{"id":637,"date":"2023-03-09T15:51:15","date_gmt":"2023-03-09T15:51:15","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&p=637"},"modified":"2024-10-18T20:50:34","modified_gmt":"2024-10-18T20:50:34","slug":"whole-numbers-learn-it-3","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/whole-numbers-learn-it-3\/","title":{"raw":"Whole Numbers: Learn It 3","rendered":"Whole Numbers: Learn It 3"},"content":{"raw":"

Rounding Whole Numbers<\/h2>\r\n

In [latex]2021[\/latex], the U.S. Census Bureau reported the population of the state of New York as [latex]20,114,745[\/latex] people. One could say that the population is approximately [latex]20[\/latex] million. The word approximately<\/em> means that [latex]20[\/latex] million is not the exact population, but is close to the exact value.<\/span><\/p>\r\n

The process of approximating a number is called rounding<\/strong>. Numbers are rounded to a specific place value depending on how much accuracy is needed. Saying that the population of New York is approximately [latex]20[\/latex] million means we rounded to the millions place. The place value to which we round to depends on how we need to use the number.<\/p>\r\n

\r\n
\r\n

rounding<\/h3>\r\n

Rounding<\/strong> is a method used to shorten or simplify numbers by adjusting them to the closest specified value.<\/p>\r\n<\/div>\r\n<\/section>\r\n

Using a number line can help you visualize and understand the rounding process. Let's look at an example.<\/p>\r\n

\r\n

Suppose we want to round the number [latex]76[\/latex] to the nearest ten. Is [latex]76[\/latex] closer to [latex]70[\/latex] or [latex]80[\/latex] on the number line?<\/p>\r\n

\"An<\/center>\r\n

 <\/p>\r\n

We can see that [latex]76[\/latex] is closer to [latex]80[\/latex] than to [latex]70[\/latex]. So [latex]76[\/latex] rounded to the nearest ten is [latex]80[\/latex].<\/p>\r\n

Now consider the number [latex]72[\/latex]. Find [latex]72[\/latex] on the number line.<\/p>\r\n

\"An<\/center>\r\n

 <\/p>\r\n

We can see that [latex]72[\/latex] is closer to [latex]70[\/latex], so [latex]72[\/latex] rounded to the nearest ten is [latex]70[\/latex].<\/p>\r\n

How do we round [latex]75[\/latex] to the nearest ten?<\/p>\r\n

Find [latex]75[\/latex] on the number line.<\/p>\r\n

\"An<\/center>\r\n

 <\/p>\r\n

The number [latex]75[\/latex] is exactly midway between [latex]70[\/latex] and [latex]80[\/latex]. So that everyone rounds the same way in cases like this, mathematicians have agreed to round to the higher number, [latex]80[\/latex]. So, [latex]75[\/latex] rounded to the nearest ten is [latex]80[\/latex].<\/p>\r\n<\/section>\r\n

Now that we have looked at this process on the number line, we can introduce a more general procedure. To round a number to a specific place, look at the number to the right of that place. If the number is less than [latex]5[\/latex], round down. If it is greater than or equal to [latex]5[\/latex], round up.<\/p>\r\n

\r\n

How to: Round a Whole Number to a Specific Place Value<\/b><\/p>\r\n

    \r\n\t
  1. Locate the given place value. All digits to the left of that place value do not change.<\/li>\r\n\t
  2. Underline the digit to the right of the given place value.<\/li>\r\n\t
  3. Determine if this digit is greater than or equal to [latex]5[\/latex].
    \r\n
      \r\n\t
    • Yes\u2014add [latex]1[\/latex] to the digit in the given place value.<\/li>\r\n\t
    • No\u2014do not change the digit in the given place value.<\/li>\r\n<\/ul>\r\n<\/li>\r\n\t
    • Replace all digits to the right of the given place value with zeros.<\/li>\r\n<\/ol>\r\n<\/section>\r\n
      \r\n

      For example, to round [latex]76[\/latex] to the nearest ten, we look at the digit in the ones place.<\/p>\r\n

      \"The<\/center>\r\n

       <\/p>\r\n

      The digit in the ones place is a [latex]6[\/latex]. Because [latex]6[\/latex] is greater than or equal to [latex]5[\/latex], we increase the digit in the tens place by one. So the [latex]7[\/latex] in the tens place becomes an [latex]8[\/latex]. Now, replace any digits to the right of the [latex]8[\/latex] with zeros. So, [latex]76[\/latex] rounds to [latex]80[\/latex].<\/p>\r\n

      \"The<\/center>\r\n

       <\/p>\r\n

      Let\u2019s look again at rounding [latex]72[\/latex] to the nearest [latex]10[\/latex]. Again, we look to the ones place.<\/p>\r\n

      \"The<\/center>\r\n

       <\/p>\r\n

      The digit in the ones place is [latex]2[\/latex]. Because [latex]2[\/latex] is less than [latex]5[\/latex], we keep the digit in the tens place the same and replace the digits to the right of it with zero. So [latex]72[\/latex] rounded to the nearest ten is [latex]70[\/latex].<\/p>\r\n

      \"The<\/center><\/section>\r\n
      Round each number to the nearest hundred:\r\n\r\n
        \r\n\t
      1. [latex]23,658[\/latex]<\/li>\r\n\t
      2. [latex]3,978[\/latex]<\/li>\r\n<\/ol>\r\n

        [reveal-answer q=\"210558\"]Show Solution[\/reveal-answer]
        \r\n[hidden-answer a=\"210558\"]<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n
        1.<\/td>\r\n<\/tr>\r\n
        Locate the hundreds place.<\/td>\r\n\"Decorative<\/td>\r\n<\/tr>\r\n
        The digit of the right of the hundreds place is [latex]5[\/latex]. Underline the digit to the right of the hundreds place.<\/td>\r\n\"Decorative<\/td>\r\n<\/tr>\r\n
        Since [latex]5[\/latex] is greater than or equal to [latex]5[\/latex], round up by adding [latex]1[\/latex] to the digit in the hundreds place. Then replace all digits to the right of the hundreds place with zeros.<\/td>\r\n\r\n

        \"Decorative<\/p>\r\n

        So [latex]23,658[\/latex] rounded to the nearest hundred is [latex]23,700[\/latex].<\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n\r\n\r\n\r\n
        2.<\/td>\r\n<\/tr>\r\n
        Locate the hundreds place.<\/td>\r\n\"Decorative<\/td>\r\n<\/tr>\r\n
        Underline the digit to the right of the hundreds place.<\/td>\r\n\"Decorative<\/td>\r\n<\/tr>\r\n
        The digit to the right of the hundreds place is [latex]7[\/latex]. Since [latex]7[\/latex] is greater than or equal to [latex]5[\/latex], round up by added [latex]1[\/latex] to the [latex]9[\/latex]. Then place all digits to the right of the hundreds place with zeros.<\/td>\r\n\r\n

        \"Decorative<\/p>\r\n

        So [latex]3,978[\/latex] rounded to the nearest hundred is [latex]4,000[\/latex].<\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

        [\/hidden-answer]<\/p>\r\n<\/section>\r\n

        [ohm2_question hide_question_numbers=1]3169[\/ohm2_question]<\/section>","rendered":"

        Rounding Whole Numbers<\/h2>\n

        In [latex]2021[\/latex], the U.S. Census Bureau reported the population of the state of New York as [latex]20,114,745[\/latex] people. One could say that the population is approximately [latex]20[\/latex] million. The word approximately<\/em> means that [latex]20[\/latex] million is not the exact population, but is close to the exact value.<\/span><\/p>\n

        The process of approximating a number is called rounding<\/strong>. Numbers are rounded to a specific place value depending on how much accuracy is needed. Saying that the population of New York is approximately [latex]20[\/latex] million means we rounded to the millions place. The place value to which we round to depends on how we need to use the number.<\/p>\n

        \n
        \n

        rounding<\/h3>\n

        Rounding<\/strong> is a method used to shorten or simplify numbers by adjusting them to the closest specified value.<\/p>\n<\/div>\n<\/section>\n

        Using a number line can help you visualize and understand the rounding process. Let’s look at an example.<\/p>\n

        \n

        Suppose we want to round the number [latex]76[\/latex] to the nearest ten. Is [latex]76[\/latex] closer to [latex]70[\/latex] or [latex]80[\/latex] on the number line?<\/p>\n

        \"An<\/div>\n

         <\/p>\n

        We can see that [latex]76[\/latex] is closer to [latex]80[\/latex] than to [latex]70[\/latex]. So [latex]76[\/latex] rounded to the nearest ten is [latex]80[\/latex].<\/p>\n

        Now consider the number [latex]72[\/latex]. Find [latex]72[\/latex] on the number line.<\/p>\n

        \"An<\/div>\n

         <\/p>\n

        We can see that [latex]72[\/latex] is closer to [latex]70[\/latex], so [latex]72[\/latex] rounded to the nearest ten is [latex]70[\/latex].<\/p>\n

        How do we round [latex]75[\/latex] to the nearest ten?<\/p>\n

        Find [latex]75[\/latex] on the number line.<\/p>\n

        \"An<\/div>\n

         <\/p>\n

        The number [latex]75[\/latex] is exactly midway between [latex]70[\/latex] and [latex]80[\/latex]. So that everyone rounds the same way in cases like this, mathematicians have agreed to round to the higher number, [latex]80[\/latex]. So, [latex]75[\/latex] rounded to the nearest ten is [latex]80[\/latex].<\/p>\n<\/section>\n

        Now that we have looked at this process on the number line, we can introduce a more general procedure. To round a number to a specific place, look at the number to the right of that place. If the number is less than [latex]5[\/latex], round down. If it is greater than or equal to [latex]5[\/latex], round up.<\/p>\n

        \n

        How to: Round a Whole Number to a Specific Place Value<\/b><\/p>\n

          \n
        1. Locate the given place value. All digits to the left of that place value do not change.<\/li>\n
        2. Underline the digit to the right of the given place value.<\/li>\n
        3. Determine if this digit is greater than or equal to [latex]5[\/latex].\n
            \n
          • Yes\u2014add [latex]1[\/latex] to the digit in the given place value.<\/li>\n
          • No\u2014do not change the digit in the given place value.<\/li>\n<\/ul>\n<\/li>\n
          • Replace all digits to the right of the given place value with zeros.<\/li>\n<\/ol>\n<\/section>\n
            \n

            For example, to round [latex]76[\/latex] to the nearest ten, we look at the digit in the ones place.<\/p>\n

            \"The<\/div>\n

             <\/p>\n

            The digit in the ones place is a [latex]6[\/latex]. Because [latex]6[\/latex] is greater than or equal to [latex]5[\/latex], we increase the digit in the tens place by one. So the [latex]7[\/latex] in the tens place becomes an [latex]8[\/latex]. Now, replace any digits to the right of the [latex]8[\/latex] with zeros. So, [latex]76[\/latex] rounds to [latex]80[\/latex].<\/p>\n

            \"The<\/div>\n

             <\/p>\n

            Let\u2019s look again at rounding [latex]72[\/latex] to the nearest [latex]10[\/latex]. Again, we look to the ones place.<\/p>\n

            \"The<\/div>\n

             <\/p>\n

            The digit in the ones place is [latex]2[\/latex]. Because [latex]2[\/latex] is less than [latex]5[\/latex], we keep the digit in the tens place the same and replace the digits to the right of it with zero. So [latex]72[\/latex] rounded to the nearest ten is [latex]70[\/latex].<\/p>\n

            \"The<\/div>\n<\/section>\n
            Round each number to the nearest hundred:<\/p>\n
              \n
            1. [latex]23,658[\/latex]<\/li>\n
            2. [latex]3,978[\/latex]<\/li>\n<\/ol>\n