Rounding Numbers Mss

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ROUNDING NUMBERS What does it mean to round a number? Rounding a number means to estimate or approximate it. Rounding reduces the digits in a number while maintaining a similar value. The result is less accurate, but easier to use. Let’s begin by making sure you are clear on place values. EXAMPLE A1: 1,234,567,890.123456789 Let’s first discuss the digits on the left side of the decimal point (the blue digits). The first (the blue) 1 is in the billions place. The first (the blue) 2 is in the hundred millions place. The first (the blue) 3 is in the ten millions place. The first (the blue) 4 is in the millions place. The first (the blue) 5 is in the hundred thousands place. The first (the blue) 6 is in the ten thousands place. The first (the blue) 7 is in the thousands place. The first (the blue) 8 is in the hundreds place. The first (the blue) 9 is in the tens place. The 0 is in the ones place. Now let’s discuss the digits on the right side of the decimal point (the red digits). EXAMPLE A2: 1,234,567,890.123456789 The second (the red) 1 is in the tenths place. The second (the red) 2 is in the hundredths place. The second (the red) 3 is in the thousandths place. The second (the red) 4 is in the ten thousandths place. The second (the red) 5 is in the hundred thousandths place. The second (the red) 6 is in the millionths place. The second (the red) 7 is in the ten millionths place. The second (the red) 8 is in the hundred millionths place. The second (the red) 9 is in the billionths place. All digits after the decimal point (the red digits) are in a place that ends in “ths”. When asked to round a number to a specific place value:

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1. Find the digit located in that place value. 2. Underline that digit. 3. Write all the digits to the left of the digit underlined in the same order. 4. Determine whether you should write the digit you have underlined or increase that digit by one. If the digit after (to the right) of the digit underlined is 5 or more, increase the digit underlined by one. If the digit after (to the right) of the digit underlined is 4 or less, write the same digit underlined. 5. DO NOT WRITE ANY MORE DIGITS, if the digit underlined is to the right of the decimal point. 6. If you are asked to round a number to a place value to the left of the decimal point, you must add zeros in remaining places up to the decimal point. EXAMPLES B: 

Rounding to the left of the decimal point (whole numbers)

Round to the nearest one: 4.75 = 5 Round to the nearest ten: 38 = 40 Round to the nearest hundred: 247 = 200 Round to the nearest thousand: 7,299.456 = 7,000 Round to the nearest ten thousand: 16,500 = 20,000 Round to the nearest hundred thousand: 945,879 = 900,000 Round to the nearest million: 3,633,271 = 4,000,000 Round to the nearest ten million: 14,999,999.999 = 10,000,000 Round to the nearest hundred million: 505,555,555.55 = 500,000,000 Round to the nearest billion: 6,550,550,555 = 7,000,000,000

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

Rounding to the right of the decimal point (decimals)

Round to the nearest tenth: 0.14789 = 0.1 Round to the nearest hundredth: 0.14789 = 0.15 Round to the nearest thousandths: 0.14789 = 0.148 Round to the nearest ten thousandth: 0.14789 = 0.1479 Round to the nearest hundred thousandth: 0.14789 = 0.14789 Round to the nearest millionth: 0.14789 = 0.147890 = 0.147890 Round to the nearest ten millionth: 79.123456789 = 79.1234568 Round to the nearest hundred millionth: 319.123456789 = 319.12345679 Round to the nearest billionth: 1,958.123456789 = 1,958.123456789 Note: Whole Numbers are the numbers 0, 1, 2, 3, 4, 5, 6… Note: Counting Numbers are the numbers 1, 2, 3, 4, 5, 6… They do not include zero. Note: Integers are the numbers …-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6… Let’s try a few together! Practice 1: Round to the nearest thousandth: 123,456.789456 First underline the digit in the thousandths place:

123,456.789456

Next, write all the digits to the left of the underlined digit in the exact same order: 123,456.78 Now determine what to do with the digit underlined. The digit after 9 is 4, so the digit 9 stays the same. 123,456.789 FINISHED!

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Practice 2: Round to the nearest hundred: 123,456.789456 First underline the digit in the hundreds place:

123,456.789456

Next, write all the digits to the left of the underlined digit in the exact same order: 123, Now determine what to do with the digit underlined. The digit after 4 is 5, so the digit 4 increases to 5. 123,5 To finish hold all the places to the decimal point with zeros: 123,500 Practice 3: Round to the nearest million: 456,789.009867 First underline the digit in the millions place:

0,456,789.009867

Next, write all the digits to the left of the underlined digit in the exact same order: There are no digits to the left of the underlined digit. Now determine what to do with the digit underlined. The digit after 0 is 4, so the digit 0 stays the same. 0, To finish hold all the places to the decimal point with zeros: 0,000,000 = 0! Practice 4: Round to the nearest hundred thousandth: 123,456 First underline the digit in the hundred thousandths place: There is no digit in the hundred thousandths place, so I must insert the zeros representing the spaces to the right of the decimal point. 123,456.00000 Next, write all the digits to the left of the underlined digit in the exact same order: 123,456.0000 Now determine what to do with the digit underlined. There is no digit after 0, so all remaining digits are 0. Therefore, 0 stays the same. 123,456.0000

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Practice 5: Round to the nearest million: 564,789. 9867 First underline the digit in the millions place:

0, 564,789. 9867

Next, write all the digits to the left of the underlined digit in the exact same order: There are no digits to the left of the underlined digit. Now determine what to do with the digit underlined. The digit after 0 is 5, so the digit 0 increases to 1. 1, To finish hold all the places to the decimal point with zeros: 1,000,000 Practice 6: Round to the nearest hundredth: 456.897 First underline the digit in the hundredths place:

456.897

Next, write all the digits to the left of the underlined digit in the exact same order: 456.8 Now determine what to do with the digit underlined. The digit after 9 is 7, therefore the digit 9 increases to 10. I cannot write the two-digit number 10 in a single space. Just as in addition of whole numbers, we would write the 0 and carry the 1 to the next column on the left. So instead of looking at the number as 9 we look at the number as 89. Therefore, 89 increases to 90. 456.90 FINISHED!

I hope this lesson was helpful. Please go to the website blog and let me know whether I successfully taught you to round numbers. The website address is http://mathbeast.angelfire.com. Copyright 2008 http://mathbeast.angelfire.com. All rights reserved.