimal in words.
   Item 2a: 16.78 is sixteen and seventy-eight hundredths. In this solution we demonstrate how this is determined using the steps outlined in the unit.

   1. Look to see if there is a number to the left of the decimal, if so write it out.
      There is a number to the left of the decimal; it is 16. This is written out as: sixteen

   2. Write an 'and ' for the decimal point.
      After adding the 'and' we have: sixteen and

   3. Look at the number to the right of the decimal, and write it out. Do not yet include the place value.
      In 16.78, the number to the right of the decimal is 78. This is written as: seventy-eight.

   4. Determine the place value of the last digit to the right of the decimal. Write the place value.

      The last digit in 16.78 is an 8. It is two places to the right of the decimal which is the hundredths place.

      If we put together the statements from steps 2 and 3 with the place value, we have:

      sixteen and seventy-eight hundredths

      Item 2b: 2,500.0045 is two thousand five hundred and forty-five ten thousandths or twenty-five hundred and forty-five ten thousandths
      

      1. Look to see if there is a number to the left of the decimal; if so write it out.
         The number to the left of the decimal is 2,500. This can be written in two different ways: two thousand five hundred or twenty-five hundred

      2. Write an 'and' for the decimal point.
         After adding the and, we have: two thousand five hundred and or twenty-five hundred and

      3. Look at the number to the right of the decimal, and write it out. Do not yet include the place value.
         To the right of the decimal, we have .0045. If we look at just the number 45, we write this as: forty-five

      4. Determine the place value of the last digit to the right of the decimal. Write the place value.

         The last digit in 2,500.0045 is a 5. It is four places to the right of the decimal in the ten thousandths place.

         If we put together the statements from steps 2 and 3 with the place value, we have:

         two thousand five hundred and forty-five ten thousandths
         or
         twenty-five hundred and forty-five ten thousandths
         

      Item 2c: .058 is fifty-eight thousandths

      1. Look to see if there is a number to the left of the decimal; if so write it out. If there is no number to the left of the decimal, skip to step 3.
         There is no number to the left of the decimal, so we can skip to step 3.

      2. Look at the number to the right of the decimal, and write it out. Do not yet include the place value.
         To the right of the decimal, we have .058. If we look at just the number 58, we write this as:
         fifty-eight

      3. Determine the place value of the last digit to the right of the decimal. Write the place value.

         The last digit in .058 is an 8. It is 3 places to the right of the decimal in thethousandths place.

         If we put together the statement from step 3 with the place value, we have:
         fifty-eight thousandths

   If you feel you need further review before trying the additional practice, reread this unit. When you are ready you should try the additional practice for this unit.

   ---

   [review section]	[ additional practice]	[table of contents]	[next unit]